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[Ques]: By how much is 70% of 120 greater than 35% of 200. Options: (A) 15 (B) 14 (C) 13 (D) 16 (E) 17 *Ans*: (B) --CoT--: (70/100) * 120 – (35/100) * 200 84 - 70 = 14 [Ques]: P and Q invested in a shop. The profits were divided in the ratio of 2 : 4 respectively. If P invested Rs. 500000, the amount invested by Q is: Options: (A) 5000000 (B) 4000000 (C) 1000000 (D) 6000000 (E) None *Ans*: (C) --CoT--: Suppose Q invested Rs. y. Then, 500000/y = 2/4 or y = [500000 x 4 / 2] = 1000000. [Ques]: Find the average of the first 21 natural numbers? Options: (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 *Ans*: (D) --CoT--: Average of the first 'n' natural numbers = (n + 1)/2 We get (21+ 1)/2 = 11 [Ques]: The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 25% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 25% less than the number there from 10 a.m. to 11 a.m. If 135 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.? Options: (A) 10 (B) 20 (C) 30 (D) 40 (E) 80 *Ans*: (E)
--CoT--: No of people from 10 - 11 is x No of people from 11 - 12 is 3x/4 No of people from 12 to 1 is (5/4)(3x/4) Given that 3x/4 + (5/4)(3x/4) = 27x/16 = 135 Then x = 80
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Reasoning: Other parts are equal to 300. Ans: (E) Question: Four of the following five parts (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer. Options: (A) 30 × 14 ÷ 7 × 5 (B) 10 3 – 100 × 7 (C) 5√3600 (D) 450 ÷ 50 × 50 – 5 × 30 (E) 10 × 3 + 120 × 2 Rationale: A = 7500(26/25)^1 = 7800 The answer: (D) Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 1 year the amount to be paid is? Options: (A) 3377 (B) 2688 (C) 2688 (D) 7800 (E) 1268 Reasoning: Average of the first 'n' natural numbers = (n + 1)/2 We get (21+ 1)/2 = 11 Ans: (D) Question: Find the average of the first 21 natural numbers? Options: (A) 8 (B) 9 (C) 10 (D) 11 (E) 12 Rationale: Age of B = Age of (A + B + C) – Age of (A + C) = 29 × 3 – 32 × 2 = 87 – 64 = 23 years The answer: (E) Question: The average age of A, B and C is 29 years. If the average age of A and C is 32 years, what is the age of B in years ? Options: (A) 19 (B) 35 (C) 20 (D) 32 (E) 23 Reasoning: In this simple alternating subtraction and addition series; The first series begins with 5 and adds 2; the second begins with 15 and subtracts 3, and so on. Ans: (B) Question: Fill in the blank with the correct number in this number series: 5, 15, 7, 12, __, 9, 11,... ? Options: (A) 6 (B) 9 (C) 8 (D) 7 (E) 5 Reasoning: 888 = 8*111 = 3*8*37 Hence 888 is a multiple of 37 and we need at least one 37 in N! Therefore least value of N! is 37!, which will contain all of 3, 8, and 37. Ans: (D)
Question: What is the least value of integer N such that N! is divisible by 888 ? Options: (A) 13 (B) 88 (C) 31 (D) 37 (E) D) 888
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Rationale: Speed = 36 * 5/18 = 10 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 1/10 = 50 sec The answer: (B) Question: A train 360 m long is running at a speed of 36 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 sec (B) 50 sec (C) 88 sec (D) 19 sec (E) 10 sec Reasoning: In this series, each number is repeated, then 13 is subtracted to arrive at the next number. Ans: (C) Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next? Options: (A) 12 (B) 15 (C) 14 (D) 18 (E) 17 Rationale: 8^10 = (2^3)^10 = 2^30 The answer: (E) Question: What is the greatest positive integer x such that 2^x is a factor of 8^10? Options: (A) 5 (B) 9 (C) 10 (D) 20 (E) 30 Reasoning: A's one day's work = 1/18 B's one day's work = 1/24 (A + B)'s one day's work = 1/18 + 1/24 = 7/72 The part of the work completed in 3 days = 2 (7/72) = 7/36. Ans: (A) Question: Two persons A and B can complete a piece of work in 18 days and 24 days respectively. If they work together, what part of the work will be completed in 2 days? Options: (A) 7/36 (B) 9/35 (C) 4/37 (D) 8/35 (E) 5/3 Rationale: If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number. The answer: (B) Question: The number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H? Options: (A) 4 (B) 3 (C) 5 (D) 8 (E) 2 Rationale: (555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025 The answer: (E)
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 25 as remainder. Find the no. is? Options: (A) 145646 (B) 236578 (C) 645353 (D) 456546 (E) 220025
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Speed = 63 * 5/18 = 35/2 m/sec Time taken = 210 * 2/35 = 12 sec A train 210 m long, running with a speed of 63 km/hr will pass a tree in? Options: (A) 18 sec (B) 16 sec (C) 76 sec (D) 12 sec (E) 17 sec (D) The simple logic is to divide total balls into three sets. Weigh any two sets against each other(these two must contain equal number of balls). From this we can identify which set contains the heavy ball. Divide this set into three and repeat until you find the heavier ball. Under this logic, the minimum number of weighings required turns out to be the smallest integer greater than or equal to log(n), where n is the total number of balls and the base of logarithm is 3. Or simply [log(n)/log(3)] with any base. Here, n = 6561. log 6561 / log 3 = 8 There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball. Options: (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 (B) Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec
A train 280 m long, running with a speed of 63 km/hr will pass a tree in? Options: (A) 65 sec (B) 16 sec (C) 87 sec (D) 99 sec (E) 96 sec (B)
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Answer: (D) Question: If 6x = 8y = 10z, then what is a possible sum of positive integers x, y, and z? Options: (A) 52 (B) 58 (C) 84 (D) 94 (E) 168 [CoT]: [6x = 8y = 10z 3x = 4y = 5z 3(4*5) = 4(3*5) = 5(3*4) Addition = 20+15+12 = 47 Answer would be multiple of 47 which is 94] Answer: (E) Question: List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K? Options: (A) 5 (B) 6 (C) 7 (D) 11 (E) 4 [CoT]: [Answer = E = 4 If least = -4, then largest = 5 Range = 5 - 1 = 4] Answer: (E) Question: Which oif the following is a prime number? Options: (A) 45 (B) 39 (C) 27 (D) 33 (E) 31 [CoT]: [Clearly, 31 is a prime number. So choice E is correct.] Answer: (E) Question:
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose? Options: (A) 3/140 (B) 1/28 (C) 3/56 (D) 3/35 (E) 7/40 [CoT]: [P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.]
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Answer: (E) Question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 36 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? Options: (A) 106.25 (B) 105.5 (C) 105.75 (D) 106 (E) 105.0 [CoT]: [Rate of flow of water in second hour = 36 gallons per hour Rate of flow of water in first hour = 36/(3/2) = 24 gallons per hour Rate of flow of water in third hour = (125/100)* 36 = (5/4) * 36 = 45 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 24+36+45 = 105 gallons] Answer: (E) Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 510 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) Options: (A) 8/3 (B) 3/8 (C) 8/5 (D) 5/8 (E) 34/15 [CoT]: [Distance traveled by Eddy = 510 km Time taken by Eddy = 3 hours Average speed of Eddy = 510/3 = 170 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 170/75 = 34/15] Answer: (D) Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? Options: (A) 80,30 kmph (B) 80,20 kmph (C) 80,10 kmph (D) 80,40 kmph (E) 80,90 kmph [CoT]: [Speed downstream = 60 + 20 = 80 kmph Speed upstream = 60 - 20 = 40 kmph] Answer: (A) Question:
If the given two numbers are respectively 6% and 30% of a third number, then what percentage is the first of the second ? Options: (A) 20% (B) 25% (C) 18% (D) 30% (E) none of these [CoT]: [Here, l = 6 and m = 30 Therefore, first number = l/m x 100% of second number = 6/30 x 100% of second number = 20% of second number]
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Question: The year next to 1991 having the same calendar as that of 1990 is – Options: (A) 1998 (B) 2001 (C) 2002 (D) 2003 (E) None of these Ans: (C) CoT: We go on counting the odd days from 1991 onward still the sum is divisible by 7. The number of such days are 14 upto the year 2001. So, the calender for 1991 will be repeated in the year 2002. ---- Question: What percent is 70 of 280? Options: (A) 12 % (B) 25 % (C) 26 % (D) 27 % (E) 28 % Ans: (B) CoT: 70/280 = 1/4 1/4 × 100 = 25 % ---- Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train? Options: (A) 49 sec (B) 50 sec (C) 48 sec (D) 43 sec (E) 32 sec Ans: (C)
CoT: D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 se ----
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Rationale: Using question number 11 and 12, we get the probability as 1 - (1/36 + 5/9) = 5/12 The answer: (B) Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is Options: (A) 5/9 (B) 5/12 (C) 1/36 (D) 7/12 (E) 4/9 Reasoning: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 210 * 2/35 = 12 sec Ans: (D) Question: A train 210 m long, running with a speed of 63 km/hr will pass a tree in? Options: (A) 15 sec (B) 16 sec (C) 18 sec (D) 12 sec (E) 25 sec Rationale: 10^2 - 20 = 80 20^2 - 30 = 370 30^2 - 40 = 860 40^2 - 50 = 1550 50^2 - 60 = 2440 60^2 - 70 = 3530. The answer: (E) Question: 80 370 860 1550 2440 ? Options: (A) 900 (B) 840 (C) 750 (D) 860 (E) 3530 Reasoning: Largest 4 digit number is 9999 After doing 9999 ÷ 88 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 Ans: (C) Question: Find the largest 4 digit number which isexactly divisible by 88? Options: (A) 8765 (B) 9543 (C) 9944 (D) 1012 (E) 2465 Rationale: 1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 The answer: (C) Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time? Options: (A) 17 1/5 (B) 17 1/8 (C) 17 1/7 (D) 17 1/1 (E) 17 1/2 Rationale: Answer A) 9600 yards need 1200 lbs 1 Yard will need 1200/7200 = 1/6 lbs 3600 Yards will need 1/6* 3600 Yards = 600lbs The answer: (B)
Question: A football field is 7200 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards? Options: (A) 450 (B) 600 (C) 750 (D) 2400 (E) 3200
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Rationale: Number of ways of selecting 4 people out of 9 people = 9C4 In the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7 Number of ways to form a 4 member team that includes George and excludes Nina = 7C3 Probability = 7C3/9C4 = 35/120 The answer: (D) Question: From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina Options: (A) 5/56 (B) 9/56 (C) 15/56 (D) 35/120 (E) 25/56 Rationale: A = 7500(26/25)^3 = 8436 The answer: (D) Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? Options: (A) 3377 (B) 2688 (C) 2688 (D) 8436 (E) 1268 Rationale: Total revenues = x Spent on marketing = x/4 Remaining amount = x-x/4 = 3x/4 1/7 of the remainder on maintenance of its facilities = 3x/4*1/7 = 3x/28 Amount left = 3x/4-3x/28 = 9x/14 The answer: (D)
Question: Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year’s original revenues did company Z have left after its marketing and maintenance expenditures? Options: (A) 5/14 (B) 1/2 (C) 17/28 (D) 9/14 (E) 9/11
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Ques: If X is the sum of first 20 positive even integers and Y is the sum of first 20 positive odd integers, what is the value of x-y? Please try to explain your answers Options: (A) 0 (B) 20 (C) 50 (D) 75 (E) 100 Ans: (B) CoT: First even minus first odd = 2-1 = 1; The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2; The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3; We can see the patterns here, so the sum of first 20 positive even integers minus the sum of first 20 positive odd integers will be 20. Ques: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 6 days? Options: (A) 2/5 (B) 1/6 (C) 1/3 (D) 1/9 (E) 2/6 Ans: (C) CoT: A's one day's work = 1/30 B's one day's work = 1/45 (A + B)'s one day's work = 1/30 + 1/45 = 1/18 The part of the work completed in 6 days = 6 (1/18) = 1/3. Ques: What distance will be covered by a city bus moving at 72 kmph in 30 seconds? Options: (A) 200 m (B) 300 m (C) 600 m (D) 500 m (E) 400 m Ans: (C) CoT: 72 kmph = 72 * 5/18 = 20 mps Dist = Speed * time = 20 * 30 = 600 m. Ques: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 7 kmph (B) 4 kmph (C) 4 kmph (D) 8 kmph (E) 5 kmph Ans: (D)
CoT: Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph
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[Ans] (B) [Question] What should come in place of the question mark (?) in the following equation? 9568 – 6548 – 1024 = ? Options: (A) 2086 (B) 1996 (C) 2293 (D) 1896 (E) None of these [CoT] ? = 9568 – 6548 – 1024 = 1996. [Ans] (A) [Question] Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next? Options: (A) 15 (B) 14 (C) 17 (D) 12 (E) 19 [CoT] This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. [Ans] (C) [Question]
The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary? Options: (A) 910% increase (B) 10% increase (C) 9% decrease (D) 12% decrease (E) 15% increase [CoT] (30 * 30)/100 = 9% decrease
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Rationale: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. The answer: (C) Question: Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so. If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides? Options: (A) 1 (B) 2 (C) 3 min (D) 4 (E) 5 Reasoning: Number of ways = 61/21 6X5X4X3X2X1 - 360 Ans: (E) Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged? Options: (A) 120 (B) 230 (C) 330 (D) 340 (E) 360 Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40 The answer: (C) Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Options: (A) 32 (B) 28 (C) 40 (D) 27 (E) 21 Reasoning: Formula = Third proportional = (b × b)/a A = 9 and B = 12 (12 × 12)/ 9 = 144/9 = 16 Ans: (C) Question: Find the third proportional to 9 and 12? Options: (A) 10 (B) 12 (C) 16 (D) 19 (E) 20 Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day. The answer: (B) Question: If 4 women can color 48 m long cloth in 2 days, then 6 women can color 36 m long cloth in Options: (A) 2 days (B) 1 day (C) 4 days (D) 3 days (E) 2 1/5 days Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 The answer: (E)
Question: Find the value of y from (12)^3 x 6^4÷432 =y? Options: (A) 4363 (B) 4765 (C) 4879 (D) 6789 (E) 5184
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Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 37 (C) 32 (D) 39 (E) 28 (A) (555 + 445) * 2 * 110 + 10 = 220000 + 10 = 220010 A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 10 as remainder. Find the no. is? Options: (A) 220010 (B) 145778 (C) 220110 (D) 235467 (E) 220001 (A) 7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors? Options: (A) 2 (B) 3 (C) 5 (D) 6 (E) 8 (B)
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Reasoning: 46 + 28 + 10 = 84% 100 – 84 = 16% 850 * 16/100 = 136 Ans: (A) Question: In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Options: (A) A) 136 (B) B) 627 (C) C) 153 (D) D) 721 (E) E) 159 Reasoning: Sum of 10 even numbers = 10 * 11 = 110 Average = 110/10 = 11 Ans: (D) Question: The average of first 10 even numbers is? Options: (A) 19 (B) 18 (C) 16 (D) 11 (E) 17 Reasoning: S = 160/8 * 18/5 = 72 kmph Ans: (E) Question: A 160 meter long train crosses a man standing on the platform in 8 sec. What is the speed of the train? Options: (A) 96 kmph (B) 94 kmph (C) 92 kmph (D) 86 kmph (E) 72 kmph Reasoning: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle. Ans: (D)
Question: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is Options: (A) 7 (B) 8 (C) 9 (D) 24 (E) 23
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Reasoning: Minumum points for (may condition): 4 Ans: (C) Question: 8 teams.each teams play twice with other teams.win =2poins. lose =0 points. no draw/match abandonment.top four go semis.if same points runrate considered. whats the minimum num of points with which a team may go to semis Options: (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Reasoning: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 410 + 140 = 550 m Required time = 550 * 2/25 = 44 sec Ans: (E) Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 87 (C) 26 (D) 21 (E) 44 Reasoning: Plug in an even integer; in this case 2 (3*2)-3 = 6-3 = 3 Odd 2+2^2 = 6 Even (5*2)-3 = 10 - 3 = 7 Odd (2*2)+1 = 4 + 1 = 5 Odd (9*2)-5 = 18 - 5 = 13 Odd Ans: (B) Question: If x is an even integer, which of the following is an even integer? Options: (A) 3x-3 (B) x+x^2 (C) 5x-3 (D) 2x+1 (E) 9x-5 Reasoning: Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 6 = 100 meter Ans: (C)
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train. Options: (A) 110 meter (B) 120 meter (C) 100 meter (D) 90 meter (E) 105 meter
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Ques: There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? Options: (A) 50 (B) 23 (C) 108 (D) 28 (E) 45 Ans: (C) CoT: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand. Ques: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 118 km (B) 162 km (C) 1767 km (D) 1887 km (E) 177 km Ans: (B) CoT: 12 m/s = 12 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km. Ques: The floor of a rectangular room is 21 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : Options: (A) 124 m2 (B) 128 m2 (C) 138 m2 (D) 148 m2 (E) None of these Ans: (D) CoT: Area of the outer rectangle = 25 × 16 = 400 m2 Area of the inner rectangle = 21 × 12 = 252 m2 Required area = (400 – 252) = 148 m2 Ques: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 140kg then find the average weight of all the 7 rounds? Options: (A) 98.5 kgs (B) 80 kgs (C) 76.5 kgs (D) 67.5 kgs (E) 58.2 kgs Ans: (B)
CoT: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 140/7 = 80 kgs
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Ques: Solve:- 333 x 333 x 333 + 555 x 555 x 555 = ?(333 x 333 - 333 x 555 + 555 x 555) Options: (A) 888 (B) 333 (C) 555 (D) 988 (E) 889 Ans: (A) CoT: Given Exp. = (a3 + b3) = (a + b) = (333 + 555) = 888(a2 - ab + b2) Ques: Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? Options: (A) 1 (B) 4 (C) 9 (D) 13 (E) 16 Ans: (E) CoT: Number of cups flour needed for 3 ounces of butter = 4 Number of cups flour needed for 1 ounce of butter = 4/3 Number of cups flour needed for 12 ounces of butter = 4/3 * 12 = 16 Ques: The edge of a cube is 4a cm. Find its surface? Options: (A) 104a2 cm2 (B) 64a2 cm2 (C) 96a2 cm2 (D) 84a2 cm2 (E) 56a2 cm2 Ans: (C) CoT: 6a2 = 6 * 4a * 4a = 96a2 Ques: The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest? Options: (A) 55 (B) 60 (C) 62 (D) 52 (E) Cannot be determined Ans: (B)
CoT: Total marks of 10 papers = 80 x 10 = 800 Total marks of 8 papers = 81 x 8 = 648 Total marks of two papers = (800 - 648) = 152 If highest total is 92, then the lowest total is (152 - 92) = 60.
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Ques: Rita can knit a pair of socks in 3 days. Sita can knit the same in 6 days. If they are knitting together, in how many days will they knit two pairs of socks. Options: (A) 4 (B) 1 (C) 2 (D) 5 (E) 6 Ans: (C) CoT: 1 /3+ 1/6 = 1 /2 Together they will take, 1/ 1/2 = 2 Ques: Twenty percent of Country Y's yearly exports come from fruit exports. One-fourth of all fruit exports from Country Y are orange exports. If country Y generates $40 million from its orange exports, how much money does it generate from its yearly total of exports? Options: (A) $21.25m (B) $800m (C) $106.25m (D) $127.5m (E) $153m Ans: (B) CoT: 20/100*1/4*(total) = 40 1/20*(total) = 40 (total) = 40*20 = 800 Ques: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 7 kmph (B) 6 kmph (C) 5 kmph (D) 8 kmph (E) 2 kmph Ans: (D) CoT: Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph Ques: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group? Options: (A) 28 (B) 27 (C) 15 (D) 19 (E) 12 Ans: (C)
CoT: Total members in the group = 7 Average amount = Rs. 20 Total amount with them = 7 * 20 = Rs. 140 One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90 The average amount with them = 90/6 = Rs. 15.
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Rationale: Marked price = 266 × 100⁄95 × 280 Cost Price = 280 × 100⁄112 = 250 The answer: (E) Question: A shopkeeper sold sarees at 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree? Options: (A) 280 (B) 260 (C) 38 mph (D) Data inadequate (E) None of these Reasoning: (80/100) * 40 – (4/5) * 25 35 - 20 = 14 Ans: (D) Question: How much is 35% of 40 is greater than 4/5 of 25? Options: (A) 29 (B) 776 (C) 66 (D) 14 (E) 99 Rationale: Distance traveled by Eddy = 540 km Time taken by Eddy = 3 hours Average speed of Eddy = 540/3 = 180 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 180/75 = 12/5 The answer: (D) Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) Options: (A) 8/3 (B) 3/8 (C) 8/5 (D) 12/5 (E) 5/3 Reasoning: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways. Ans: (C) Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are Options: (A) 4 (B) 8 (C) 12 (D) 16 (E) None of these Rationale: 2 2 × 4 - 1 = 7 7 × 4 - 1 = 27 27 × 4 - 1 = 107 107 × 4 - 1 = 427 427 × 4 - 1 = 1707 The answer: (C) Question: What will come in place of the x in the following Number series? 2, 7, 27, 107, 427, x Options: (A) 1427 (B) 1607 (C) 1707 (D) 2047 (E) 2147 Rationale: (80/100) * 40 – (10/100) * 15 32 - 15 = 17 The answer: (E)
Question: How much 80% of 40 is greater than 10% of 15? Options: (A) 18 (B) 99 (C) 19 (D) 18 (E) 17
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[Ques]: Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? Options: (A) 4 (B) 8 (C) 12 (D) 14 (E) 16 *Ans*: (D) --CoT--: The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. [Ques]: For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%. Options: (A) 10 (B) 5 (C) 2 (D) 3 (E) 1 *Ans*: (C) --CoT--: Rule of Subtraction: P(A) = 1 - P(A') Rule of Multiplication: P(A ∩ B) = P(A) P(B) The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50% [Ques]: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 5 kmph (B) 7 kmph (C) 9 kmph (D) 8 kmph (E) 1 kmph *Ans*: (D) --CoT--: Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph [Ques]: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform? Options: (A) 150m (B) 200m (C) 250m (D) 750m (E) 300 m *Ans*: (D)
--CoT--: D = 72 * 5/18 = 50 = 1000 – 250 = 750m
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Reasoning: Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition. Ans: (E) Question: Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24. Options: (A) 9974 (B) 9125 (C) 9565 (D) 9997 (E) None of these Rationale: Option 'B' The total number of arrangements is 10P10 = 10! = 3628800 The answer: (B) Question: In how many different ways can the letters of the word "NEGLIGENCE" be rearrangement? Options: (A) 3628800 (B) 3628800 (C) 3628812 (D) 3428800 (E) 3368800 Reasoning: P = (P*8*R)/100 R = 12 1/2% Ans: (E) Question: In what time a sum of money double itself at 8% per annum simple interest? Options: (A) 33 1/8% (B) 33 1/3% (C) 83 1/3% (D) 33 4/3% (E) 12 1/2% Rationale: 70 + 65 = 135 * 5/18 = 75/2 mps D = 150 + 100 = 250 m T = 250 * 2/75 = 20/3 - 6 2/3 sec The answer: (A) Question: Two trains are moving at 65 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? Options: (A) 6 2/3 sec (B) 7 1/7 sec (C) 7 2/2 sec (D) 8 1/2 sec (E) 7 1/9 sec Reasoning: (900*3*3)/100 = 81 920 + 81 = 1001 Ans: (B) Question: Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? Options: (A) Rs.1056 (B) Rs.1001 (C) Rs.2056 (D) Rs.1026 (E) Rs.1856 Reasoning: D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 se Ans: (C)
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train? Options: (A) 49 sec (B) 50 sec (C) 48 second (D) 43 sec (E) 32 sec
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Ques: Find the average of the first 9 natural numbers? Options: (A) 8 (B) 5 (C) 10 (D) 11 (E) 12 Ans: (B) CoT: Average of the first 'n' natural numbers = (n + 1)/2 We get (9 + 1)/2 = 5 Ques: A man rows his boat 80 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 1 kmph (B) 6 kmph (C) 5 kmph (D) 8 kmph (E) 7 kmph Ans: (E) CoT: Speed downstream = d/t = 80/(2 1/2) = 32 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (32 - 18)/2 = 7 kmph Ques: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, and yellow. This pattern continues (red, green, blue, and yellow) until it ends with a red shirt. If there are more than 4 people in line, which of the following cannot be the number of people in the line? Options: (A) 17 (B) 37 (C) 49 (D) 61 (E) 72 Ans: (E) CoT: The correct answer should not take the form: 4x + 1. Hence, it is Ques: A train 210 m long, running with a speed of 63 km/hr will pass a tree in? Options: (A) 15 sec (B) 16 sec (C) 18 sec (D) 12 sec (E) 25 sec Ans: (D)
CoT: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 210 * 2/35 = 12 sec
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Reasoning: Answer = B. 70 miles Relational speed = 130 - 100 = 30 miles per hour In 3 hours, difference = 30 * 3 = 90 miles Fast train trailing 20 miles, so effective difference = 90 - 20 = 70 miles Ans: (B) Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock? Options: (A) 60 miles (B) 70 miles (C) 90 miles (D) 120 miles (E) 400 miles Reasoning: (1 man + 1 woman)’s 1 day work = 1/3 + 1/4 = 7/12 Work done by 1 man and 1 women in 1/4 day = ((7/12) x (1/4)) = 7/48 Remaining work = 1 - 7/48 = 41/48 Work done by 1 boy in 1/4 day = ((1/12) x (1/4)) = 1/48 Therefore, Number of boys required = ((41/48) x 48) = 41 Ans: (A) Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day? Options: (A) 41 (B) 43 (C) 31 (D) 84 (E) 81 Reasoning: Work done by X in 1 day = 1/36 Work done by Y in 1 day = 1/24 Work done by Y in 12 days = 12/24 = 1/2 Remaining work = 1 – 1/2 = 1/2 Number of days in which X can finish the remaining work = (1/2) / (1/36) = 18 Ans: (E) Question: X can finish a work in 36 days. Y can finish the same work in 24 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work? Options: (A) 12 (B) 13 (C) 16 (D) 17 (E) 18 Reasoning: 2x2 + x – 3 < 0 ⇒ (x – 1)(2x + 3) < 0 or, -3⁄2 < x < 1 Ans: (A)
Question: Which value of x does statisfy the inequality 2x2 + x – 3 < 0? Options: (A) -3⁄2 < x < 1 (B) -1 < x < 3⁄2 (C) x > 1 (D) x < -2⁄5 (E) None of these
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Answer: (E) Question: The purchase price of an article is $48. In order to include 20% of cost for overhead and to provide $12 of net profit, the markup should be Options: (A) 15% (B) 25% (C) 35% (D) 40% (E) 45% [CoT]: [Cost price of article = 48$ % of overhead cost = 20 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 20 = 45%] Answer: (C) Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.4 km long? Options: (A) 2 mins 14 sec (B) 2 mins 34 sec (C) 2 mins 54 sec (D) 4 mins 54 sec (E) 2 mins 44 sec [CoT]: [D = 25 * 60 + 1400 = 2900 m T = 2900/60 * 18/5 = 174 sec = 2 mins 54 se] Answer: (A) Question: At what rate percent on simple interest will a sum of money double itself in 30 years? Options: (A) 3 1/3% (B) 3 1/8% (C) 3 7/3% (D) 3 1/7% (E) 3 1/1% [CoT]: [P = (P*30*R)/100 R = 3 1/3%] Answer: (B) Question:
How many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph? Options: (A) 54 sec (B) 35 sec (C) 25 sec (D) 45 sec (E) 24 sec [CoT]: [D = 100 + 250 = 350 S = 36 * 5/18 = 10 mps T = 350/10 = 35 sec]
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Reasoning: {Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 53 - {both} + 40 {both} = 18%. Ans: (D) Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 53% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? Options: (A) 60% (B) 50% (C) 25% (D) 18% (E) 10% Reasoning: Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 12 = 200 meter Ans: (B) Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train. Options: (A) 225 meter (B) 200 meter (C) 250 meter (D) 190 meter (E) 180 meter Reasoning: Sum of all the 13 numbers = 13 * 58 = 754 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 754 = 72. Ans: (A) Question: The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? Options: (A) 72 (B) 83 (C) 45 (D) 53 (E) 64 Reasoning: 8-(2*0) = 8 8-(2*1) = 6 6-(2*2) = 2 2-(2*3) = -4 Ans: (A)
Question: What is the next number of the following sequence. 8, 8, 6, 2,.... ? Options: (A) -4 (B) -5 (C) -6 (D) -7 (E) -8
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Ques: Find the odd man out 445, 221, 109, 46, 25, 11, 4 Options: (A) 221 (B) 109 (C) 46 (D) 25 (E) 21 Ans: (C) CoT: 4*2+3 = 11 11*2+3 = 25 25*2+3 = 53 53*2+3 = 109 109*2+3 = 221 221*2+3 = 445 Ques: Ravi can do a piece of work in 11 days while Prakash can do it in 22 days. In how many days will they finish it together? Options: (A) 5 7/3 days (B) 7 1/3days (C) 5 1/9 days (D) 5 7/3 days (E) 4 7/9 days Ans: (B) CoT: 1/11 + 1/22 = 3/22 22/3 = 7 1/3 days Ques: Divide Rs.32000 in the ratio 1:9? Options: (A) 12000, 20000 (B) 12000, 200098 (C) 12000, 20007 (D) 3200, 28800 (E) 12000, 20001 Ans: (D) CoT: 1/10 * 32000 = 3200 9/10 * 32000 = 28800 Ques: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much? Options: (A) 288 (B) 200 (C) 279 (D) 992 (E) 208 Ans: (D)
CoT: (800*3*3)/100 = 72 920 + 72 = 992
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Reasoning: S = 640/16 * 18/5 = 144 kmph Ans: (C) Question: A train 640 m in length crosses a telegraph post in 16 seconds. The speed of the train is? Options: (A) 22 kmph (B) 77 kmph (C) 144 kmph (D) 71 kmph (E) 88 kmph Rationale: 90 * 10/60 = 15 kmph The answer: (A) Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes? Options: (A) 15 (B) 66 (C) 77 (D) 52 (E) 42 Reasoning: If he draws any combination of 3 socks he will definitely have the matching pair of either colour. Ans: (A) Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair? Options: (A) 1 (B) 3 (C) 5 (D) 8 (E) 9 Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X So it should be multiple of 8, 30 is not a multiple of 8. The answer: (C) Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students? Options: (A) 3 (B) 4 (C) 8 (D) 9 (E) 12 Reasoning: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister. Ans: (C) Question: A man pointing to a photo says "The lady in the photograph is my nephew’s maternal grandmother". How is the lady in the photograph related to the man’s sister who has no other sister ? Options: (A) Cousin (B) Sister-in-law (C) Mother (D) Mother-in-law (E) None of these Reasoning: Saving = (45-30)% of 48000 = 7200. Ans: (D)
Question: If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000? Options: (A) $3500 (B) $5000 (C) $3150 (D) $7200 (E) $10000
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(Ans). (D) (Question). If a company allocates 25 percent of its budget to advertising, 15 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations? Options: (A) 4/5 (B) 3/5 (C) 3/10 (D) 1/20 (E) 1/40 (CoT). 25 + 15 + 55 = 95% 100 - 95 = 5% to all others (Ans). (A) (Question). Find the smallest number which should be multiplied with 1152 to make it a perfect square. Options: (A) 2 (B) 1 (C) 3 (D) 5 (E) 6 (CoT). 1152 = 2*2*2*2*2*2*2*3*3 Required smallest number = 2 2 is the smallest number which should be multiplied with 1152 to make it a perfect square. (Ans). (B) (Question). In what time a sum of money double itself at 3% per annum simple interest? Options: (A) 36 1/3% (B) 33 1/3% (C) 33 1/6% (D) 63 1/3% (E) 23 1/3% (CoT). P = (P*3*R)/100 R = 33 1/3% (Ans). (A) (Question).
There are different 5 circles. What is the number of the greatest possible points with which the circles intersect? Options: (A) 20 (B) 10 (C) 15 (D) 22 (E) 21 (CoT). Maximum points of intersection between n different circles = n*(n - 1) = 5*4 = 20
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Ques: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? Options: (A) 20 (B) 99 (C) 77 (D) 63 (E) 61 Ans: (A) CoT: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. Ques: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 82. How many points altogether did the team score? Options: (A) 662 (B) 672 (C) 652 (D) 646 (E) 721 Ans: (D) CoT: 8 * 82 = 656 – 10 = 646 Ques: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 20, and 20 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? Options: (A) 4/11 (B) 1/2 (C) 15/22 (D) 10/1 (E) 11/4 Ans: (D) CoT: P1 takes 12 hrs Rate for P2P3 together = 1/20 + 1/20 = 1/10 Therefore they take 10 Ratio = 10/1 = Ques: If n is an integer, then the least possible value of |15 - 8n| is? Options: (A) 0 (B) 2 (C) 1 (D) 3 (E) 5 Ans: (C)
CoT: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1.
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Rationale: 14 m/s = 14 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 14 * 18/5 * 15/4 km = 189 km. The answer: (A) Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 189km (B) 195km (C) 197km (D) 200km (E) 205km Reasoning: S = 160/16 * 18/5 = 36 kmph Ans: (A) Question: A 160 meter long train crosses a man standing on the platform in 16 sec. What is the speed of the train? Options: (A) 36 kmph (B) 54 kmph (C) 92 kmph (D) 86 kmph (E) 76 kmph Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200. The answer: (A) Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Options: (A) 25200 (B) 2543 (C) 2344 (D) 233445 (E) 52757 Reasoning: Clearly, 97 is a prime number. Ans: (C) Question: Which of the following is a prime number ? Options: (A) 27 (B) 45 (C) 97 (D) 98 (E) 100 Rationale: Numbers are alternatively multiplied by 2 and increased by 3 5 × 2 = 10 10 + 3 = 13 13 × 2 = 26 26 + 3 = 29 29 × 2 = 58 58 + 3 = 61 61 × 2 = 122 The answer: (C) Question: 5, 10, 13, 26, 29, 58, 61, (....) Options: (A) 128 (B) 64 (C) 122 (D) 125 (E) 130 Rationale: Distance covered by the car = 80 × 10 = 800 km \ Speed = 800⁄8 = 100 km/hr \ Speed gain = 100 – 80 = 20 km/hr The answer: (E)
Question: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain? Options: (A) 8 km/hr (B) 10 km/hr (C) 12 km/hr (D) 16 km/hr (E) None of these
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Reasoning: (1056 / 23) gives remainder 21 21 + 2 = 23, So we need to add 2 Ans: (B) Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23? Options: (A) 1 (B) 2 (C) 3 (D) 5 (E) 6 Rationale: 1/2:1/2:1/4 = 2:2:1 1/5*1000 = 200 400-200 = 200 The answer: (A) Question: Rs. 1000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/2:1/4? Options: (A) 200 (B) 992 (C) 772 (D) 552 (E) 312 Reasoning: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 Ans: (C) Question: If six persons sit in a row, then the probability that three particular persons are always together is? Options: (A) 1/6 (B) 1/3 (C) 1/5 (D) 1/1 (E) 1/2 Rationale: Given Speed = k/n To Find distance in x hours with same speed Distance = speed * time Distance = k/n*x = kx/n The answer: (E) Question: A racng car travels k kilometres in n hours. How many miles will it travel in x hours at the same rate? Options: (A) knx (B) k⁄n (C) kn⁄x (D) kx (E) kx⁄n Reasoning: Distance traveled by Eddy = 450 km Time taken by Eddy = 3 hours Average speed of Eddy = 450/3 = 150 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 150/75 = 2 Ans: (B) Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) Options: (A) 8/3 (B) 2 (C) 8/5 (D) 5/8 (E) 5/3 Reasoning: 1/2:1/3:1/4 = 6:4:3 3/13*1300 = 300 Ans: (C)
Question: Rs.1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4? Options: (A) 387 (B) 736 (C) 300 (D) 345 (E) 635
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Rationale: This is a simple alternating subtraction and addition series; The first series begins with 1 and adds 6; the second begins with 20 and subtracts 4, and so on. The answer: (C) Question: Fill in the blank with the correct number in this number series: 1, 20, 7, 16, __, 12, 19, ? Options: (A) 14 (B) 12 (C) 13 (D) 15 (E) 11 Reasoning: 1/3: 1/5: 1/1 = 5:3:15 Ans: (B) Question: The inverse ratio of 3: 5: 1 is? Options: (A) 2:3:7 (B) 5:3:15 (C) 2:3:2 (D) 2:3:6 (E) 2:3:1 Rationale: A = 2000(21/20)2 = 2205 The answer: (A) Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit. Options: (A) Rs.2205 (B) Rs.2200 (C) Rs.2160 (D) Rs.2040 (E) Rs.2050 Reasoning: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40 Volume of 1/40 part = 3 gallons\ Volume of whole = 3 * 40 = 120 gallons. Ans: (A) Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is? Options: (A) 120 gallons (B) 200 gallons (C) 170 gallons (D) 180 gallons (E) 250 gallons Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 25 possibilities (5*5) since each team has 5 players. So there are a total of 75 possibilities (25*3). The answer: (C) Question: There are 3 teams each with 5 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? Options: (A) 50 (B) 23 (C) 75 (D) 28 (E) 45 Rationale: 1 to 9 = 9 * 9 = 81 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5th = 50 + 40 = 90 – 81 = 9 The answer: (A)
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation? Options: (A) 9 (B) 8 (C) 7 (D) 6 (E) 4
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Reasoning: 1/2:1/3:1/4 = 6:4:3 Ram = 6/13 * 3250 = 1500 Shyam = 4/13 * 3250 = 1000 Mohan = 3/13 * 3250 = 750 Ans: (A) Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460? Options: (A) 750 (B) 888 (C) 261 (D) 787 (E) 17` Rationale: Distance covered by the car = 80 × 10 = 800 km \ Speed = 800⁄8 = 100 km/hr \ Speed gain = 100 – 80 = 20 km/hr The answer: (E) Question: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain? Options: (A) 8 km/hr (B) 10 km/hr (C) 12 km/hr (D) 16 km/hr (E) None of these Reasoning: ∴ 6x + 3x + 2x = 132 ⇒ x = 12. Second number = 3x = 3×12 = 36. Ans: (E) Question: Let the second number be 3x, so that the first number is 6x and the third number is 2x. Options: (A) 22 (B) 77 (C) 98 (D) 27 (E) 36 Rationale: Number of ways of selecting 2 fiction books = 10C2 Number of ways of selecting 2 non fiction books = 6C2 10C2 * 6C2 = 45 * 15 = 675 The answer: (C) Question: There are 10 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them? Options: (A) 90 (B) 120 (C) 675 (D) 180 (E) 200 Reasoning: 20000(11/10)4 - 20000(6/5)2 = 482 Ans: (A) Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? Options: (A) 482 (B) 887 (C) 299 (D) 277 (E) 200 Reasoning: (30*30)/100 = 9%loss Ans: (A)
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss? Options: (A) 9% loss (B) 400 (C) 4000 (D) 324 (E) 200
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Ques: In case L is the only individual sewing on committee B, which among the following shouldserve on committee A? Options: (A) V and U (B) V and T (C) U and S (D) M and N (E) T and U Ans: (D) CoT: M and N should serve on A Ques: In wardrobe Marry has 3trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4shirts. One of them is grey and the other 3are white. He openshiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey? Options: (A) 1/2 (B) 2/3 (C) 3/5 (D) 4/7 (E) 4/9 Ans: (A) CoT: Probability that trouser is not grey = 2/3 Probability that shirt is not grey = 3/4 ∴ Required probability = 2/3 x 3/4 = 1/2 Ques: Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so. If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides? Options: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Ans: (C) CoT: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. Ques: Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next? Options: (A) A) 23 (B) B) 14 (C) C) 27 (D) D) 53 (E) E) 86 Ans: (A)
CoT: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
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Reasoning: In 10s the train crosses the pole and in 30 sec the train crosses one more stationary train In 20 sec the train travels a distance of 600 mtrs Speed = 600/20 = 30 m/s = 30 (3600/1000) = 30 * 18/5 = 108 kmph Ans: (C) Question: A Train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long. Find the speed of the train. Options: (A) 110 kmph (B) 120 kmph (C) 108 kmph (D) 100 kmph (E) 98 kmph Rationale: P = (P*3*R)/100 R = 33 1/3% The answer: (B) Question: In what time a sum of money double itself at 3% per annum simple interest? Options: (A) 33 1/4% (B) 33 1/3% (C) 33 7/3% (D) 33 5/3% (E) 33 1/7% Reasoning: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. Ans: (B) Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle. When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left. So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left. Finally, they woke up the 7th thief and this time the diamonds were divided equally. How many diamonds did they steal in total? Options: (A) 1101 (B) 1141 (C) 1120 (D) 1130 (E) None Rationale: Speed downstream = d/t = 95/(2 1/2) = 38 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (38 - 18)/2 = 10 kmph The answer: (E) Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 5 kmph (B) 7 kmph (C) 9 kmph (D) 8 kmph (E) 10 kmph Reasoning: P = (P*3*R)/100 R = 33 1/3% Ans: (B) Question: In what time a sum of money double itself at 3% per annum simple interest? Options: (A) 33 1/9% (B) 33 1/3% (C) 332 1/3% (D) 33 9/3% (E) 13 1/3% Reasoning: Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% Ans: (C)
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? Options: (A) 45% (B) 47% (C) 57% (D) 60% (E) 62%
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Reasoning: 9 = (1*54*R)/100 R = 16 2/3 % Ans: (E) Question: If rupee one produces rupees nine over a period of 54 years, find the rate of simple interest? Options: (A) 22 1/7 % (B) 22 3/2 % (C) 22 1/8 % (D) 22 1/2 % (E) 16 2/3 % Reasoning: 1/20 - 1/40 = 1/40 40 minutes Ans: (C) Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full? Options: (A) 17 minutes (B) 87 minutes (C) 40 minutes (D) 27 minutes (E) 11 minutes Reasoning: 16 m/s = 16 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 16 * 18/5 * 15/4 km = 216 km. Ans: (C) Question: If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 118 km (B) 162 km (C) 216 km (D) 1887 km (E) 177 km Reasoning: 142 + 110 = 252/14 = 18 (Remainder) Ans: (C)
Question: A no.when divided by 142 gives a remainder 110, what remainder will be obtainedby dividingthe same no.14? Options: (A) 16 (B) 17 (C) 18 (D) 19 (E) 20
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12 m/s = 12 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km. If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 228 (B) 162 (C) 5528 (D) 256 (E) 191 (B) 40x⁄100 + y = 125x⁄100 ⇒ x⁄y = 20⁄17 If 40 per cent of a number is added to an other number then it becomes 125 per cent of itself. What will be the ratio of first and second numbers? Options: (A) 8 : 5 (B) 5 : 7 (C) 5 : 8 (D) Data inadequate (E) None of these (E) P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose? Options: (A) 3/140 (B) 1/28 (C) 7/40 (D) 3/35 (E) 5/40 (C)
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Ques: There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights? Options: (A) 8300 (B) 14500 (C) 7700 (D) 13000 (E) 5900 Ans: (C) CoT: Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700 Ques: In what time a sum of money double itself at 7% per annum simple interest? Options: (A) 33 1/8% (B) 33 1/3% (C) 14 2/7% (D) 33 4/3% (E) 73 1/3% Ans: (C) CoT: P = (P*7*R)/100 R = 14 2/7% Ques: A man rows his boat 90 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 9 kmph (B) 6 kmph (C) 5 kmph (D) 8 kmph (E) 7 kmph Ans: (A) CoT: Speed downstream = d/t = 90/(2 1/2) = 36 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (36 - 18)/2 = 9 kmph Ques: Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2? Options: (A) x^2 (B) x^2+1 (C) x^2 +4 (D) x^2+2x (E) x^2+4x Ans: (B)
CoT: Avg = [(x+1)^2 + (x-1)^2] / 2 Expanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1
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Rationale: S = 180/6 * 18/5 = 108 kmph The answer: (C) Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train? Options: (A) 48 kmph (B) 52 kmph (C) 108 kmph (D) 100 kmph (E) 98 kmph Reasoning: 1/2 * 20(9 + 6) = 150 cm2 Ans: (B) Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm? Options: (A) 128 (B) 150 (C) 887 (D) 279 (E) 771 Rationale: 1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 1/4 *2 = 22 1/2 days The answer: (B) Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? Options: (A) 22 1/8 days (B) 22 1/2 days (C) 22 6/2 days (D) 72 1/2 days (E) 23 1/2 days Reasoning: Since today's is Daniel's birthday, his age must be an integer. As per the question, let A = 12, B = 2, and C = 6. Plugging these into the answer choices, only C does not yield an integer. Ans: (C) Question: Amy, Bob, Cindy, and Daniel all have the same birthday, but they are all different ages. Today is their birthday. Cindy's age is divisible by Bob's age, and Amy's age is divisible by Cindy's age. If A is Amy's age in years, B is Bob's age, and C is Cindy's age, which of the following CANNOT be Daniel's age? Options: (A) AC/B (B) (A+C) /B (C) (A+B) /C (D) AB/C (E) (A-C) /B Rationale: Total number of letters = 8 Using these letters the number of 8 letters words formed is 8P8 = 4. The answer: (A) Question: Using all the letters of the word "THURSDAY", how many different words can be formed? Options: (A) 8! (B) 1 (C) 7 (D) 6 (E) 5 Rationale: Number of times wheel moves in 1 hour = 20 * 60 = 1200 :. Distance moves = (1200*20) cms = 24000 cms In metres = 240 metre The answer: (C)
Question: A wheel rotates 20 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour? Options: (A) 4 metre (B) 12 metre (C) 240 metre (D) 2400 metre (E) 130 metre
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Reasoning: Let the average after 7th inning = x Then average after 16th inning = x - 3 \inline \fn_jvn \therefore 16(x-3)+87 = 17x \inline \fn_jvn \therefore x = 87 - 48 = 39 Ans: (A) Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning? Options: (A) 39 (B) 88 (C) 3 (D) 7 (E) 62 Rationale: P = (P*60*R)/100 R = 1 2/3% The answer: (C) Question: At what rate percent on simple interest will a sum of money double itself in 60 years? Options: (A) 3 1/3% (B) 3 1/9% (C) 1 2/3% (D) 3 2/3% (E) 3 6/3% Reasoning: Hint: y^2-5 (y is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Ans: (B) Question: For some integer y, y^2 - 5 is divisible by all of the following EXCEPT Options: (A) 29 (B) 30 (C) 31 (D) 38 (E) 41 Rationale: Cost price of article = 48$ % of overhead cost = 30 Net profit = 12 $ We need to calculate % markup Net profit as % of cost price = (12/48)*100 = 25% Total markup should be = 25 + 30 = 55% The answer: (E) Question: The purchase price of an article is $48. In order to include 30% of cost for overhead and to provide $12 of net profit, the markup should be Options: (A) 15% (B) 25% (C) 35% (D) 40% (E) 55% Reasoning: Must be once on twice and once on tails 1/2*1/2*1/2 = 1/8 Ans: (E) Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land twice on heads and once on tails? Options: (A) 1/16 (B) 1/3 (C) 1/6 (D) 1/2 (E) 1/8 Reasoning: Start with the prime factorization: 33150 = 50*663 = (2*5*5)*3*221 = (2)*(3)*(5^2)*(13)*(17) There are five distinct prime factors, {2, 3, 5, 13, and 17} Ans: (B)
Question: How many distinct prime numbers are factors of 33150? Options: (A) Four (B) Five (C) Six (D) Seven (E) Eight
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Reasoning: Total age of students is 32X16 = 512 Years Total age inclusive of teacher = 33X (16+1) = 561 So, Teacher's age is 561-512 = 49 Yrs There is a shortcut for these type of problems Teacher's age is 16+(33X1) = 49 Years Ans: (E) Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Options: (A) 28 Years (B) 30 Years (C) 32 Years (D) 37 Years (E) 49 Years Rationale: 1/5:1/5:1/10 = 2:2:1 1/5*5000 = 1000 2000-1000 = 1000 The answer: (A) Question: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10? Options: (A) 1000 (B) 992 (C) 772 (D) 552 (E) 312 Reasoning: Total age of students is 14X10 = 140 Years Total age inclusive of teacher = 15X (10+1) = 165 So, Teacher's age is 165-140 = 25 Yrs There is a shortcut for these type of problems Teacher's age is 10+(15X1) = 25 Years Ans: (E) Question: The average age of a class of 14 students is 10 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Options: (A) 30 Years (B) 31 Years (C) 32 Years (D) 34 Years (E) 25 Years Rationale: One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days. The answer: (A) Question: A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work? Options: (A) 6 3/4 days (B) 7 3/4 days (C) 5 3/4 days (D) 6 1/4 days (E) 6 2/4 days Reasoning: 6 people can be prized with 4 distinct prizes in 6^4 ways Ans: (C) Question: In a race with 30 runners where 4 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? Options: (A) 8^8 ways (B) 8^9 ways (C) 6^4 ways (D) 8^7 ways (E) 8^6 ways Reasoning: Simple interest = (18000 * 5 * 15)/100 = Rs. 13500 Amount = P + I = 18000 + 13500 = Rs. 31500 Ans: (A)
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for five years? Options: (A) 31500 (B) 27773 (C) 29989 (D) 28800 (E) 29883
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Answer: (B) Question: In how many different ways can the letters of the word "CLAIM" be rearrangement? Options: (A) 110 (B) 120 (C) 125 (D) 130 (E) 140 [CoT]: [The total number of arrangements is 5P5 = 5! = 120] Answer: (C) Question: Ann invested a certain sum of money in a bank that paid simple interest. The amount grew to $240 at the end of 2 years. She waited for another 3 years and got a final amount of $300. What was the principal amount that she invested at the beginning? Options: (A) $150 (B) $175 (C) $200 (D) $210 (E) $220 [CoT]: [Amount at end of 2 years = 240$ Amount at end of 5 years = 300$ Difference in amount for time period of 3 years = 60$ Annual Interest earned = 60/3 = 20$ Principal amount invested at the beginning = 240 - 2*20 = 200$] Answer: (A) Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds. What is the length of the platform in meters? Options: (A) 200 meters (B) 360 meters (C) 420 meters (D) 600 meters (E) Cannot be determined [CoT]: [Speed of the train in metres/sec = 72000/3600 = 20 Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform Distance travelled by train to cross the man = 20 * 20 = 400 = Length of train Length of platform = 600 - 400 = 200] Answer: (B) Question:
Look at this series: 0.25, 1.75, ____, 85.75, 600.25, ... What number should fill the blank? Options: (A) 11.25 (B) 12.25 (C) 13.25 (D) 9.25 (E) 10.75 [CoT]: [This is a simple multiplication series. Each number is 7 times greater than the previous number.]
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Reasoning: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450 ≈ 576 + 740 + 450 ≈ 1760 ≈ 1800 Ans: (D) Question: What approximate value should come in place of the question mark (?) in the following equation’? 3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30 Options: (A) 1200 (B) 1500 (C) 1600 (D) 1800 (E) 2100 Rationale: I think answer on this one should be C too. Since we know that 14^7>16^4, as Will said one should always check if the number is positive. The answer: (C) Question: What is the units digit of the expression 14^7−16^4? Options: (A) 0 (B) 3 (C) 8 (D) 6 (E) 4 Reasoning: Probability that trouser is not grey = 2/3 Probability that shirt is not grey = 3/4 ∴ Required probability = 2/3 x 3/4 = 1/2 Ans: (A) Question: In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey? Options: (A) 1/2 (B) 2/3 (C) 3/5 (D) 3/7 (E) 4/9 Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes The answer: (A) Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? Options: (A) 27 (B) 22 (C) 24 (D) 26 (E) 30 Reasoning: Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 12 = 200 meter Ans: (D) Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train? Options: (A) 150 (B) 872 (C) 287 (D) 200 (E) 212 Reasoning: Largest 4 digit number is 9999 After doing 9999 ÷ 88 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 Ans: (C)
Question: Find the largest 4 digit number which isexactly divisible by 88? Options: (A) 3454 (B) 4586 (C) 9944 (D) 10564 (E) 18664
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Reasoning: 12 12 × 4 + 2 = 50 50 × 4 + 2 = 202 202 × 4 + 2 = 810 810 × 4 + 2 = 3242 3242 × 4 + 2 = 12970 Ans: (C) Question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____ Options: (A) 12400 (B) 12800 (C) 12970 (D) 13015 (E) 16000 Rationale: Dick saved = $ 3240 Jane saved = $ 1760 (jane saved $1240 less than she did the prior year) Jane saved approximately $1240/$3000 (close to 41%) less in 1990 The answer: (C) Question: Dick and Jane each saved $3,000 in 1989. In 1990 Dick saved 8 percent more than in 1989, and together he and Jane saved a total of $5,000. Approximately what percent less did Jane save in 1990 than in 1989? Options: (A) 8% (B) 25% (C) 41% (D) 59% (E) 70% Reasoning: Speed = 81 * 5/18 = 45/2 m/sec Total distance covered = 650 + 340 = 990 m Required time = 990 * 2/45 = 44 se Ans: (C) Question: A train 650 m long is running at a speed of 81 km/hr. In what time will it pass a bridge 340 m long? Options: (A) 42 (B) 43 (C) 44 (D) 45 (E) 46 Rationale: Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10 The answer: (C) Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ? Options: (A) Equal to 3 (B) Less than 3 (C) More than 10 (D) Less than 10 (E) none of these Reasoning: Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7 Ans: (A) Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ? Options: (A) more than 7 (B) Less than 3 (C) More than 3 (D) Less than 1/3 (E) none of these Reasoning: Total expenditure = 40 + 25 + 15 + 15 = 95% Saving = (100 - 95) = 5% 5/100 × Salary = 1200, Salary = 24000 Rs. Ans: (B)
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 15% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is: Options: (A) 4000 (B) 24000 (C) 8000 (D) 10000 (E) None of these
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[Ques]: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train? Options: (A) 287 (B) 699 (C) 677 (D) 168 (E) 200 *Ans*: (E) --CoT--: Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 12 = 200 m [Ques]: In what time a sum of money double itself at 3% per annum simple interest? Options: (A) 33 1/9% (B) 33 1/3% (C) 332 1/3% (D) 33 9/3% (E) 13 1/3% *Ans*: (B) --CoT--: P = (P*3*R)/100 R = 33 1/3% [Ques]: if deepak has 5 pants and 3 shirts how many combinations can deepak make? Options: (A) 10 (B) 9 (C) 15 (D) 20 (E) 25 *Ans*: (C) --CoT--: If deepak can only choose one of each, there are 5*3 = 15 possible combinations. [Ques]: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 5 kmph (B) 7 kmph (C) 9 kmph (D) 8 kmph (E) 1 kmph *Ans*: (D)
--CoT--: Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph
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## Solution 70 + 75 = 145 * 5/18 = 725/18 mps D = 150 + 100 = 250 m T = 250 * 18/725 = 180/29 = 6 6/29 sec ## What the question and answer could be Two trains are moving at 75 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? Options: (A) 6 6/29 sec (B) 7 1/7 sec (C) 7 2/2 sec (D) 8 1/2 sec (E) 7 1/19 sec (A) ## Solution In this series, each number is repeated, then 13 is subtracted to arrive at the next number. ## What the question and answer could be Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next? Options: (A) 12 (B) 15 (C) 14 (D) 18 (E) 17 (C) ## Solution 252 = 2 x 2 x 3 x 3 x 7. ## What the question and answer could be 252 can be expressed as a product of primes as: Options: (A) 2 x 2 x 3 x 3 x 7 (B) 2 x 2 x 2 x 3 x 7 (C) 3 x 3 x 3 x 3 x 7 (D) 2 x 3 x 3 x 3 x 7 (E) 7 x 3 x 3 x 3 x 7 (A) ## Solution Total ways to choose 4 employees from 8 employees = 8C3 Two men = 5C2 Two women = 3C1 P = (5C2 * 3C1)/8C2 = 5/7 hence ## What the question and answer could be
A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men? Options: (A) 5/7 (B) 1/7 (C) 2/7 (D) 3/7 (E) 1/2 (A)
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Reasoning: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence Ans: (A) Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible? Options: (A) 2 (B) 4 (C) 6 (D) 8 (E) 10 Reasoning: 9 = (1*40*R)/100 R = 22 1/2 % Ans: (D) Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? Options: (A) 22 1/6 % (B) 22 8/2 % (C) 25 1/2 % (D) 22 1/2 % (E) 22 5/2 % Reasoning: Probability that trouser is not grey = 2/3 Probability that shirt is not grey = 3/4 ∴ Required probability = 2/3 x 3/4 = 1/2 Ans: (A) Question: In wardrobe Marry has 3trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4shirts. One of them is grey and the other 3are white. He openshiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey? Options: (A) 1/2 (B) 2/3 (C) 3/5 (D) 4/7 (E) 4/9 Reasoning: 10^2 - 20 = 80 20^2 - 30 = 370 30^2 - 40 = 860 40^2 - 50 = 1550 50^2 - 60 = 2440 60^2 - 70 = 3530. Ans: (A)
Question: 80 ? 860 1550 2440 3530 Options: (A) 370 (B) 840 (C) 750 (D) 860 (E) 960
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Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3 All the three pipes together will fill the tank in 3 hours. The answer: (C) Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled? Options: (A) 2 (B) 2.2 (C) 3 (D) 3.5 (E) 4 Reasoning: Original perimeter = x Hence original side = x/4 New side = 5x/4 New perimeter = 4*5x/4 = 5x Ans: (C) Question: The measure of the side of a square is multiplied by 5. If x represents the perimeter of the original square, what is the value of the new perimeter? Options: (A) 3x (B) 4x (C) 5x (D) 12x (E) 27x Rationale: Original perimeter = x Hence original side = x/4 New side = 4x/4 New perimeter = 4*4x/4 = 4x The answer: (B) Question: The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter? Options: (A) 3x (B) 4x (C) 9x (D) 12x (E) 27x Reasoning: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 360 pastries would take 360 ÷ 60 = 6 hours. Ans: (A) Question: Anmol can eat 27 pastries in a hour. Aakriti can eat 2 pastries in 10 minutes. Divya can eat 7 pastries in 20 minutes. How long will it take them to eat a 360 pastries ? Options: (A) 6 hours. (B) 1 hours. (C) 5 hours. (D) 4 hours. (E) 3 hours. Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% The answer: (C) Question: 3 candidates in an election & received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidategot in that election? Options: (A) 50% (B) 52% (C) 57% (D) 60% (E) 65% Rationale: 1 also gives the remainder of 1 when divided by 4. So, there are total of 15 numbers. The answer: (C)
Question: How many positive integers less than 60 have a reminder 01 when divided by 4? Options: (A) 13 (B) 14 (C) 15 (D) 16 (E) 17
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Rationale: 1/30 + 1/40 = 7/120 120/7 = 17 1/7 days The answer: (A) Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? Options: (A) 17 1/7 (B) 17 1/5 (C) 17 1/8 (D) 17 1/1 (E) 17 1/2 Reasoning: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3 All the three pipes together will fill the tank in 3 hours. Ans: (B) Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled? Options: (A) 2 (B) 3 (C) 3.5 (D) 4 (E) 4.5 Rationale: 45 + 31 = 76/15 = 1 (Remainder) The answer: (D) Question: A certain number when divided by 45 leaves a remainder 31, what is the remainder if the same number be divided by 15? Options: (A) 13 (B) 11 (C) 9 (D) 1 (E) 3 Reasoning: No of people from 10 - 11 is x No of people from 11 - 12 is 11x/10 No of people from 12 to 1 is (6/5)(11x/10) Given that 11x/10 + (6/5)(11x/10) = 121x / 50 = 242 Then x = 100 Ans: (A) Question: The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 20% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 10% more than the number there from 10 a.m. to 11 a.m. If 242 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.? Options: (A) 100 (B) 20 (C) 30 (D) 40 (E) 50 Rationale: (60/100) * 50 – (40/100) * 30 30 - 12 = 18 The answer: (A) Question: How much 60% of 50 is greater than 40% of 30? Options: (A) 18 (B) 99 (C) 66 (D) 55 (E) 71 Rationale: 10000(11/10)4 - 10000(6/5)2 = 241 The answer: (A)
Question: How much more would Rs.10000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? Options: (A) 241 (B) 725 (C) 992 (D) 837 (E) 923
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Rationale: 2/10*1/6*(total) = 5 1/30*(total) = 5 (total) = 5*30 = 150 The answer: (E) Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports? Options: (A) $21.25m (B) $25.5m (C) $106.25m (D) $127.5m (E) $150m Reasoning: Sum of all the 13 numbers = 13 * 60 = 780 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 780 = 46. Ans: (A) Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number? Options: (A) 46 (B) 77 (C) 88 (D) 544 (E) 33 Rationale: Total age of students is 32X16 = 512 Years Total age inclusive of teacher = 33X (16+1) = 561 So, Teacher's age is 561-512 = 49 Yrs There is a shortcut for these type of problems Teacher's age is 16+(33X1) = 49 Years The answer: (A) Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Options: (A) 49 Years (B) 51 Years (C) 53 Years (D) 54 Years (E) 55 Years Reasoning: 15 + 10 + 60 = 85% 100 - 85 = 15% to all others Ans: (C) Question: If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations? Options: (A) 4/5 (B) 3/5 (C) 3/20 (D) 1/5 (E) 1/10 Rationale: 200/36 * 18/5 = 20 km/hr The answer: (A) Question: A boy runs 200 metres in 36 seconds. What is his speed ? Options: (A) 20 km/hr (B) 24 km/hr (C) 30 km/hr (D) 32 km/hr (E) 34 km/hr Rationale: Here both numbers are less than 100. So they are deficient of - 5 and - 3 compared with 100. So The answer: (E)
Question: Find 95 ×× 97 Options: (A) 92/198 (B) 92/12 (C) 92/13 (D) 92/10 (E) 92/15
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Reasoning: One day work of A and B = 1/2 One day work of B and C = 1/6 One day work of C and A = 1/8 2(A + B + C) = 1/2 + 1/6 + 1/8 2(A + B + C) = 19/24 (A + B + C) = 19/48 Number of days required = 48/19 days. Ans: (B) Question: A and B can do a work in 2 days, B and C in 6 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together? Options: (A) 12/28 (B) 48/19 (C) 16/48 (D) 18/48 (E) 12/64 Rationale: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec The answer: (A) Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 sec (B) 22 sec (C) 27 sec (D) 17 sec (E) 37 sec Reasoning: D = 100 + 150 = 250 S = 36 * 5/18 = 10 mps T = 250/10 = 25 se Ans: (C) Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? Options: (A) 22 sec (B) 77 sec (C) 25 sec (D) 18 sec (E) 17 sec Rationale: Area of tile = 25*65 = 1625 Area of floor = 150*390 = 58500 No of tiles = 58500/1625 = 36 So, the no of tile = 36 The answer: (D) Question: Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Options: (A) 50 (B) 40 (C) 25 (D) 36 (E) 45 Reasoning: Profit = q Profit to company founder = 2q/3 Profit to other partners = q/3 Number of other partners = 3 Profit to each partner = (q/3)/3 = q/9 Ans: (A) Question: Last year, Company X made q dollars in profit. two Thrid of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive? Options: (A) q/9 (B) q/5 (C) q/6 (D) q/7 (E) q/8 Reasoning: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Ans: (C)
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is Options: (A) 1/9 (B) 1/7 (C) 1/5 (D) 1/1 (E) 1/2
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## Solution He lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut. ## What the question and answer could be A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change. Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill. Later that day he tries to figure out how much money he lost. What did he lose? Options: (A) $5 (B) $10 (C) $12 (D) $15 (E) $20 (A) ## Solution Maximum points of intersection between n different circles = n*(n - 1) = 5*4 = 20 ## What the question and answer could be There are different 5 circles. What is the number of the greatest possible points with which the circles intersect? Options: (A) 20 (B) 10 (C) 15 (D) 22 (E) 21 (A) ## Solution T = 60/36 * 18/5 = 6 sec ## What the question and answer could be In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way? Options: (A) 3 (B) 5 (C) 4 (D) 6 (E) 7 (D) ## Solution Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 510 + 140 = 650 m Required time = 650 * 2/25 = 52 sec ## What the question and answer could be
A train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 52 (C) 26 (D) 21 (E) 14 (B)
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[Ques]: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 24 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours? Options: (A) 61.25 (B) 62.5 (C) 63.75 (D) 70.0 (E) 77.5 *Ans*: (D) --CoT--: Rate of flow of water in second hour = 24 gallons per hour Rate of flow of water in first hour = 24/(3/2) = 16 gallons per hour Rate of flow of water in third hour = (125/100)* 24 = (5/4) * 24 = 30 gallons per hour Number of gallons of water that flowed through the pipe during the entire 3 hours = 16+24+30 = 70 gallons [Ques]: John has 5 flavors of chocolate in him shop. How many options are there for Jones to pick a one-flavor, two-flavor, three-flavor, four-flavor or five-flavor order? Options: (A) 22 (B) 31 (C) 43 (D) 37 (E) 38 *Ans*: (B) --CoT--: 5C1 + 5C2+ 5C3+5C4+5C5 = 31. [Ques]: A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long? Options: (A) 17 (B) 18 (C) 19 (D) 20 (E) 21 *Ans*: (B) --CoT--: Speed = 99 * 5/18 = 55/2 m/sec Total distance covered = 300 + 195 = 495 m Required time = 495 * 2/55 = 18 sec [Ques]: Find the odd man out 3, 5, 7, 12, 13, 17, 19 Options: (A) 3 (B) 5 (C) 7 (D) 12 (E) 13 *Ans*: (D)
--CoT--: 12 is an even number while the others are od
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Reasoning: Work done by X in 1 day = 1/18 Work done by Y in 1 day = 1/15 Work done by Y in 10 days = 10/15 = 2/3 Remaining work = 1 – 2/3 = 1/3 Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6 Ans: (C) Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work? Options: (A) 1 (B) 3 (C) 6 (D) 8 (E) 9 Reasoning: Average of 20 numbers = 0 Sum of 20 numbers = (0 * 20) = 0 It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a). Ans: (D) Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? Options: (A) 17 (B) 16 (C) 17 (D) 19 (E) 62 Reasoning: The total of seven numbers = 7X20 = 140 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (140 - 99 ) = 41 Ans: (D) Question: The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? Options: (A) 27 (B) 29 (C) 31 (D) 41 (E) 35 Reasoning: Suppose the amount in the beginning was Rs ’x’ Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3 Money spent on food = 1/5 of 2x/3 = Rs 2x/15 Balance = 2x/3 - 2x/15 = Rs 8x/15 Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5 Therefore 2x/5 = 200 = 500 Ans: (B)
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 200. How much did he have with him in the beginning? Options: (A) s 200 (B) s 500 (C) s 300 (D) s 450 (E) s 550
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Rationale: 200/72 * 18/5 = 10 km/hr The answer: (A) Question: A boy runs 200 metres in 72 seconds. What is his speed ? Options: (A) 10 km/hr (B) 14 km/hr (C) 20 km/hr (D) 12 km/hr (E) 24 km/hr Reasoning: Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Ans: (E) Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train. Options: (A) 150 m (B) 145 m (C) 240 m (D) 135 m (E) 250 m Rationale: Here, l = 7 and m = 14 Therefore, first number = l/m x 100% of second number = 7/14 x 100% of second number = 50% of second number The answer: (D) Question: If the given two numbers are respectively 7% and 14% of a third number, then what percentage is the first of the second ? Options: (A) 20% (B) 25% (C) 18% (D) 50% (E) none of these Reasoning: The worst scenario is when she takes 9 red and 5 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket. Ans: (E) Question: Grace has 18 jellybeans in her pocket. She has 9 red ones, 5 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? Options: (A) 4 (B) 8 (C) 12 (D) 13 (E) 15 Rationale: The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 The answer: (B) Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? Options: (A) 25 (B) 27 (C) 29 (D) 32 (E) 34 Rationale: The term (998-998) makes the whole expression = 0. The answer: (E)
Question: (998-1)(998-2)(998-3)........(998-n)=....... when n>1000 Options: (A) 4 (B) 3 (C) 2 (D) 1 (E) 0
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Reasoning: Divisibility rule of 3: The sum of the digits of the number should be divisible by 3 Option A: 10394, Sum = 17. Not divisible by 3. Hence the number 10394 is also not divisible by 3 Option B: 15363, Sum = 18, Divisible by 3 Option C: 29340, Sum = 18, Divisible by 3 Option D: 30753, Sum = 18, Divisible by 3 Option E: 41715, Sum = 18, Divisible by 3 Ans: (E) Question: Which of the following is not divisible by 3? Options: (A) 10394 (B) 15363 (C) 29340 (D) 30753 (E) 41715 Rationale: S = (100 + 300)/45 = 400/45 * 18/5 = 32 The answer: (A) Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Options: (A) 32 (B) 545 (C) 88 (D) 66 (E) 09 Reasoning: Divisibility rule of 4: Last two digits of the number should be divisible by 4 Option A: 10236, last two digits = 36. Divisible by 4 Option B: 21792, last two digits = 92. Divisible by 4 Option C: 47816, last two digits = 16. Divisible by 4 Option D: 91232, last two digits = 32. Divisible by 4 Option E: 72034, last two digits = 34. Not divisible by 4. Hence 72034 is not divisible by 4 Ans: (E) Question: Which of the following is not divisible by 4? Options: (A) 10236 (B) 21792 (C) 47816 (D) 91232 (E) 72034 Rationale: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 460 + 140 = 600 m Required time = 600 * 2/25 = 48 se The answer: (C) Question: A train 460 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 87 (C) 48 (D) 21 (E) 14 Reasoning: (average) = (perimeter)/3; 12 = (perimeter)/3; (perimeter) = 36. Ans: (E) Question: The average length of the sides of triangle ABC is 12. What is the perimeter of triangle ABC? Options: (A) 4 (B) 6 (C) 12 (D) 24 (E) 36 Reasoning: D = 72 * 5/18 = 50 = 1000 – 250 = 750m Ans: (D)
Question: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform? Options: (A) 150m (B) 200m (C) 250m (D) 750m (E) 300 m
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[Ans] (C) [Question] A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train. Options: (A) 150 (B) 180 (C) 250 (D) 200 (E) 225 [CoT] Speed = 90*(5/18) m/sec = 25 m/sec Length of Train (Distance) = Speed * Time 25 *10 = 250 meter [Ans] (A) [Question] If sushi rows 27 km upstream and 81 km down steam taking 9 hours each, then the speed of the stream Options: (A) 12 kmph (B) 13 kmph (C) 22 kmph (D) 20 kmph (E) 15 kmph [CoT] Speed upstream = 27/9 = 3 kmph Speed down stream = 81/3 = 27 kmph Speed of stream = ½ (27-3) = 12 kmph [Ans] (D) [Question]
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? Options: (A) 1227 (B) 2088 (C) 26788 (D) 8112 (E) 1871 [CoT] A = 7500(26/25)2 = 8112
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Rationale: 60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 The answer: (B) Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? Options: (A) 2277 (B) 3000 (C) 2682 (D) 7222 (E) 2682 Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter The answer: (A) Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. Options: (A) 150 meter (B) 250 meter (C) 200 meter (D) 480 meter (E) 153 meter Rationale: Six members can be selected from ten members in 10C6 = 10C4 ways. The answer: (B)
Question: in how many ways can six members be selected from a group of ten members? Options: (A) 10C6 (B) 10C4 (C) 10C9 (D) 10C2 (E) 10C1
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Rationale: T = 192/32 = 6 h T = 6 - 3 = 3 Time Ratio = 6:3 = 2:1 Speed Ratio = 1:2 The answer: (A) Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? Options: (A) 1:2 (B) 1:0 (C) 1:87 (D) 1:6 (E) 1:1 Reasoning: Original perimeter = x Hence original side = x/4 New side = 3x/4 New perimeter = 4*3x/4 = 3x Ans: (A) Question: The measure of the side of a square is tripled. If x represents the perimeter of the original square, what is the value of the new perimeter? Options: (A) 3x (B) 4x (C) 9x (D) 12x (E) 27x Rationale: P(at least one Snicker's Bar) = 1 - P(no Snicker's Bar, so 2 Milky Way Bars) = 1- 2/5*1/4 = 9/10. The answer: (A) Question: In a bag there are 3 Snicker's bars and 2 Milky Way bars. What is the probability of choosing at least one Snickers when choosing two consecutive candy bars randomly? Options: (A) 9/10 (B) 16/20 (C) 2/5 (D) 3/5 (E) ½ Reasoning: Answer = B) Three Numbers between 10 - 99 giving remainder 8 when divided by 10 = 18, 28, 38, 48, 58, 68, 78, 88, 98 The above Numbers giving remainder 2 when divided by 8 = 18, 58, 98 = 3 Ans: (B) Question: How many numbers between 10 - 99 yield a reminder of 8 when divided by 10 and also yield a remainder of 2 when divided by 8? Options: (A) One (B) Three (C) Two (D) Five (E) Four Rationale: E + H = (55 × 2) = 110; E + S = (65 × 2) = 130 ∴ Reqd difference = 130 – 110 = 20 The answer: (C) Question: The average of Suresh’s marks in English and History is 55. His average of marks in English and Science is 65. What is the difference between the marks which he obtained in History and Science? Options: (A) 40 (B) 60 (C) 20 (D) Data inadequate (E) None of the above Rationale: My ans is 15C4 = 1365 The answer: (E)
Question: Fifteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of four members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? Options: (A) 120 (B) 126 (C) 252 (D) 1200 (E) 1365
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Reasoning: Area of an equilateral triangle = √3/4 S2 If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2; Ans: (C) Question: What is the are of an equilateral triangle of side 8 cm? Options: (A) 64√5 (B) 64√9 (C) 16√3 (D) 64√3 (E) 64√2 Rationale: 100 * 100 = 10000 115 * 80 = 9200 The answer: (E) Question: The length of a rectangle is increased by 15% and its breadth is decreased by 20%. What is the effect on its area? Options: (A) 1288 (B) 1299 (C) 1000 (D) 10000 (E) 9200 Reasoning: 70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 1/2 sec Ans: (D) Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? Options: (A) 7 1/2 sec (B) 7 1/7 sec (C) 7 8/2 sec (D) 7 1/9 sec (E) 7 2/2 sec Rationale: Integer is divisible by 9 - Sum of digits is divisible by 9 The answer: (C) Question: The number N is 5,1H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H? Options: (A) 1 (B) 3 (C) 8 (D) 7 (E) 9 Reasoning: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 Ans: (C) Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ? Options: (A) 1/8 (B) 1/2 (C) 1/5 (D) 1/5 (E) 1/3 Reasoning: 252 = 2 x 2 x 3 x 3 x 7. Ans: (A)
Question: 252 can be expressed as a product of primes as : Options: (A) 2 x 2 x 3 x 3 x 7 (B) 2 x 2 x 2 x 3 x 7 (C) 3 x 3 x 3 x 3 x 7 (D) 2 x 3 x 3 x 3 x 7 (E) 2 x 3 x 7 x 3 x 2
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Reasoning: Let the number of dogs be 'x' and the number of peacocks by 'y'. Then, number of legs in the group = 4x + 2y. Number of heads in the group = x+y So, 4x+2y = 4(x+y) – 18 ⇒ 2y = 18 ⇒ y = 9 Number of peacocks in that group = 9. Ans: (A) Question: In a group of dogs and peacocks, the number of legs are 18 less than four times the number of heads How many peacocks are there in that group? Options: (A) 9 (B) 8 (C) 7 (D) 6 (E) 5 Rationale: Age of B = Age of (A + B + C) – Age of (A + C) = 28 × 3 – 29 × 2 = 84 – 58 = 26 years The answer: (B) Question: The average age of A, B and C is 28 years. If the average age of A and C is 29 years, what is the age of B in years ? Options: (A) 19 (B) 26 (C) 20 (D) 32 (E) 21 Reasoning: Purchase = 8748/(1-10/100^3) = 12000 Ans: (A) Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was : Options: (A) 12000 (B) 10000 (C) 15000 (D) 20000 (E) 25000 Rationale: Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec The answer: (B) Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in? Options: (A) 18 sec (B) 16 sec (C) 76 sec (D) 15 sec (E) 17 sec Reasoning: The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 Ans: (B) Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? Options: (A) 26 (B) 27 (C) 29 (D) 32 (E) 36 Reasoning: 1/12 - 1/18 = 1/36 36 minutes Ans: (D)
Question: A pipe can fill a cistern in 12 minutes whereas the cistern when fill can be emptied by a leak in 18 minutes. When both pipes are opened, find when the cistern will be full? Options: (A) 17 (B) 16 (C) 70 (D) 36 (E) 12
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Answer: (A) Question: Find the product of the localvalue and absolutevalue of 1 in 20168? Options: (A) 100 (B) 110 (C) 151 (D) 120 (E) 140 [CoT]: [Local value of 1 = 1 x 100 = 100 Place value of 1 = 1 There fore = 1 x 100 = 100] Answer: (D) Question: 5,9,17,29,49,__ Options: (A) 79 (B) 80 (C) 81 (D) 82 (E) 83 [CoT]: [(9+5) +3 = 17 (16+9) +4 = 29 (28+16)+5 = 49 (48+28)+6 = 82] Answer: (C) Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train? Options: (A) 49 sec (B) 50 sec (C) 48 sec (D) 43 sec (E) 32 sec [CoT]: [D = 540 + 180 = 720 S = 54 * 5/18 = 15 mps T = 720/15 = 48 se] Answer: (B) Question:
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $222 for it, the cost price of the Cricket Bat for A is: Options: (A) 150 (B) 148 (C) 130 (D) 160 (E) 210 [CoT]: [125% of 120% of A = 222 125/100 * 120/100 * A = 222 A = 222 * 2/3 = 148.]
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Ques: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 44 men reap in 54 days? Options: (A) 820 acres (B) 660 acres (C) 620 acres (D) 720 acres (E) 920 acres Ans: (B) CoT: 12 men 120 acres 36 days 44 men ? 54 days 120 * 44/12 * 54/36 10 * 44 * 3/2 44 * 15 = 660 Ques: From the set of numbers x, y, t, z, s and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x,s), etc and (x,y)=(y,x) Options: (A) 10 (B) 14 (C) 15 (D) 16 (E) 31 Ans: (E) CoT: Another way: Any letter (x, y, z, w, s) can be included or not. So, we have 2^5 combinations - 1 empty combination = 31 combinations Ques: A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight? Options: (A) 36 (B) 40 (C) 42 (D) 54 (E) 65 Ans: (D) CoT: Distance from nest to lake = d, Speed = 60, Time = d/60 Distance from lake to cave = d/2, Speed = 45, Time = d/90 Average speed = (d + d/2)/(d/60 + d/90) = (3/2)/(1/36) = 54 Ques: Twenty percent of Country Y's yearly exports come from fruit exports. One-fourth of all fruit exports from Country Y are orange exports. If country Y generates $40 million from its orange exports, how much money does it generate from its yearly total of exports? Options: (A) $21.25m (B) $800m (C) $106.25m (D) $127.5m (E) $153m Ans: (B)
CoT: 20/100*1/4*(total) = 40 1/20*(total) = 40 (total) = 40*20 = 800
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My ans is 10C3 = 120 Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? Options: (A) 120 (B) 126 (C) 252 (D) 1200 (E) 1260 (A) 1/18 + 1/30 = 8/90 = 4/45 45/4 = 11 1/4 *2 = 22 1/2 days A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days? Options: (A) 22 1/8 days (B) 22 1/2 days (C) 22 6/2 days (D) 72 1/2 days (E) 23 1/2 days (B) Age of B = Age of (A + B + C) – Age of (A + C) = 25 × 3 – 29 × 2 = 75 – 58 = 17 years
The average age of A, B and C is 25 years. If the average age of A and C is 29 years, what is the age of B in years ? Options: (A) 17 (B) 35 (C) 20 (D) 32 (E) 21 (A)
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Rationale: Must be twice on heads and twice on tails 1/2*1/2*1/2*1/2 = 1/16 The answer: (C) Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land twice on heads and twice tails? Options: (A) 1/8 (B) 1/4 (C) 1/16 (D) 1/32 (E) 1/2 Reasoning: Each of the numbers except 66 is multiple of 5. Ans: (C) Question: Find the odd man out.10, 25, 45, 50, 66, 70, 80 Options: (A) 45 (B) 50 (C) 66 (D) 70 (E) 80 Rationale: 4*2+3 = 11 11*2+3 = 25 25*2+3 = 53 53*2+3 = 109 109*2+3 = 221 221*2+3 = 445 The answer: (C) Question: Find the odd man out 445, 221, 109, 46, 25, 11, 4 Options: (A) 221 (B) 109 (C) 46 (D) 25 (E) 21 Reasoning: (600*3*4)/100 = 72 600 + 72 = 672 Ans: (A) Question: Rs.600 amounts to Rs.900 in 3 years at simple interest. If the interest is increased by 4%, it would amount to how much? Options: (A) 672 (B) 246 (C) 258 (D) 856 (E) 653 Rationale: Answer = C. 75 miles Relational speed = 130 - 100 = 30 miles per hour In 3 hours, difference = 30 * 3 = 90 miles Fast train trailing 15 miles, so effective difference = 90 - 15 = 75 miles The answer: (C) Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock? Options: (A) 60 miles (B) 80 miles (C) 75 miles (D) 120 miles (E) 400 miles Rationale: (30*30)/100 = 9%loss The answer: (A)
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss? Options: (A) 9 % loss (B) 10% gain (C) 450 (D) 12% loss (E) 12% gain
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Reasoning: {Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 52 - {both} + 40 {both} = 17%. Ans: (D) Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 52% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? Options: (A) 60% (B) 50% (C) 25% (D) 17% (E) 10% Rationale: If the number is divisible by 3, the sum of the digits must also be divisible by 3. Only 4 yields such a number. The answer: (E) Question: The number N is 5,2H7, where H represents the ten's digit. If N is divisible by 3, what is the value of H? Options: (A) 3 (B) 8 (C) 5 (D) 6 (E) 4 Reasoning: 3-letter codes = 26^3; 4-letter codes = 26^4; 5-letter codes = 26^5; Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5. Ans: (D) Question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes? Options: (A) 26(26^3 + 26^4) (B) 26(26^3 + 26^5) (C) 27(26^3 + 26^5) (D) 27(26^3) + 26^5 (E) 26^3 + 27(26^5) Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% The answer: (C) Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? Options: (A) 45% (B) 47% (C) 57% (D) 48% (E) 50% Reasoning: Simple interest = (18000 * 2 * 15)/100 = Rs. 5400 Amount = P + I = 18000 + 5400 = Rs. 23400 Ans: (E) Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years? Options: (A) 29893 (B) 27773 (C) 29989 (D) 28800 (E) 23400 Reasoning: The lattice points that are in the circle that lie on the perspective axes is as follows: since the diameter is 8, 9 points lie on the horizontal axis (8 + center), but the end points are not in the circle, so 9 - 2 (the same for the vertical axis, but don't count center again), 7 - 1. The lattice points in the circle and not on the horizontal and vertical axes is as follows: lattice points can be found at 45, 45/2 and 30 degrees of axes (30 and 45/2 degrees from horizontal and vertical axes), so same numbers as before, but don't count center again. So, 13 + 5 * 12 = 73 There are a total of 73 lattice points in the circle. Ans: (C)
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. Circle C has a center at (-2, -2) and a diameter of 8. Some points, such as the center (-2, -2), are inside the circle, but a point such as (-2, 2) is on the circle but not in the circle. How many lattice points are in circle C? Options: (A) 40 (B) 10 (C) 73 (D) 60 (E) 63
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Answer: (A) Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? Options: (A) 150 (B) 872 (C) 287 (D) 288 (E) 212 [CoT]: [Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 9 = 150 meter] Answer: (D) Question: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism? Options: (A) 1 (B) 3/2 (C) 2 (D) 3 (E) 6 [CoT]: [Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3] Answer: (C) Question: Count the two-digit whole numbers which yield a remainder of 5 when divided by 10 and also yield a remainder of 0 when divided by 3? Options: (A) Two (B) Five (C) Three (D) One (E) Six [CoT]: [Answer = C) Three Two digit Numbers giving remainder 5 when divided by 10 = 15, 25, 35, 45, 55, 65, 75, 85, 95 The numbers giving remainder 0 when divided by 3 = 15, 45, 75 = 3] Answer: (B) Question:
What is the maximum number of pieces of birthday cake of size 2” by 2” that can be cut from a cake 20” by 20”? Options: (A) 5 (B) 100 (C) 16 (D) 20 (E) 25 [CoT]: [The prompt is essentially asking for the maximum number of 2 x 2 squares that can be cut from a larger 20 by 20 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 10 'pieces' each, we have (10)(10) = 100 total smaller squares (at maximum).]
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Reasoning: D = 72 * 5/18 = 40 = 800 – 250 = 450m Ans: (A) Question: A train 250 m long running at 72 kmph crosses a platform in 40 sec. What is the length of the platform? Options: (A) 450m (B) 200m (C) 250m (D) 270m (E) 300 m Rationale: 35 * 18/5 = 126 kmph The answer: (C) Question: Express 35 mps in kmph? Options: (A) 122 (B) 188 (C) 126 (D) 140 (E) 124 Reasoning: Speed = 30 * 5/18 = 25/3 m/sec Length of the train = speed * time = 25/3 * 9 = 75 m Ans: (A) Question: A train running at the speed of 30 km/hr crosses a pole in 9 sec. What is the length of the train? Options: (A) 75 m (B) 180 m (C) 324 m (D) Cannot be determined (E) None of these Rationale: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec The answer: (A) Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 87 (C) 26 (D) 21 (E) 14 Reasoning: 2/3 * 6/7 * 1/3 * 1/8 = 1/42 Ans: (B) Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by? Options: (A) 1/48 (B) 1/42 (C) 1/40 (D) 1/41 (E) 1/43 Reasoning: 120/60 = 2/1 2 × 100 = 200 % Ans: (C)
Question: What percent is 120 of 60? Options: (A) 133 1/3 % (B) 134 1/3 % (C) 200 % (D) 140 1/3 % (E) 143 1/3 %
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Answer: (D) Question: If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate? Options: (A) 5 (B) 10 (C) 15 (D) 20 (E) 0 [CoT]: [Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20] Answer: (C) Question: The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface? Options: (A) 27 (B) 16 (C) 12 (D) 18 (E) 11 [CoT]: [2 * π * 2r * 3r = 12 πr2] Answer: (C) Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is? Options: (A) 1/6 (B) 1/7 (C) 1/5 (D) 1/9 (E) 1/2 [CoT]: [10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5] Answer: (B) Question:
There are 25 balls in a jar. You take out 5 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning? Options: (A) 12. (B) 9. (C) 8. (D) 7. (E) 6. [CoT]: [9 = 5 blue balls + 20/ 5]
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Reasoning: Since average price of a pencil = 2 ∴ Price of 75 pencils = 150 ∴ Price of 30 pens = (570 – 150) = 360 ∴ Average price of a pen = 420⁄60 = 14 Ans: (E) Question: 30 pens and 75 pencils were purchased for 570. If the average price of a pencil was 2.00, find the average price of a pen. Options: (A) 10 (B) 11 (C) 12 (D) 13 (E) 14 Reasoning: Largest 4 digit number is 99999 After doing 99999 ÷ 77 we get remainder 53 Hence largest 5 digit number exactly divisible by 77 = 99999 - 53 = 99946 Ans: (B) Question: Calculate the largest 5 digit number which is exactly divisible by 77? Options: (A) 99111 (B) 99946 (C) 99869 (D) 99792 (E) 99654 Reasoning: 10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 Ans: (D) Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? Options: (A) 288 (B) 299 (C) 266 (D) 450 (E) 291 Reasoning: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) - 8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44) 20 + 3*14 -8 * 4 = 25 Ans: (C)
Question: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 7 students left the lab, how many students were in the computer lab at 15:44 ? Options: (A) 7 (B) 14 (C) 25 (D) 27 (E) 30
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Rationale: Using Speed Formula: Speed = Distance / Time Distance to be covered = 51-11 = 40 Speed of approach = 57 + 63 floors/min Time = 40/120 = 1/3 So Steve will cover 57x 1/3 floors in that time = 19 So he will be in 19 + 11 floor = 30th Floor The answer: (C) Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross? Options: (A) 19 (B) 28 (C) 30 (D) 32 (E) 44 Reasoning: Vowel: E O Consonants: V R M N T First letter can be filled in 5 Ways ( As the question states that first letter has to be a consonant) Fifth letter can be filled in 4 Ways ( As the question states that the last letter has to be a consonant) Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter Second letter can be filled in 5 Ways Third letter can be filled in 4 Ways Fourth letter can be filled in 3 Ways So, Total number of ways = 5 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 1500 Ans: (C) Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a consonant and the last letter has to be a consonant, and each letter can be used only once? Options: (A) 21 (B) 42 (C) 1500 (D) 600 (E) 720 Rationale: 1: 2/5 = 5: 2 2/7 * 70 = 20 The answer: (B) Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? Options: (A) 21 (B) 20 (C) 17 (D) 12 (E) 18 Reasoning: 2nd day he earns = 2(2 – 2) 3rd day he earns = 2(3 – 2) On 20th day he earns 2(20 -2) = 36 rupees Ans: (C) Question: An businessman earns an income of Re 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 20th day of business, he earns an income of: Options: (A) 21 (B) 22 (C) 36 (D) 20 (E) 30 Rationale: Speed downstream = d/t = 65/(2 1/2) = 26 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (26 - 18)/2 = 4 kmph The answer: (B) Question: A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 5 kmph (B) 4 kmph (C) 9 kmph (D) 8 kmph (E) 1 kmph Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1 (11K -1)/4 = 85 11K = 85 * 4 +1 = 340 +1 = 341 K = 253 / 11 = 31. The answer: (C)
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 85, what is the value of K? Options: (A) 11 (B) 15 3/4 (C) 31 (D) 23 (E) 25 3/10
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Reasoning: Original perimeter = x Hence original side = x/4 New side = 6x/4 New perimeter = 4*6x/4 = 6x Ans: (C) Question: The measure of the side of a square is multiplied by 6. If x represents the perimeter of the original square, what is the value of the new perimeter? Options: (A) 3x (B) 4x (C) 6x (D) 12x (E) 27x Rationale: (80/100) * 45 – (4/5) * 25 36 - 20 = 16 The answer: (C) Question: How much is 80% of 45 is greater than 4/5 of 25? Options: (A) 15 (B) 57 (C) 16 (D) 16 (E) 73 Reasoning: Sum of the numbers 2345672 is 29 which is not multiple of 9 Add 7 which makes the sum 36 which is multiple of 9 So digit becomes 2345679 (as we know that if sum multiple of 9 then it is divisible of 9) Ans: (C) Question: How should be added in order to make 2345672 this number is divisible by 9? Options: (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Rationale: 23 + 29 + 31 + 37 = 120/4 = 30 The answer: (C) Question: The average of first four prime numbers greater than 20 is? Options: (A) 10 (B) 20 (C) 30 (D) 40 (E) 50 Reasoning: S = (150 + 320)/40 = 470/40 * 18/5 = 42 Ans: (B) Question: A train 150 meters long completely crosses a 320 meters long bridge in 40 seconds. What is the speed of the train is? Options: (A) 32 (B) 42 (C) 54 (D) 66 (E) 09 Reasoning: Work done by X in 1 day = 1/18 Work done by Y in 1 day = 1/15 Work done by Y in 10 days = 10/15 = 2/3 Remaining work = 1 – 2/3 = 1/3 Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6 Ans: (C)
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work? Options: (A) 2 (B) 3 (C) 6 (D) 7 (E) 8
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Reasoning: Speed in still water = 1 (11 + 5)/2 kmph = 8 kmph. Ans: (C) Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is: Options: (A) 6 (B) 7 (C) 8 (D) 9 (E) 5 Rationale: Plug in an odd integer; in this case 3 (2*3)-3 = 3 Odd 3+1 = 4 Even (2*3)+3 = 9 Odd 3^3 = 27 Odd (3*3)+(2*3) = 9 + 6 = 15 Odd The answer: (B) Question: If x is an odd integer, which of the following is an even integer? Options: (A) 2x-x (B) x+1 (C) 2x+3 (D) x^3 (E) 3x+2x Reasoning: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros. Ans: (C) Question: How many terminating zeroes W does 200! have? Options: (A) 40 (B) 48 (C) 49 (D) 55 (E) 64 Rationale: 639 is not divisible by 7; 2079 is divisible by each one of 3, 7, 9, 11. The answer: (B) Question: Which of the following numbers is divisible by each one of 3, 7, 9 and 11? Options: (A) 639 (B) 2079 (C) 3791 (D) 37911 (E) None of these Reasoning: 221 + 43 = 264/17 = 9 (Remainder) Ans: (C) Question: A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.67? Options: (A) 4 (B) 6 (C) 9 (D) 11 (E) 14 Reasoning: A + B = 1/20 + 1/15 = 7/60 A + C = 1/20 + 1/12 = 8/60 7/60 + 8/60 = 15/60 = 1/4 4 days * 2 = 8 days Ans: (B)
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately? Options: (A) 9 days (B) 8 days (C) 5 days (D) 54 days (E) 2 days
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[Ans] (E) [Question] If a man can cover 18 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 288 (B) 162 (C) 878 (D) 168 (E) 243 [CoT] 18 m/s = 12 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 18 * 18/5 * 15/4 km = 243 km. [Ans] (A) [Question] A 400 meter long train crosses a man standing on the platform in 10 sec. What is the speed of the train? Options: (A) 144 (B) 108 (C) 278 (D) 126 (E) 112 [CoT] S = 400/10 * 18/5 = 144 kmph [Ans] (A) [Question]
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes? Options: (A) 15 (B) 66 (C) 77 (D) 52 (E) 42 [CoT] 90 * 10/60 = 15 kmph
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Rationale: This is a simple alternating subtraction and addition series; The first series begins with 3 and adds 5; the second begins with 9 and subtracts 2, and so on. The answer: (E) Question: Fill in the blank with the correct number in this number series: 3, 9, 8, 7, __, 5, 18, ? Options: (A) 6 (B) 7 (C) 9 (D) 10 (E) 13 Reasoning: We have 3 scenarios here: 1) 1 tech2 businessmen: 4C1 x 5C2 = 40 2) 2 tech1 businessman: 4C2 x 5C1 = 30 3) 3 tech0 businessmen: 4C3 = 4 Total: 144+54+4 = 74 Ans: (A) Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 5 businessmen, how many possible team submissions are possible? Options: (A) 74 (B) 100 (C) 162 (D) 198 (E) 202 Rationale: D = 100 + 180 = 280 S = 36 * 5/18 = 10 mps T = 280/10 = 28 sec The answer: (B) Question: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph? Options: (A) 54 sec (B) 28 sec (C) 25 sec (D) 45 sec (E) 24 sec Reasoning: Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% Ans: (C) Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election? Options: (A) 34% (B) 54% (C) 57% (D) 78% (E) 87% Rationale: T = 64/46 * 18/5 = 5 sec The answer: (B) Question: In what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way? Options: (A) 3 (B) 5 (C) 4 (D) 6 (E) 7 Rationale: Answer: Option A Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (distance) = speed * Time (50/3) * 9 = 150 meter The answer: (A)
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. Options: (A) 150 m (B) 155 m (C) 180 m (D) 190 m (E) 205 m
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Ques: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 150 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 5 o'clock? Options: (A) 60 miles (B) 80 miles (C) 90 miles (D) 140 miles (E) 400 miles Ans: (D) CoT: Answer = D. 140 miles Relational speed = 150 - 100 = 50 miles per hour In 3 hours, difference = 50 * 3 = 150 miles Fast train trailing 10 miles, so effective difference = 150 - 10 = 140 miles Ques: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers? Options: (A) 277 (B) 665 (C) 662 (D) 552 (E) 281 Ans: (B) CoT: 8 * 84 = 672 – 7 = 665 Ques: How much is 80% of 40 is greater than 4/5 of 25? Options: (A) 22 (B) 77 (C) 15 (D) 12 (E) 88 Ans: (D) CoT: (80/100) * 40 – (4/5) * 25 32 - 20 = 12 Ques: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is? Options: (A) 124432 (B) 145366 (C) 157768 (D) 178432 (E) 220030 Ans: (E)
CoT: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
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Reasoning: As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only A does not yield an integer. Ans: (A) Question: If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer? Options: (A) (x + y) /z (B) (y + z) /x (C) yz/x (D) (2y + 3z) /x (E) (xy + z) /y Rationale: Speed downstream = d/t = 75/(2 1/2) = 30 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (30 - 18)/2 = 6 kmph The answer: (B) Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? Options: (A) 1 kmph (B) 6 kmph (C) 5 kmph (D) 8 kmph (E) 7 kmph Reasoning: Answer = A Please refer diagram below 85 - 10 = 75 Ans: (A) Question: 85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used? Options: (A) 75 (B) 80 (C) 85 (D) 90 (E) 95 Rationale: (80/100) * 170 – (35/100) * 300 136 - 105 = 31 The answer: (E) Question: What is the difference between 80% of 170 and 35% of 300. Options: (A) 30 (B) 29 (C) 37 (D) 36 (E) 31 Reasoning: His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24 He can buy a new house in 24 years Ans: (E) Question: A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house? Options: (A) 12 (B) 20 (C) 30 (D) 15 (E) 24 Reasoning: Bass = 2/7 = 10/35 Tuna = 1/5 = 7/35 Trout = 1/7 = 5/35 Catfish = 1 - (10/35 +7/35 + 5/35) = 13/35 Purchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and Catfish = 13/35 - (13/35)(1/7) = 12/35 Stocked: doubling the number of bass (2)(10/35) = 20/35 Now: 20 + 6 + 5 + 12 = 43 Trout proportion is now 5/43. Ans: (C)
Question: At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout? Options: (A) 30/71 (B) 4/7 (C) 5/43 (D) 1/2 (E) 1/5
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Reasoning: Total expenditure = 40 + 25 + 15 + 5 = 85% Saving = (100 - 85) = 15% 15/100 × Salary = 1200, Salary = 8000 Rs. Ans: (C) Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is: Options: (A) 4000 (B) 6000 (C) 8000 (D) 10000 (E) None of these Rationale: 221 + 43 = 264/17 = 9 (Remainder) The answer: (C) Question: A no. x when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? Options: (A) 1 (B) 4 (C) 9 (D) 11 (E) 13 Reasoning: 15*14*13/3*2*1 = 455 Ans: (C) Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 15 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions? Options: (A) 2,060 (B) 1,320 (C) 455 (D) 315 (E) 220 Rationale: (x + 1)(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d 6(x + 1)(x - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d 6(x2x2 - 1)(x + 1) = ax3+bx2+cx+dax3+bx2+cx+d ⇒6(x3+x2−x−1)⇒6(x3+x2−x−1) = ax3+bx2+cx+dax3+bx2+cx+d ⇒6x3+6x2−6x−6⇒6x3+6x2−6x−6 = ax3+bx2+cx+dax3+bx2+cx+d Equating the coefficients of like learns on both the sides, a = 6, b = 6, c = -6 and d = -6. The answer: (C) Question: (x +1 )(2x - 2)(3x + 3) = ax3+bx2+cx+dax3+bx2+cx+d What are the values of a, b, c and d? Options: (A) 2 (B) 7 (C) 6 (D) 1 (E) 9 Reasoning: T = 64/46 * 18/5 = 5 sec Ans: (B) Question: In what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way? Options: (A) 3 (B) 5 (C) 4 (D) 6 (E) 7 Reasoning: 17^200 % 18 (17-18)^200 % 18 (-1)^200 % 18 1 % 18 = 1 Ans: (A)
Question: What will be the remainder when 17^200 is divided by 18 Options: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
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Rationale: Answer: Option D This is an alternating division and addition series: First, divide by 2, and then add 8. The answer: (D) Question: Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank? Options: (A) 85 (B) 97 (C) 109 (D) 178 (E) 112 Reasoning: 1/2:1/3:1/4 = 6:4:3 Ram = 6/13 * 3250 = 1500 Shyam = 4/13 * 3250 = 1000 Mohan = 3/13 * 3250 = 750 Ans: (A) Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are? Options: (A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750 (B) Ram = Rs.7500, Shyam = Rs.1000, Mohan = Rs.750 (C) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.250 (D) Ram = Rs.1500, Shyam = Rs.1080, Mohan = Rs.750 (E) Ram = Rs.1500, Shyam = Rs.1002, Mohan = Rs.750 Rationale: 10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 – 1050 = 600 The answer: (E) Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.165. Find the unknown rate of two towels? Options: (A) A) 400 (B) B) 450 (C) C) 500 (D) D) 550 (E) E) 600 Reasoning: Other parts are equal to 2x2 + y2 – 3xy. Ans: (B) Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer. Options: (A) 2x2 – 3xy + y2 (B) (2x + y) (x – y) (C) (x – y) 2 + x(x – y) (D) (2x – y) 2 – x(2x – y) (E) (2x – y) 2 – 2x2 + xy Rationale: Sum of 14 even numbers = 14 * 15 = 210 Average = 210/14 = 15 The answer: (E) Question: The average of first 14 even numbers is? Options: (A) 19 (B) 18 (C) 16 (D) 11 (E) 15 Rationale: Answer = D = 8 If least = -4, then largest = 9 Range = 9 - 1 = 8 The answer: (D)
Question: List K consists of 14 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K? Options: (A) 5 (B) 6 (C) 7 (D) 8 (E) 12
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Rationale: Increase = (12/60)*100 = (1/5)*100 = 20%. The answer: (A) Question: John makes $60 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase? Options: (A) 20% (B) 16.66% (C) 16.56% (D) 17.66% (E) 18.1% Reasoning: One day work of A and B = 1/12 One day work of B and C = 1/30 One day work of C and A = 1/36 2(A + B + C) = 1/12 + 1/30 + 1/36 2(A + B + C) = 13/90 (A + B + C) = 13/180 Number of days required = 180/13 days. Ans: (C) Question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together? Options: (A) 180/15 (B) 180/10 (C) 180/13 (D) 180/15 (E) 180/11 Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes The answer: (D) Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? Options: (A) 20 (B) 22 (C) 24 (D) 27 (E) 30 Reasoning: 44 + 28 + 10 = 82% 100 – 82 = 18% 850 * 18/100 = 153 Ans: (C) Question: In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Options: (A) 277 (B) 267 (C) 153 (D) 188 (E) 151 Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot) The probability that she misses all shots = (prob that she misses from 30 yards)*(prob that she misses from 40 yards)*(prob that she misses from 50 yards) Prob that she misses from 30 yards = 1 - 5/6 = 1/6; Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4 Thus the probability that she misses all shots = (1/6)*(1/5)*(1/4) = 1/120 Thus the probability that she makes at least one shot = 1 - (1/120) = 119/120 The answer: (B) Question: An archer is shooting arrows from various distances. She shoots at a target from 30 yards, 40 yards, and 50 yards. The probability that she hits within the bullseye from 30 yards is 5/6, the probability that she hits within the bullseye from 40 yards is 4/5, and the probability that she hits within the bullseye from 50 yards is 3/4. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed. Options: (A) 104/105 (B) 119/120 (C) 139/140 (D) 9/10 (E) 14/15 Rationale: Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence The answer: (C)
Question: There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round? Options: (A) 15 (B) 30 (C) 120 (D) 240 (E) 256
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Rationale: 7C3 * 4C2 * 3C2 = 35*6*3 = 630. The answer: (E) Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 7 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible? -- Options: (A) 12 (B) 19 (C) 60 (D) 180 (E) 630 Reasoning: Diver = (4*3)+2 = 14 2* Quotient = 14 Quotient = 7 Dividend = (Divisor * Quotient) + Remainder Dividend = (14 * 7) + 2 = 100 Ans: (C) Question: In a division sum, the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is: Options: (A) 72 (B) 90 (C) 100 (D) 110 (E) 120 Rationale: S = 600/40 = 15 mps S = 3600/15 = 240 sec = 4 min The answer: (A) Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? Options: (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Reasoning: Mother has a fixed place and father, so there are 3*2 ways to arrange the children, hence Ans: (C) Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 2 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other one children on either side of him, how many seating arrangements are possible? Options: (A) 3 (B) 4 (C) 6 (D) 8 (E) 10 Rationale: Work done by X in 1 day = 1/30 Work done by Y in 1 day = 1/15 Work done by Y in 10 days = 10/15 = 2/3 Remaining work = 1 – 2/3 = 1/3 Number of days in which X can finish the remaining work = (1/3) / (1/30) = 10 The answer: (B) Question: X can finish a work in 30 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work? Options: (A) 3 (B) 10 (C) 6 (D) 8 (E) 9 Rationale: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450 ≈ 576 + 740 + 450 ≈ 1760 ≈ 1800 The answer: (D)
Question: What approximate value should come in place of the question mark (?) in the following equation’? 3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30 Options: (A) 1200 (B) 1500 (C) 1600 (D) 1800 (E) 2100
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Reasoning: Since the total number of skeins is X, then X = Blue + Yellow + Red Because there are twice as many Blue as Yellow, then Blue = 2*Yellow Thus X = 2*Yellow + Yellow + Red, which simplifies to X = 3*Yellow + Red Because there are twice as many Yellow as Red, then Yellow = 2*Red Thus X = 3*(2*Red) + Red, which simplifies to X = 7*Red Therefore Red = X/7 Ans: (B) Question: Suzy has a lot of skeins of yarn, she has blue, yellow, and red yarn. She has twice as much blue yarn as yellow yarn, and she has twice as much yellow yarn as she has red yarn. If she has X skeins of yarn, how many of the skeins are red, in terms of X? Options: (A) X/8 (B) X/7 (C) X/6 (D) X/5 (E) X/4 Reasoning: Each group has 8 = 8+8+8 = 24 max 4 people are in 2 groups, subtract 4 people twice as they are counted twice Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group Ans: 8+8+8-(2(4)) - 3 = 13 Ans: (B) Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors? A. B. C. D. E. Options: (A) 8 (B) 13 (C) 16 (D) 24 (E) 27 Reasoning: Simple interest = (18000 * 2 * 15)/100 = Rs. 5400 Amount = P + I = 18000 + 5400 = Rs. 23400 Ans: (E) Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years? Options: (A) 29893 (B) 27773 (C) 29989 (D) 28800 (E) 23400 Reasoning: I = (500*9*6)/100 = 270 Ans: (B)
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month? Options: (A) 288 (B) 270 (C) 999 (D) 278 (E) 121
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Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 49 possibilities (7*7) since each team has 7 players. So there are a total of 147 possibilities (49*3). I hope this method is easier for you to understand. The answer: (C) Question: There are 3 teams each with 7 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice? Options: (A) 50 (B) 23 (C) 147 (D) 28 (E) 45 Reasoning: T = 52/24 * 18/5 = 8 se Ans: (C) Question: In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way? Options: (A) 3 sec (B) 4 sec (C) 8 sec (D) 6 sec (E) 7 sec Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 The answer: (C) Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is? Options: (A) 1/6 (B) 1/7 (C) 1/5 (D) 1/9 (E) 1/2 Reasoning: (80/100) * 40 – (4/5) * 25 32 - 20 = 12 Ans: (D) Question: How much is 80% of 40 is greater than 4/5 of 25? Options: (A) 17 (B) 19 (C) 11 (D) 12 (E) 10 Rationale: Percentage of profit = 20/30 * 100 = 67% The answer: (E) Question: If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is? Options: (A) 16 (B) 127 (C) 12 (D) 18 (E) 67 Rationale: A's one day's work = 1/20 B's one day's work = 1/40 (A + B)'s one day's work = 1/20 + 1/40 = 3/40 The part of the work completed in 5 days = 5 (3/40) = 3/8. The answer: (D)
Question: Two persons A and B can complete a piece of work in 20 days and 40 days respectively. If they work together, what part of the work will be completed in 5 days? Options: (A) 1/8 (B) 1/3 (C) 3/6 (D) 3/8 (E) 5/3
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Reasoning: 9 = (1*40*R)/100 R = 22 1/2 % Ans: (D) Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? Options: (A) 22 1/7 % (B) 22 3/2 % (C) 22 1/8 % (D) 22 1/2 % (E) 22 1/2 % Rationale: (1056 / 27) gives remainder 3 24 + 3 = 27, So we need to add 24 The answer: (D) Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 27? Options: (A) 21 (B) 22 (C) 23 (D) 24 (E) 25 Reasoning: Sum of the ages of the group having 4 persons and average 40 = 4x40 = 160 Sum of the ages of the group having 5 persons and average 38 = 5x38 = 190 Age of the new person added to the group = 190-160 = 30 Ans: (C) Question: If we need to change the average age of a group containing 4 persons from 40 to 38 by adding a person. What should be the age of the person newly added to the group? Options: (A) 20 (B) 25 (C) 30 (D) 38 (E) 40 Rationale: {Total} = {finance} + {marketing} - {both} + {neither} 100 = 25 + 51 - {both} + 40 {both} = 16%. The answer: (D) Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 51% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class? Options: (A) 60% (B) 50% (C) 25% (D) 16% (E) 10% Reasoning: 12 12 × 2 + 2 = 26 26 × 2 + 2 = 54 54 × 2 + 2 = 110 110 × 2 + 2 = 222 222 × 2 + 2 = 446 Ans: (B) Question: What will come in place of the x in the following number series? 12, 26, 54, 110, 222, x Options: (A) 444 (B) 446 (C) 448 (D) 452 (E) 454 Reasoning: Odd x Odd = Odd Odd x Even = Even Even x Even = Even To fulfill condition Either (A+1) or (B+1) needs to be Even So either A or B needs to be odd Or At Least one of them is odd. Ans: (C)
Question: A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B? Options: (A) They are both even numbers. (B) At least one of them is even (C) At least one of them is odd. (D) They are both odd. (E) Nothing can be said surly on A and B
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Reasoning: Purchase = 8748/(1-10/100^3) = 12000 Ans: (A) Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was : Options: (A) 12000 (B) 10000 (C) 15000 (D) 20000 (E) 25000 Rationale: 100 * 100 = 10000 145 * 80 = 11600 The answer: (E) Question: The length of a rectangle is increased by 45% and its breadth is decreased by 20%. What is the effect on its area? Options: (A) 1288 (B) 1299 (C) 1000 (D) 10000 (E) 11600 Reasoning: Each side is 3p A = (3p)^2 = 9p^2 Ans: (C) Question: What is the area of a square with perimeter 12P ? Options: (A) 16p^2 (B) 4P (C) 9P^2 (D) P/16 (E) P^2/16 Rationale: Suppose the amount in the beginning was Rs ’x’ Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3 Money spent on food = 1/5 of 2x/3 = Rs 2x/15 Balance = 2x/3 - 2x/15 = Rs 8x/15 Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5 Therefore 2x/5 = 100 = 250 The answer: (B) Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 100. How much did he have with him in the beginning? Options: (A) Rs 200 (B) Rs 250 (C) Rs 300 (D) Rs 450 (E) Rs 550 Reasoning: (1056 / 23) gives remainder 21 21 + 2 = 23, So we need to add 2 Ans: (B) Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23? Options: (A) 1 (B) 2 (C) 5 (D) 6 (E) 8 Reasoning: Tried to locate a '0' ending multiple of 8 between 500599 Only 560 is present 560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5 Ans: (A)
Question: If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ? Options: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1
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In Badminton game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1: P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. In Badminton game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once? Options: (A) 1/3 (B) 4/9 (C) 5/9 (D) 2/3 (E) 3/4 (C) 1/3: 1/5: 1/1 = 5:3:15 The inverse ratio of 3: 5: 1 is? Options: (A) 2:3:7 (B) 5:3:15 (C) 2:3:2 (D) 2:3:6 (E) 2:3:1 (B) First even minus first odd = 2-1 = 1; The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2; The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3; We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.
If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y? Please try to explain your answers Options: (A) 0 (B) 25 (C) 50 (D) 75 (E) 100 (E)
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Rationale: Dist = (100/45*9) = 20 m The answer: (E) Question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: Options: (A) 10 (B) 12 (C) 30 (D) 40 (E) 20 Reasoning: The sum all three digits comes to 10 except 323 Ans: (A) Question: Find the odd man out 253, 136, 352, 323, 631, 244 Options: (A) 323 (B) 136 (C) 352 (D) 631 (E) 531 Rationale: Other number = (12 x 600)/480 = 15. The answer: (D) Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is: Options: (A) 11 (B) 10 (C) 8 (D) 15 (E) 12 Reasoning: (555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025 Ans: (E) Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 25 as remainder. Find the no. is? Options: (A) 145646 (B) 236578 (C) 645353 (D) 456546 (E) 220025 Rationale: The century divisible by 400 is The answer: (A) Question: Which of the following is not a leap year ? Options: (A) 700 (B) 800 (C) 900 (D) 1000 (E) 1200 Rationale: 1/15 + 1/6 = 7/30 30/7 = 4 2/7 days The answer: (E)
Question: Ravi can do a piece of work in 15 days while Prakash can do it in 6 days. In how many days will they finish it together? Options: (A) 5 7/9 days (B) 6 7/9 days (C) 5 1/9 days (D) 5 7/2 days (E) 4 2/7 days
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Reasoning: 11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes Ans: (E) Question: A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship? Options: (A) 13 (B) 25 (C) 17 (D) 12 (E) 11 Rationale: Speed = 90*(5/18) m/sec = 25 m/sec Length of Train (Distance) = Speed * Time 25 *10 = 250 meter The answer: (C) Question: A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train. Options: (A) 150 (B) 180 (C) 250 (D) 200 (E) 225 Reasoning: 91 is divisible by 7. So, it is not a prime number. Ans: (E) Question: Which one of the following is not a prime number? Options: (A) 51 (B) 61 (C) 71 (D) 82 (E) 91 Rationale: Number of females = 156800 × 100⁄80 = 196000 \ Number of males = 7⁄8 × 196000 = 171500 \ Total population = 196000 + 171500 = 367500 The answer: (B) Question: The ratio of males and females in a city is 7 : 8 and the percentage of children among males and females is 25% and 20% respectively. If the number of adult females in the city is 156800 what is the total population? Options: (A) 245000 (B) 367500 (C) 196000 (D) 171500 (E) None of these Reasoning: Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec Ans: (A) Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Options: (A) 40 (B) 37 (C) 32 (D) 39 (E) 28 Reasoning: Total number of letters = 8 Using these letters the number of 8 letters words formed is ⁸P₈ = 8!. Ans: (B)
Question: Using all the letters of the word "THURSDAY", how many different words can be formed? Options: (A) 7 (B) 8! (C) 9 (D) 3 (E) 1
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Question: Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Options: (A) 50 (B) 40 (C) 25 (D) 36 (E) 45 Ans: (D) CoT: Area of tile = 25*65 = 1625 Area of floor = 150*390 = 58500 No of tiles = 58500/1625 = 36 So, the no of tile = 36 ---- Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? Options: (A) 20 (B) 99 (C) 88 (D) 77 (E) 61 Ans: (A) CoT: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph. ---- Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and repetition is allowed? Options: (A) 3441 (B) 3433 (C) 3333 (D) 3430 (E) 3773 Ans: (D)
CoT: Vowel: E O Consonants: V R M N T First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel) Fifth letter can be filled in 5 Ways ( As the question states that the last letter has to be a consonant) Second letter can be filled in 7 Ways Third letter can be filled in 7 Ways Fourth letter can be filled in 7 Ways So, Total number of ways = 2 Ways x 7 Ways x 7 ways x 7 ways x 5 ways = 3430 ----
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Reasoning: 300/10 = 30. The difference is 30 - 25 = 5. Ans: (C) Question: A certain car uses 12 gallons of gasoline in traveling 300 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased? Options: (A) 2 (B) 4 (C) 5 (D) 8 (E) 10 Reasoning: Final number = Initial number + 50%(original number) = 60 + 50%(60) = 60 + 30 = 90. Ans: (C) Question: 60 is increased by 50%. Find the final number. Options: (A) 100 (B) 110 (C) 90 (D) 30 (E) 160 Reasoning: The ratio is 2:3 = gym:ride, so (16)(3/2) = 24 minutes at the gym, and 24 + 16 = 40 minutes exercise, so (2/3)(40) = 27 minutes yoga. Ans: (C) Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 16 minutes, how much time will she spend doing yoga? (rounded to minutes) Options: (A) 10 min. (B) 41 min. (C) 27 min. (D) 23 min. (E) 25 min. Reasoning: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 Ans: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Options: (A) 3446 (B) 2345 (C) 5467 (D) 4767 (E) 5184
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Rationale: Number of newborns that can die in first month = 1/10 * 700 = 70 Survived = 630 Number of newborns that can die in second month = 1/10 * 630 = 63 Survived = 567 Number of newborns that can die in third month = 1/10 * 567 = 56 Survived = 511 The answer: (A) Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 700 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Options: (A) 511 (B) 546 (C) 552 (D) 562 (E) 570 Reasoning: 750 = 3*222 + (22*3) + 9*2 K weight of 600 = 3 +3+9 = 15 Ans: (E) Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 750? Options: (A) 10 (B) 11 (C) 12 (D) 13 (E) 15 Rationale: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36. The answer: (A) Question: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected? Options: (A) 36 (B) 45 (C) 50 (D) 55 (E) 60 Reasoning: 8 m/s = 8 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 8 * 18/5 * 15/4 km = 108 km. Ans: (A) Question: If a man can cover 8 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Options: (A) 108 (B) 180 (C) 107 (D) 168 (E) 122 Rationale: 8C4 [Select any four] - 7C4 [Select all hard backs] = 35. The answer: (A) Question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected? Options: (A) 35 (B) 45 (C) 50 (D) 55 (E) 60 Rationale: Total subjects = 4 +3 +3 = 10 Max subjects by 1 teacher = 2 So, min of teachers required = 10/2 = 5 The answer: (B)
Question: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required Options: (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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Reasoning: Answer = A. 45 miles Relational speed = 130 - 100 = 30 miles per hour In 2 hours, difference = 30 * 2 = 60 miles Fast train trailing 15 miles, so effective difference = 60 - 15 = 45 miles Ans: (A) Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 3 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock? Options: (A) 45 miles (B) 80 miles (C) 90 miles (D) 120 miles (E) 400 miles Rationale: 221 + 43 = 264/17 = 9 (Remainder) The answer: (C) Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? Options: (A) 2 (B) 7 (C) 9 (D) 11 (E) 15 Reasoning: Integer is divisible by 9 - Sum of digits is divisible by 9 Ans: (C) Question: The number N is 5,1H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H? Options: (A) 1 (B) 3 (C) 8 (D) 7 (E) 9 Rationale: 2^3^2 = 29 2^2^3 = 28 3^2^3 = 38 3^3^3 = 327 As 327 > 38, 29 > 28 and 327 > 29. Hence 327 is the greatest among the four. The answer: (D) Question: Which among the following is the greatest? Options: (A) 2^3^2 (B) 2^2^3 (C) 3^2^3 (D) 3^3^3 (E) 5^3^3 Reasoning: The total of seven numbers = 7X9 = 63 The total of first 3 and last 3 numbers is = 3 X 7+3 X 11 = 54 So, the middle number is (63 - 54 ) = 9 Ans: (C) Question: The average of seven numbers is 9. The average of first three numbers is 7 and the average of last three numbers is 11. What is the middle number? Options: (A) 7 (B) 8 (C) 9 (D) 11 (E) 10 Reasoning: Answer will be D. Straightforward question. Ans: (D)
Question: Sarah's seafood restaurant gets a delivery of fresh seafood every day, 6 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ? Options: (A) 6cdx/100 (B) d + 6cx/100 (C) 6d + xc/100 (D) 6d + 6xc/100 (E) 6cdx
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Rationale: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on. The answer: (A) Question: Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next? Options: (A) 15 (B) 14 (C) 17 (D) 12 (E) 19 Reasoning: 1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = 1/6 15 women's 1 day work = (1/6 - 10/100) = 1/15 1 woman's 1 day work = 1/225 1 woman alone can complete the work in 225 days. Ans: (E) Question: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? Options: (A) 2267 (B) 287 (C) 268 (D) 228 (E) 225 Rationale: B's 1 day work = (1/12 - 1/20) = 1/30 Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15 So, A and B together will complete the work in 15 days. The answer: (C) Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work? Options: (A) 11 days (B) 77 days (C) 15 days (D) 18 days (E) 19 days Reasoning: 120/60 = 2/1 2 × 100 = 200 % Ans: (C) Question: What percent is 120 of 60? Options: (A) 133 1/3 % (B) 134 1/3 % (C) 200 % (D) 140 1/3 % (E) 143 1/3 % Rationale: This is a simple multiplication series. Each number is 3 times greater than the previous number. The answer: (A) Question: Look at this series: 0.7, 2.1, ____, 18.9, 56.7, ... What number should fill the blank? Options: (A) 6.3 (B) 5.3 (C) 6.2 (D) 6.1 (E) 4.3 Rationale: 10^2 - 20 = 80 20^2 - 30 = 370 30^2 - 40 = 860 40^2 - 50 = 1550 50^2 - 60 = 2440 60^2 - 70 = 3530. The answer: (E)
Question: ? 370 860 1550 2440 3530 Options: (A) 900 (B) 840 (C) 750 (D) 860 (E) 80
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Reasoning: 20 + 24 + 8 * 2 = 60/2 = 30 Ans: (C) Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women? Options: (A) 29 (B) 78 (C) 30 (D) 28 (E) 12 Rationale: Distance traveled by Eddy = 600 km Time taken by Eddy = 3 hours Average speed of Eddy = 600/3 = 200 km/hour Distance traveled by Freddy = 360 km Time taken by Freddy = 4 hours Average speed of Freddy = 360/4 = 90 km/hour Ratio of average speed of Eddy to Freddy = 200/90 = 20/9 The answer: (E) Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 360 kms. What is the ratio of their average speed of travel? (Eddy: Freddy) Options: (A) 8/3 (B) 3/8 (C) 8/5 (D) 5/8 (E) 20/9 Reasoning: Population after n years = P [1 + (R/100)]2 Population after 2 years = 140000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 157304 Ans: (E) Question: he population of a city is 140,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence? Options: (A) 1797787 (B) 1597723 (C) 159776 (D) 159728 (E) 157304 Rationale: Integer is divisible by 3 - Sum of digits is divisible by 3 The answer: (D) Question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H? Options: (A) 2 (B) 3 (C) 5 (D) 4 (E) 9 Reasoning: 21-12 < no of hrs < 21-5 9< no of hrs < 16. Ans: (D) Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 5 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week? Options: (A) 30 (B) 20 (C) 18 (D) 12 (E) 6 Reasoning: 60*5:36*6:75*3 100: 72: 75 100/247 * 7410 = 3000 Ans: (B)
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A? Options: (A) 3002 (B) 3000 (C) 3018 (D) 3019 (E) 3012
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(Ans). (C) (Question). The total number of apples and oranges in the refrigerator is 7 more than the total number of oranges and peaches in the refrigerator. How much lesser is the number of peaches in the refrigerator as compared to apples? Options: (A) 2 (B) 8 (C) 7 (D) 6 (E) 4 (CoT). (Apples + Oranges) - (Oranges + Peaches) = 7 Apples - Peaches = 7 (Ans). (A) (Question). A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work? Options: (A) 6 3/4 days (B) 7 3/4 days (C) 5 3/4 days (D) 6 1/4 days (E) 6 2/4 days (CoT). One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days. (Ans). (A) (Question). How long does a bus 100 m long traveling at 50 kmph takes to cross a bridge of 150 m in length? Options: (A) 18 (B) 16 (C) 15 (D) 11 (E) 12 (CoT). D = 100 + 150 = 250 m S = 50 * 5/18 = 125/9 T = 250 * 9/125 = 18 sec (Ans). (A) (Question).
A train 560 m in length crosses a telegraph post in 16 seconds. The speed of the train is? Options: (A) 126 kmph (B) 77 kmph (C) 54 kmph (D) 71 kmph (E) 88 kmph (CoT). S = 560/16 * 18/5 = 126 kmph
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Reasoning: 2/3 * 6/7 * 1/3 * 3/8 = 36/504 = 3/42 Ans: (E) Question: The compound ratio of 2/3, 6/7, 1/3 and 3/8 is given by? Options: (A) 7/98 (B) 1/48 (C) 1/98 (D) 1/96 (E) 3/42 Rationale: Number of ways of choosing 4 stocks = 8C4 Number of ways of ranking the chosen stocks = 4! Hence total ways of chosing and ranking = 8C4 * 4! = 1680 The answer: (B) Question: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks? Options: (A) 1200 (B) 1680 (C) 2102 (D) 4020 (E) 1840 Reasoning: 222 + 43 = 265/17 = 10 (Remainder) Ans: (D) Question: A no.when divided by 222 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? Options: (A) 2 (B) 7 (C) 9 (D) 10 (E) 15 Rationale: He lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut. The answer: (A) Question: A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change. Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill. Later that day he tries to figure out how much money he lost. What did he lose? Options: (A) $5 (B) $10 (C) $12 (D) $15 (E) $20 Reasoning: 8597 – ? = 7429 – 4358 ∴ ? = 5526 Ans: (B) Question: What should come in place of question mark(?) in the following equation? 8597 – ? = 7429 – 4358 Options: (A) 5706 (B) 5526 (C) 5426 (D) 5626 (E) None of these Reasoning: Overall, there can be 81 minuses. Tus, it is Ans: (A)
Question: A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion? Options: (A) 81 (B) 83 (C) 85 (D) 86 (E) 89
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Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62 The answer: (E) Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Options: (A) 3456 (B) 4567 (C) 4789 (D) 5678 (E) 5184 Reasoning: Answer: Option B This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2. Ans: (B) Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank? Options: (A) 8 (B) 14 (C) 43 (D) 44 (E) 9 Rationale: D = 25 * 60 + 4500 = 6000 m T = 6000/60 * 18/5 = 360 sec = 6 mins The answer: (D) Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 4.5 km long? Options: (A) 4 (B) 3 (C) 5 (D) 6 (E) 9 Reasoning: Out of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3 Out of 3 forwards we have to select 2 -> selection means we use C -> so 3C2 Total ways = 6C3 x 3C2 = 60 Ans: (D) Question: 9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen? Options: (A) 23 (B) 30 (C) 42 (D) 60 (E) 126 Rationale: In each number except 427, the middle digit is the sum of other two. The answer: (B) Question: 396, 462, 572, 427, 671, 264 Options: (A) 396 (B) 427 (C) 671 (D) 264 (E) 572 Rationale: Total age of 60 students (45X 10+15 X 10) = 630 Average = 600/60 = 10 Years The answer: (C)
Question: In a class, the average age of 45 boys is 10 years and the average of 15 girls is 10 years. what is the average age of the whole class? Options: (A) 12 Years (B) 12.3 Years (C) 10 Years (D) 13 Years (E) 15 Years
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Answer: (B) Question: a student got 70% in one subject,80% in other.to get overall 75% how much he should get in third subject. Options: (A) 65% (B) 75% (C) 85% (D) 95% (E) 88% [CoT]: [Already average of two subjects is (70+80)/2 = 75% To maintain the percentage at 75%, he shouls get 75% marks in third subject] Answer: (B) Question: John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase? Options: (A) 16% (B) 100% (C) 17% (D) 17.61% (E) 17.56% [CoT]: [Increase = (60/60)*100 = (6/6)*100 = 100%.] Answer: (A) Question: A boy runs 200 metres in 72 seconds. What is his speed ? Options: (A) 10 km/hr (B) 14 km/hr (C) 20 km/hr (D) 12 km/hr (E) 24 km/hr [CoT]: [200/72 * 18/5 = 10 km/hr] Answer: (E) Question:
Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Options: (A) 2560 (B) 3400 (C) 3690 (D) 4500 (E) 5184 [CoT]: [Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184 432 12 x 62]
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Reasoning: 8/12 + 6/x = 1 X = 18 days Ans: (A) Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? Options: (A) 28 days (B) 76 days (C) 16 days (D) 18 days (E) 19 days Rationale: C 23 This is an alternating addition and subtraction series. In the first pattern, 10 is added to each number to arrive at the next. In the second, 10 is subtracted from each number to arrive at the next. The answer: (C) Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 5, 43, 15, 33, 25, ...What number should come next? Options: (A) 10 (B) 40 (C) 23 (D) 13 (E) 20 Reasoning: 1/15 + 1/25 = 8/75 75/8 = 9 3/8 days Ans: (C) Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together? Options: (A) 9 3/9 (B) 9 3/7 (C) 9 3/8 (D) 9 3/2 (E) 9 3/1 Rationale: T = 224/32 = 7 h T = 7 - 3 = 4 Time Ratio = 7:4 Speed Ratio = 4:7 The answer: (C) Question: A motorcyclist goes from Bombay to Pune, a distance of 224 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? Options: (A) 1:2 (B) 1:5 (C) 4:7 (D) 1:1 (E) 1:8 Reasoning: B 360 This is an alternating addition and subtraction series. In the first pattern, 120 is added to each number to arrive at the next. In the second, 5 is subtracted from each number to arrive at the next. Ans: (B) Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 120, 30, 240, 25, ___, 20, 480, 15... Which number is missing? Options: (A) 120 (B) 360 (C) 340 (D) 960 (E) 280 Reasoning: 20/ (2 * 2) = 5 days Ans: (C)
Question: Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in? Options: (A) 3 (B) 4 (C) 5 (D) 6 (E) 8
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Reasoning: 2/10*1/6*(total) = 5 1/30*(total) = 5 (total) = 5*30 = 150 Ans: (E) Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports? Options: (A) $21.25m (B) $25.5m (C) $106.25m (D) $127.5m (E) $150m Rationale: 100 * 100 = 10000 125 * 80 = 10000 The answer: (A) Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? Options: (A) 10000 (B) 28869 (C) 10002 (D) 18089 (E) 10004 Reasoning: (60/100) * 50 – (30/100) * 30 30 - 9 = 21 Ans: (A) Question: How much 60% of 50 is greater than 30% of 30? Options: (A) 21 (B) 91 (C) 11 (D) 17 (E) 12 Rationale: At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half. The answer: (B) Question: You have found a mutant algae that doubles in size every hour. It takes 18 hours for one algae plant to take up half of a certain lake. How long would it take for two of these plants to take up half of the same lake? Options: (A) 7 (B) 17 (C) 27 (D) 37 (E) 47 Reasoning: Since average price of a pencil = 2 ∴ Price of 75 pencils = 150 ∴ Price of 30 pens = (510 – 150) = 360 ∴ Average price of a pen = 360⁄60 = 12 Ans: (C) Question: 30 pens and 75 pencils were purchased for 510. If the average price of a pencil was 2.00, find the average price of a pen. Options: (A) 10 (B) 11 (C) 12 (D) 13 (E) 14 Reasoning: A = 7500(26/25)^5 = 9125 Ans: (D)
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is? Options: (A) 3377 (B) 2688 (C) 2688 (D) 9125 (E) 1268
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