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The average of first six prime numbers which are odd is? | Explanation: Sum of first 6 prime no. which are odd = 56 Average = 56/6 = 9.33 | deepmind/aqua_rat |
Farm Tax is levied on the 50% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : | Only trick n this question is to ignore 50% information as farm tax is levied uniformly in the village and that includes Mr William's land. What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/38... | deepmind/aqua_rat |
You enter a weight loss challenge game and manage to lose 13% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in? | (100%-13%)*(100%+2%) = 0.87*1.02 = 11.26% The weigh in records your weight loss at 11.26%! | deepmind/aqua_rat |
An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had: | The cost of the first stock was 36/1.2=30, so the profit from it is 6. The cost of the second stock was 36/0.8=45, so loss from it is 9. Overall the loss is $3. | deepmind/aqua_rat |
2^2*3^3*2^3*3^2*2^2 = | 2^2*3^3*2^3*3^2*2^2 = A) 3^5*2^5 B) 2^9*3^4 C) 2^4*3^9 D) 2^7*3^5 E) 6^10 If the base is same, powers are added so that follows D) 2^7*3^5. | deepmind/aqua_rat |
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ? | Let number of cars sold in 1st quarter = x Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x 1.24 x = 2,976,000 => x = 2,400,000 | deepmind/aqua_rat |
If a large pizza has a radius that is 40% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza? | Let the radius of medium pizza be r. Then the radius of large pizza is 1.4r. The area of the medium pizza is pi*r^2 The area of the large pizza is pi*(1.4*r)^2 = 1.96*pi*r^2, an increase of 96%. | deepmind/aqua_rat |
For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <3>*<4>? | Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive. Hence <3> is the sum of all integers from 1 to 2*3=6 and <4> is the sum of all integers from 1 to 2*4=8--> <3>=21 and <4>=36 --> <3>*<4>=21*36=756. | deepmind/aqua_rat |
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12400 after a year? | 6300:4200:10500 3:2:5 | deepmind/aqua_rat |
Which of the following ratios is greatest ? | 7/15 = 0.466, 15/23 = 0.652, 17/25 = 0.68 21/29 = 0.724 Clearly, 0.724 is greatest therefore, 21 : 29 is greatest | deepmind/aqua_rat |
A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? | Relative speed of the policeman = 20-16 = 4 km/hr time taken by policeman to cover 200m = (200/1000)*(1/4) = 1/20 hr In 1/20 hr the thief covers a distance of 16/20 km = 4/5 km = 800m | deepmind/aqua_rat |
The average expenditure of a man for the first five months is Rs.60 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is : | Explanation: Total income = Rs.(60×5+130×7+290)=Rs.1500 Average monthly income = Rs. (1500/12)=Rs.125 | deepmind/aqua_rat |
A gambler bought $3,000 worth of chips at a casino in denominations of $30 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $30 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have receive... | In order to maximize the amount of money that the gambler kept, we should maximize # of $30 chips lost and minimize # of $100 chips lost, which means that # of $30 chips lost must be 2 more than # of $100 chips lost. So, if # of $30 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chi... | deepmind/aqua_rat |
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score O that Lindsey could... | If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midt... | deepmind/aqua_rat |
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is? | Let us name the trains A and B. Then, (A's speed) : (B's speed) | deepmind/aqua_rat |
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? | Markup = x x = 0.25(60 + x) => 3x/4 = 15 => x = 20 So SP = 80 But Actual SP = 0.8 * 80 = 64 So profit = $4 | deepmind/aqua_rat |
A lady bought five books namely A,B,C,D,E to distribute her 4 children. How many ways she can distribute books? | 4*4*4*4*4 4^5 | deepmind/aqua_rat |
If Jack walked 7 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour? | Distance walked in 1 hour and 15 mins = 7 miles Speed per hour = Distance/Time = 7/(5/4) = 5.6 miles per hour | deepmind/aqua_rat |
If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer x? | Let two consecutive positive integers be x and x-1 (Greater integer is x) So, (1/x) + [1/(x-1)] = (2x-1)/x(x-1) =(2x-1)/(x^2- x) | deepmind/aqua_rat |
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors n... | Back-solving is the best way to solve this problem. You basically need 12 combinations (including single colors) If we start from option 1-> 1=> 4C2 + 4 = 10 (Not enough) 2=> 5C2 + 5 = 15 (Enough) Since the minimum number is asked. It should be 5. | deepmind/aqua_rat |
Ajay pays Rs 6.4 per litre of spirit, He adds water and sells the mixture at Rs 8 per Iitre, thereby making 37.5% profit. Find the proportion of the water to that of the spirit received by the customers. | Suppose the quantity of spirit purchased= X litres Suppose quantity of water mixed = Y litres Required ratio of the water and the spirit in the mixture = Y : X C.P of X lts of spirit = Rs 6.4X S.P of X lts of milk = Rs 8(X + Y) profit % = 37.5 Thus, C.P = S.P x 100/(100 + gain% ) => 64 =( 8X + 8Y)/(100 + 37.5) x 100 88... | deepmind/aqua_rat |
Smita Was Making A Cube With Dimensions 5*5*5 Using 1*1*1 Cubes. What Is The Number Of Cubes Needed To Make A Hollow Cube Looking Of The Same Shape? | cube use to make perfect 5 * 5 * 5 = 125 No need of cube to make hollow=(5-2)*(5-2)*(5-2)=27 so total cube need to make hollow cube is=125-27 =98 | deepmind/aqua_rat |
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year? | Explanation: Ratio in which they should share the profit = Ratio of the investments multiplied by the time period =45000×12:30000×9=45×12:30×9=3×12:2×9=2:1 | deepmind/aqua_rat |
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a >0.1. Which of the following operations would decrease the standard deviation of Set J? | CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e. 1) It depends on the separation between the successive terms of the set 2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence... | deepmind/aqua_rat |
If a/b = 4/5, Then (5a - 3b) / (5a + 3b) = ? | Answer Dividing numerator as well as denominator by b, we get Given Exp. = (5a - 3b) / (5a + 3b) = (5a/b - 3) / (5a/b + 3) Since a/b = 4/5 this implies that =[(5*4)/5 -3]/[(5*4)/5 +3)] = (4- 3) / (4 + 3) = 1/7 | deepmind/aqua_rat |
If the units digit of n^33 is 7, which of the following could be the value of n? I. n = 41 II. n = 43 III. n = 47 | Given n^33 units digit is 7. If at all we have to get 7 as units digits only 3 and 7 series has 7 3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81 7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units) We have n^33 - then divide 33 by 4 = remainder 1. Then we have for only 7^1 - we have units digit as 7. Hence 47^33 = 7 (units)... | deepmind/aqua_rat |
Tom is 7 years older than Sam, and Jack is thrice as old as Tom. If S is Sam’s age and J is Jack’s age, what is the relationship between S and J? | T=S+7 and J=3T --> J=3S+21 | deepmind/aqua_rat |
Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet? | Explanation: Assume both trains meet after x hours after 7 am Distance covered by train starting from P in x hours = 20x km Distance covered by train starting from Q in (x-1) hours = 25(x-1) Total distance = 110 => 20x + 25(x-1) = 110 => 45x = 135 => x= 3 Means, they meet after 3 hours after 7 am, ie, they meet at 10 a... | deepmind/aqua_rat |
A and B together can do a work in 4 days. If A alone can do it in 14 days. In how many days can B alone do it? | 1/4 – 1/12 = 1/6 => 6 | deepmind/aqua_rat |
Tough and Tricky questions: Ratios 1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to joi... | let total no. of students be 30 students left on a field trip = 1/5(30) =6 thus 24 students left behind 1/3(24)=8 students did not want to go. thus 16 students want to go on the trip 1/2(16)=8 were able to join the other students on the field trip. thus total number of students that went on a field trip =6+8 =14 thus r... | deepmind/aqua_rat |
Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is | Explanation: Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s We are calculating the time taken by the slower train to pass the driver of the faster one .Hence the distance = length of the smaller train = 500 m Time = distance/speed = 500/(125/6) = 24 sec | deepmind/aqua_rat |
(51+ 52 + 53 + ... + 100) = ? | This is an A.P. in which a = 51, l = 100 and n = 50. Sum = n (a + l) = 50 x (51 + 100) = (25 x 151) = 3775. 2 2 | deepmind/aqua_rat |
In one day, Juan sends Keith three times as many messages as he sends Laurence, and Laurence sends Missy 2 times as many messages as he receives from Juan. If Missy received 18 messages from Laurence, how many messages does Keith receive from Juan? | Juan --> Laurence = x messages; Juan --> Keith = 3x messages (Juan sends Keith three times as many messages as he sends Laurence); Laurence --> Missy = 2x =18 (Laurence sends Missy 2 times as many messages as he receives from Juan). 2x =18 --> x = 9 --> 3x = 27. | deepmind/aqua_rat |
A bus trip of 550 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip? | The time is the distance/speed. The time difference is 1 hour. 550/V - 550/(V+5) = 1 550(V+5) - 550V = (V)(V+5) 2750 = (V)(V+5) 50*55 = (V)(V+5) V = 50 mph | deepmind/aqua_rat |
If abc^2 = b^3 , which of the following must be true? I. ac = b^2 II. b = 0 III. ac = 1 | C | deepmind/aqua_rat |
A boat having a length 8 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: | Volume of water displaced = (8 x 3 x 0.01) m3 = 0.24 m3. Mass of man = Volume of water displaced x Density of water = (0.24 x 1000) kg = 240 kg. | deepmind/aqua_rat |
P is three times as old as Q. In 11 years, P will be twice as old as Q. How old was P three years ago? | P = 3Q so Q = P/3 P+11 = 2(Q+11) = 2(P/3+11) P/3 = 11 P = 33 Three years ago, P was 30. | deepmind/aqua_rat |
What is the next number: 2, 10, 82, __ | 3^0 + 1 = 2 3^2 + 1 = 10 3^4 + 1 = 82 3^6 + 1 = 730 | deepmind/aqua_rat |
Carol and Blake invested 12000 and 24000, respectively in a business. Carol manages the business and for this he receives 9% of the profit while the rest is divided in proportion to their capitals. Find the share of Carol in a profit of 4000. | The Carol gets for managing = 9% of Rs. 4000 = 360 Remaining profit = 4000 – 360 = 3640 This is to be divided in the ratio 12000 :24000=12: 24=1:2. Share of Carol = 1/3 of 3640 = 1213.3 ⇒ Total share of Carol = 360 + 1213.3 = 1573.3. | deepmind/aqua_rat |
There are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed. | First of all you should remember that there is a difference in left and right sock. now no. of way to select any of the sock = 9 and for second = 8 so total methods = 9*8 = 72 | deepmind/aqua_rat |
Two numbers are in the ratio of 5:7. If 7 is subtracted from each number, they are in the ratio of 2:3. What are the two numbers? | (5x-7):(7x-7) = 2y:3y 5x - 7 = 2y 7x - 7 = 3y 49-35 = 15y - 14y 14 = y 5x-7 = 28 x = 7 The two numbers are 5x and 7x which are 35 and 49. | deepmind/aqua_rat |
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 790. If each member of the club paid at least $ 32, then what is the greatest possible number of members in the club? | Given: Each person spends $32. By looking at the options, we see that if there were 20 members, each person will spend atleast $32 | deepmind/aqua_rat |
A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour? | Explanation: Speed = {\color{Blue} \left ( \frac{600}{5\times 60} \right )m/ sec =2m/ sec=\left ( 2\times \frac{18}{5} \right )km/hr=7.2km/hr} | deepmind/aqua_rat |
A tin of oil was 4/5 full. when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain? | Suppose x bottles can fill the tin completely Then 4/5x-3/4x=6-4 X/20=2 X=40 Therefore required no of bottles =40 | deepmind/aqua_rat |
A, B, and C working alone can finish constructing a house in 6, 12, and 18 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish? | A completes 1/6 of the job each hour. B completes 1/12 of the work each hour. C completes 1/18 of the work each hour. A completes 1/6 of the work in the first hour. Working together, A and B complete another 3/12 for a total of 5/12. Working together, A, B, and C can complete 11/36 of the work each hour. To complete 7/... | deepmind/aqua_rat |
The speed of a car is 120 km in the first hour and 60 km in the second hour. What is the average speed of the car? | S = (120 + 60)/2 = 90 kmph | deepmind/aqua_rat |
It takes Avery 2.5 hours to build a brick wall while Tom can do it in 4 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own? | Avery's efficiency is 100/2.5 = 40% Tom's = 100/4= 25% they worked together for 1 hour and finished 65% of the job remaining = 35 % Tom will complete 25 % in 60 minutes , and 10% in 60*10/25 minutes = 24 minutes Time taken by Tom to finish the remaining on his own = 60+24 = 84 minutes | deepmind/aqua_rat |
A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1242. Find the number to be multiplied. | Let the required number be x. Then, 43x – 34x = 1242 or 9x = 1242 or x = 138. Required number = 138. | deepmind/aqua_rat |
Insert the missing number. 2, 7, 10, 22, 18, 37, 26 | There are two series here 2, 10, 18, 26, ... (Increase by 8) 7, 22, 37, ... (Increase by 15) Hence, next term is 37+15 = 52 | deepmind/aqua_rat |
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