NurErtug/MNLP_M3_mcqa_dataset · Datasets at Hugging Face

question stringlengths 1 1.14k	options listlengths 4 4	answer stringclasses 4 values	correct_option stringlengths 1 219	explanation stringlengths 0 3.68k ⌀	dataset stringclasses 5 values
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability G that the sum of the three numbers on the balls selected from the box will be odd?	[ "1/4", "3/8", "1/2", "5/8" ]	C	1/2	The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd); P(OOO)=(1/2)^3; P(EEO)=3(1/2)^21/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE); So finally G=1/8+3/8=1/2. Answer: C.	aqua_rat
A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?	[ "340 yr", "330 yr", "350 yr", "360 yr" ]	D	360 yr	nepo's age=x yr nepo's son's age=x/3 yr nepo's father's age=2x+40 yr total age=1240 x+x/3+2x+40=1240 3x+x+6x+120=1240*3 10x=3720-120 x=360 Hence nepo's age is 360 yr ANSWER:D	aqua_rat
One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?	[ "Rs. 14", "Rs. 5", "Rs 20", "Rs 7" ]	D	Rs 7	Explanation : Let work done by a man in one day = x Then, work done by a woman in 1 day = x/2. work done by a child in 1 day = x/6. estate owner hires total 39 persons men : women : children = 6:5:2 Number of men = 39 × 6 / 13 = 18 Number of women = 39 × 5 / 13 = 15. Number of children = 39 × 2 / 13 = 6. Work done by 18 men in 1 day = 18x Work done by 15 women in 1 day = 15x/2 Work done by 6 children in 1 day = 6x/6 = x. Total amount given to 6 children = 1113 × x / ( 18x + 15x/2 + x) = 2226 / (36 + 15 + 2 ) = 42. Daily wage of a child = 42 / 6 = Rs. 7. Answer : D	aqua_rat
How many three letter words are formed using the letters of the word TIME?	[ "12", "20", "16", "24" ]	D	24	Explanation: The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2 = 24. ANSWER IS D	aqua_rat
A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B	[ "Rs. 3400", "Rs. 2700", "Rs. 1720", "Rs. 7200" ]	D	Rs. 7200	Explanation: Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y Then, savings of A = 5x-3y = 1800—?(1) Savings of B = 6x-4y = 1600—?(2) By solving equations (1) and (2) y = 1400 Monthly income of B = Expenses of B + savings of B = 4y+1600 = 4(1400) + 1600 = Rs. 7200 Answer: D	aqua_rat
If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a six-percent vinegar solution, what was the concentration of the original solution?	[ "19.3%", "31%", "16.67%", "15.5%" ]	B	31%	Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 6%, thus (12 - X)/62 = 6/100 From this equation X = 8.28 Answer (12-8.28)/12 = 31% ANSWER:B	aqua_rat
A and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?	[ "30days", "35days", "40days", "45days" ]	A	30days	Explanation: (A+B)’s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2 A complete remaining work in 1/2*40 = 20 Total work = 10+20 = 30days Answer: Option A	aqua_rat
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:	[ "0.4", "0.004", "0.04", "0.0004" ]	C	0.04	Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is C.	aqua_rat
Evolution changes the characteristics of what over time?	[ "the Moon", "Man", "life", "trees" ]	D	trees	evolution changes the characteristics of trees over time	qasc
If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?	[ "35", "42", "45", "147" ]	D	147	First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so, (105)^3 = 3 * 7 * 5 * 5 3 5 b Therefore (3 5 * 7) ^ 3 = 3^2 * 5^3 * 7 b Therefore, b = 3^3 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7 b = 37^2 =3 49=147 Correct answer D.	aqua_rat
What is one way dogs learn to behave?	[ "exercise", "mating", "ligt", "playing" ]	D	playing	Playing is one way dogs learn to behave.	qasc
A coin is tossed four times. What is the probability that there is at the least one tail?	[ "15/16", "15/37", "15/67", "15/17" ]	A	15/16	Let P(T) be the probability of getting least one tail when the coin is tossed four times. = There is not even a single tail. i.e. all the outcomes are heads. = 1/16 ; P(T) = 1 - 1/16 = 15/16 Answer: A	aqua_rat
If the average (arithmetic mean) of five consecutive negative integers is 8k – 1, what is the difference between the greatest and least of the five integers?	[ "4K", "4k^2 -4k", "4-4k", "4" ]	D	4	(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 8k - 1 => n = 40k - 5 Greatest = n + 2 = 40k - 5 + 2 = 40k - 3 Least = n - 2 = 40k - 5 - 2 => Difference = 40k - 3 - (40k - 7) = 4 Answer - D	aqua_rat
The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.	[ "121", "123", "125", "122" ]	A	121	Let 6x and 5x be sides of the rectangle 6x × 5x = 1331 11xpower2 = 1331 xpower2 = 1331/11 = 121 => x = 11 Length = 6x = 6 × 11 = 66 Breadth = 5x => 5 × 11 = 55 Perimeter = 2 (l+b) => 2 (66+55) = 121 m Answer is A.	aqua_rat
10, 14, 16, 18, 21, 24, 26	[ "17", "20", "21", "25" ]	C	21	Each of the numbers except 21 is an even number ANSWER :C	aqua_rat
Arun and Amit started walking from two different points 'A' and 'B' respectively.Arun walks 2 kms North and turns to the East and walks 3 kms and again turns to North walks 4 kms and finally turns to East and Walks 5kms to reach point 'C'. Similarly, Amit walks 2 kms North and turns to west and walks 3 kms and finally turns to North, walks 4 kms and meets Arun at point 'C'. What is the distance between Arun and Amit's starting points?	[ "5 km", "8 km", "11 km", "13 km" ]	C	11 km	Explanation: Where A= Arun's starting point; B = Amit's starting point; C = The point where Arun and Amit meet PQ + RC + ST = 3 + 5 + 3 = 11 kms. ANSWER IS C	aqua_rat
A person want to give his money of $1800 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?	[ "$700", "$600", "$900", "$500" ]	B	$600	B's share = 1800*3/9 = $600 Answer is B	aqua_rat
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score D of team B?	[ "1)8", "2)10", "3)20", "4)40" ]	A	1)8	A to B = 3 : 4 So, on doubling we get 6 : 4 A to C = 3 : 5 So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20 So final ratio = 6 : 4 : 20. If 20x = 40 4x = 8 Hence, answer is A	aqua_rat
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?	[ "298", "280", "279", "267" ]	B	280	x*(85/100) = (480 - x)119/100 x = 280 Answer:B	aqua_rat
he ratio between the sale price and the cost price of an article is 3:1. What is the ratio between the profit and the cost price of that article?	[ "2:1", "2:9", "2:4", "2:1" ]	A	2:1	Let C.P. = Rs. x and S.P. = Rs. 3x. Then, Gain = Rs. 2x Required ratio = 2x : x = 2:1. Answer:A	aqua_rat
At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number E of different possible seating arrangements for the group?	[ "5", "10", "24", "32" ]	C	24	Circular arrangements= (n-1)! Hence (4!) = 24=E Answer is C	aqua_rat
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?	[ "$150", "$175", "$200", "$210" ]	C	$200	Amount at end of 2 years = 240$ 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 C	aqua_rat
The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :	[ "4", "8", "12", "16" ]	B	8	Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer : B	aqua_rat
Several people are sitting around a round table playing a card game with a deck of 49 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?	[ "4", "5", "7", "11" ]	A	4	Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 49/n has a remainder of 1 and so 49-1 = 48 is a multiple of n. The answer is A.	aqua_rat
John purchased a fridge and a mobile for Rs.5000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.	[ "Rs. 100", "Rs. 150", "Rs. 200", "Rs. 260" ]	C	Rs. 200	Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C	aqua_rat
A car takes 6 hours to cover a distance of 450 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	[ "60", "50", "40", "70" ]	B	50	Time = 6 Distance = 450 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 450/9 = 50 Kmph Answer B.	aqua_rat
The duplicate ratio of 1:4 is?	[ "1:2", "1:4", "1:8", "1:18" ]	C	1:8	1^2: 4^2 = 2:16=1:8 ANSWER:C	aqua_rat
Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $195 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?	[ "17,010", "2,100", "1,890", "1,950" ]	D	1,950	10% ---- 195 millions for 100% => ( 195 * 100% )/10% = 1950. Option D.	aqua_rat
A family made a down payment of $100 and borrowed the balance on a set of encyclopedias that cost $400. The balance with interest was paid in 20 monthly payments of $17.2 each and a final payment of $3. The amount of interest paid was what percent of the amount borrowed?	[ "6%", "12%", "14%", "15.6%" ]	D	15.6%	interest paid = 17.220+3 - 300=47 % off the balance = (47/300) 100 = 15.67% Answer is D.	aqua_rat
If n ≠ 0, which of the following must be greater than n? I. n^4 II. 2n III. 2 - n	[ "I only", "II only", "I and II only", "II and III only" ]	A	I only	n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only I =>answer is A	aqua_rat
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?	[ "2480", "3490", "6785", "8215" ]	D	8215	sum of square of n numbers is found using the formula [n (n+1) (2n+1)]/6 we have sum of 1st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1st 30 +ve integers - sum of squares of 1st 15 +ve integers. we will get D - 8215;ANSWER:D	aqua_rat
Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is	[ "Rs 429", "Rs 412", "Rs 400", "Rs 129" ]	C	Rs 400	Let C = x. Then B = x/2 and A = x/4 A:B:C = 1:2:4. C's share Rs.[(4/7)*700) = 400 Answer: C	aqua_rat
The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?	[ "12300", "12350", "12100", "12500" ]	C	12100	Formula : ( After =100 denominator Ago = 100 numerator) 10000 Ã— 110/100 Ã— 110/100 = 12100 C	aqua_rat
Positive integer n leaves a remainder of 4 after division by 5 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?	[ "3", "12", "18", "22" ]	D	22	The theory says: if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder. e.g: 9 when devided by 5 leves the remainder 4 : 9=51+4 it can also leave the remainder 4-5 = -1 : 9=52 -1 back to the original qtn: n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5 ==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5 ==> n when devided by 5 and 6 leaves the same remainder -2. what is n? LCM (5,6)-2 = 30-2 = 28 CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3 However, the qtn says n > 30 so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5 nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders. hence n could be anything that is in the form 28 + (some multiple of 6 and 5) observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30. hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 22. D	aqua_rat
What can cause a rainbow?	[ "sunlight", "cold fronts", "heating liquids", "earthquakes" ]	B	cold fronts	Cold fronts can cause a rainbow.	qasc
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?	[ "11 days", "14 days", "13 days", "10 days" ]	A	11 days	x/24 + x/30 + x/40 = 1 x = 11 days ANSWER A	aqua_rat
A table is bought for Rs.400/- and sold at Rs.250/- find gain or loss percentage	[ "5%loss", "10%gain", "20%gain", "37.5%loss" ]	D	37.5%loss	Formula = (Selling price ~ Cost price)/Cost price * 100 = (250 - 400)/400 = 37.5% loss D	aqua_rat
The average age of 20 students in a class is 5years. If teacher's age is also included then average increases 1year then find the teacher's age?	[ "28", "24", "20", "22" ]	C	20	Total age of 50 students = 205 = 100 Total age of 51 persons = 206 = 120 Age of teacher = 120-100 = 20years Answer is C	aqua_rat
Which of the following is a prime number ?	[ "81", "90", "97", "99" ]	C	97	Explanation: Clearly, 97 is a prime number. C)	aqua_rat
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	[ "288", "270", "289", "480" ]	D	480	Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer: D	aqua_rat
if each of its sides of a rectangle is increased by 18%, what is the percentage increase in the area of the rectangle, ?	[ "39.24%", "38.24%", "36.24%", "37.24%" ]	A	39.24%	Assume original length = 100m by 50m original area = 10050= 5000 18% increase on each side l = 100 + 18= 118 w = 50 + 9 = 59 new area = 11859= 6962 increase in area = 6962 - 5000 = 1962 %increase =39.24% Answer A	aqua_rat
The bankers discount of a certain sum of money is Rs. 144 and the true discount on the same sum for the same time is Rs. 120. The sum due is:	[ "715", "716", "718", "720" ]	D	720	Sum = (B.DT.D)/(B.D-T.D) (144120)/144-120; 720 ANSWER: D	aqua_rat
At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?	[ "1/12", "5/14", "4/9", "1/2" ]	B	5/14	"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind). C23∗C46C49=514C32∗C64C94=514. C23C32 - # of ways to choose which 2 samples will be tasted; C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups); C49C94 - total # of ways to choose 4 cups out of 9. Answer: B	aqua_rat
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:	[ "Rs. 3500", "Rs. 3600", "Rs. 3900", "Rs. 4000" ]	C	Rs. 3900	Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C	aqua_rat
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?	[ "230", "9927", "267", "1268" ]	A	230	Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A	aqua_rat
A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/5 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?	[ "x/3", "x/2", "2x/3", "3x/2" ]	D	3x/2	x/(x+y) = 2/5 5x = 2x+2y 3x = 2y y = 3x/2 Answer D	aqua_rat
Average of six numbers is 30, and the sum of three of the numbers is 99, wat is the average of the other 3 numbers?	[ "27", "34", "29", "35" ]	A	27	Let the six numbers be a, b, c, d, e,f. Then their average is (a+b+c+d+e+f)/6=30 a+b+c=99 (99+d+e+f)/6=30 99+d+e+f=180 d+e+f=81 average=81/3=27 Ans A	aqua_rat
a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c	[ "8/30", "9/30", "10/30", "11/30" ]	D	11/30	c/(a+b)-(a+b)/c = (c/(a+b))-((a+b)/c) = (6/(2+3))-((2+3)/6) = (6/5)-(5/6) = 11/30 ANSWER:D	aqua_rat
Combine terms: 10a + 26b -4b – 16a.	[ "4a + 22b", "-28a + 30b", "-6a + 22b", "28a + 30b" ]	C	-6a + 22b	Solution: 10a + 26b -4b – 16a. = 10a – 16a + 26b – 4b. = -6a + 22b. Answer: (C)	aqua_rat
How many numbers from 29 to 119 are exactly divisible by 11?	[ "5", "7", "9", "8" ]	D	8	29/11 = 2 and 119/11 = 10 ==> 10 - 2 = 8 Numbers Answer : D	aqua_rat
A work as fast as B. If B can complete a work in 12days independently,the number of days in which A and B can together finish the work in?	[ "2days", "3days", "4days", "5days" ]	C	4days	Ratio of rates of working of A and B = 2:1 ratio of times taken = 1:2 A's 1day work = 1/6 B's 1day work = 1/12 A+B 1day work = 1/6 + 1/12 = 3/12 = 1/4 A and B can finish the work in 4days Answer is C	aqua_rat
The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?	[ "101!", "100!", "99^2(98!)", "100^2(99!)" ]	D	100^2(99!)	According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out: 101! - 100! Both these terms have something in common: 100! so we can factor that out of each piece... 101! - 100! 100!(101 - 1) Simplifying the parentheses, we get... 100!(100) Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices... 100! = (100)(99!) so our answer can be rewritten as... (100)(99!)(100) Or.... (100^2)(99!) ANSWER:D	aqua_rat
The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?	[ "30, 40", "30, 46", "30, 29", "31, 40" ]	A	30, 40	Their present ages be 3X and 4X. 5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7 X = 35 - 25 => X = 10. Their present ages are: 30, 40. Answer: A	aqua_rat
If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added?	[ "1", "2", "3", "4" ]	A	1	Given there are 20 apples.If 1 extra apple is added, then it becomes 21 which can be divided equally that is 7 apples to each baby. Option A is correct.	aqua_rat
It is known that no more than 5 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?	[ "35", "105", "60", "210" ]	C	60	The question states that there are no more than 5 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4 or 5 children. If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally. similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally. or if there were 210 cookies, and 4 children, cookies cannot be distributed equally. Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 5). And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5), i.e., 60. Answer (C)	aqua_rat
If taxi fares were $1.00 for the first 1/5 mile and $0.25 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was	[ "$1.56", "$2.40", "$3.80", "$4.50" ]	D	$4.50	In 3 miles , initial 1/5 mile charge is $1 rest of the distance = 3 - (1/5) = 14/5 rest of the distance charge = 14(0.25) = $3.5 (as the charge is 0.25 for every 1/5 mile) => total charge for 3 miles = 1+3.5 = 4.5 Answer is D.	aqua_rat
A class has 10 students.Teacher decided to go the tour.But the seats are available only 7.What is the probability that 7 students have to go out of 10 students?	[ "150", "125", "120", "105" ]	C	120	out of 10 students, 7 students must be go to tour. The probablity is 10C7=120 120 possible ways to go to tour	aqua_rat
In a sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?	[ "3/5", "5/8", "8/5", "5/3" ]	C	8/5	First term = 1 Second term = (1/1)+1 = 2 Third Term = (1/2)+1 = 3/2 Forth Term = [1/(3/2)]+1 = 5/3 Fifth Term = [1/(5/3)]+1 = 8/5 Answer: Option C	aqua_rat
Jessica can text 85 words per minute, while Maurice can text 25 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?	[ "0.3", "1.3", "3", "2.6" ]	D	2.6	Since the answer choices are reasonably spaced out, we can approximate and save time Combined words per day = 1106024 410400/158400 will be closest to only 2.6 So, Answer should be D.	aqua_rat
A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?	[ "3/64", "1/20", "1/16", "1/12" ]	B	1/20	Note that we want the first marble selected to be red and the second marble selected to be blue. P=4/16*3/15=1/20. Answer: B.	aqua_rat
Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?	[ "12", "36", "72", "240" ]	C	72	in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B). Total ways = 2C13!3! =266 =72 Ans - C	aqua_rat
The ratio between the number of sheep and the number of horses at the Stewart farm is 5 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?	[ "18", "28", "40", "56" ]	C	40	Let the number of sheeps and horses be 4x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 5x = 5*8 = 40. Hence C.	aqua_rat
At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.6 minutes per mile and then turn around and drive at 0.6 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?	[ "a) 10", "b) 11", "c) 55/3", "d) 13" ]	C	c) 55/3	0.8 minutes --> 1 mile 1 minute --> 1/0.6 = 10/6 = 5/3 miles/minute Distance covered in 40 minutes = 5/3 * 40 = 200/3 miles Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point) Let x be the miles driven before turning 30 + x = 200/3 - x 2x = 200/3 -30 x = 55/3 Answer: C	aqua_rat
In order to obtain an income of Rs. 900 from 20% stock at Rs. 102, one must make an investment of	[ "Rs.6000", "Rs.4590", "Rs.4560", "Rs.4500" ]	B	Rs.4590	Explanation : Market Value = Rs. 102. Required Income = Rs. 900. Here face value is not given. Take face value as Rs.100 if it is not given in the question To obtain Rs.20(ie,20% of the face value 100), investment = Rs.102 To obtain Rs.900, investment = 102/20Ã—900=Rs.4590 Answer : Option B	aqua_rat
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?	[ "79.5", "79.0", "79.4", "79.2" ]	D	79.2	Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr. Answer: D	aqua_rat
Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?	[ "8% p.a.", "6% p.a.", "4% p.a.", "5% p.a." ]	D	5% p.a.	Let the rate of interest be R% p.a. 17400[1 + R/100]2 = 17400 + 1783.50 [1 + R/100]2 = (17400 + 1783.50)/17400 = 1 + 1025/10000 = 1 + 41/400 = 441/400 = [21/20]2 [1 + R/100] = 21/20 R/100 = 1/20 Therefore R = 5 ANSWER:D	aqua_rat
A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?	[ "200", "250", "350", "800" ]	D	800	science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 D	aqua_rat
The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 220 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?	[ "44", "64", "70", "80" ]	A	44	Let x be the number of new boarders. The ratio changed from 5:12 up to 1:2 = 6:12. 220 / (220+x) = 5/6 x = 44 The answer is A.	aqua_rat
What number should replace the question mark? 105, 87, 70, 52, ?	[ "49", "35", "70", "55" ]	B	35	B 35 The sequence progresses -18, -17, -18, -17.	aqua_rat
The percentage increase in the area of rectangle , if each of its side is increased by 20% is?	[ "30%", "44%", "50%", "55%" ]	B	44%	Let original length = x meters original breadth = y meters original area = xy m^2 New length = 120x/100 New breadth = 120y/100 = 6y/5 New area = 6x/5 * 6y/5 = 36xy/25 m^2 Increase percent = 11xy/25 * 1/xy *100 = 44% Answer is B	aqua_rat
There are 3 teams each with 8 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?	[ "50", "23", "192", "28" ]	C	192	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 64 possibilities (88) since each team has 8 players. So there are a total of 192 possibilities (643). I hope this method is easier for you to understand.	aqua_rat
If a2 + b2 + c2 = 390 and ab + bc + ca = 5, then a + b + c is	[ "19", "20", "25", "30" ]	B	20	by formula , (a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca), since, a^2 + b^2 + c^2 = 390 and ab + bc + ca = 5, (a + b + c)^2 = 390 + 2(5) = 400 = 20^2 therefore: a + b + c = 20 ANSWER:B	aqua_rat
the movement what over Earth 's surface causes local weather changes	[ "lava", "Temperature", "moon", "frontal zones" ]	D	frontal zones	the movement frontal zones over Earth 's surface causes local weather changes	qasc
Mike earns $12per hour and Phil earns $6 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?	[ "50%", "32.5%", "37%", "37.5%" ]	A	50%	What % less of 12 is 6 let it be x % less ,then =12(1-x/100)=6 1-x/100=6/12 x=100/2 x=50% Ans A	aqua_rat
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?	[ "1/5", "1/3", "2/5", "1/2" ]	B	1/3	John = (1/2)Karen --> Karen = 2(John) John = 1/3(Luke) --> Luke = 3(John) Total = 6(John) Karen/Total = 2/6 = 1/3 Answer: B	aqua_rat
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:	[ "251", "253", "255", "257" ]	B	253	Let the middle digit be x. Then, 2x = 10 or x = 5. So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit. Hence, required number = 253. Option B	aqua_rat
A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.	[ "4 hours", "5 hours", "6 hours", "7 hours" ]	A	4 hours	Explanation: It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only. Lets see the question now. Speed downstream = (16 + 5) = 21 kmph Time = distance/speed = 84/21 = 4 hours ANSWER IS A	aqua_rat
A charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?	[ "60", "64", "66", "68" ]	B	64	Min fund = 20 Total = 1299 The closest multiple of 20 to 1299 is : 63 Which implies 63 people gave 20 and 1 person gave 39 Ans. B	aqua_rat
Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 4x + 2 = 0?	[ "8", "10", "2", "16" ]	C	2	a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab = [(a + b)2 - 2ab]/ab a + b = -4/1 = -4 ab = 2/1 = 2 Hence a/b + b/a = [(-4)2 - 2(2)]/2 = 4/2= 2. C)	aqua_rat
How many bricks, each measuring 25 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 1 m x 5 cm?	[ "5600", "6000", "242", "7200" ]	C	242	Number of bricks =Volume of the wall/Volume of 1 brick = (800 x 100 x 5)/(25 x 11 x 6) = 242. Answer: Option C	aqua_rat
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	[ "432", "444", "2881", "287" ]	A	432	1h ----- 5 ? ------ 60 12 h RS = 15 + 21 = 36 T = 12 D = 36 * 12 = 432 Answer:A	aqua_rat
n a certain flower shop, which stocks four types of flowers, there are 1/3 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?	[ "62", "63", "64", "66.66" ]	D	66.66	Given :- Violets - C/3 Carnations - C Tulip - C/12 Rose - C/12 Total flowers in terms of C = C/3+C+C/12+C/12 = 18C/12 Percentage of Carnations = C/3C/2 *100 =66.66% Answer D	aqua_rat
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?	[ "79.0", "79:9", "79.1", "79.2" ]	D	79.2	Let the length of the train be x metres and its speed by y m/sec. Then, Now, 8y + 264 = 20y y = 22. Speed = 22 m/sec =km/hr = 79.2 km/hr. Answer: D) 79.2 km/hr	aqua_rat
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 40 minutes?	[ "80", "100", "160", "240" ]	C	160	Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 40 minutes the population increases by 40 x 4 = 160 people. Answer. C.	aqua_rat
A train 500m long takes 10 sec to cross a man walking at 6 kmph in a direction opposite to that of the train. Find the speed of the train?	[ "A)175kmph", "B)150kmph", "C)162kmph", "D)176kmph" ]	D	D)176kmph	Let the speed of the train be x kmph Speed of the train relative to man = x+6 = (x+6)5/18 m/sec 500/[(x+6)5/18] = 10 10(x+6) = 1800 x = 176kmph Answer is D	aqua_rat
what are light bulbs powered by?	[ "heat", "metal", "wind", "sun" ]	A	heat	light bulbs are powered by heat	qasc
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?	[ "72", "64", "36", "18" ]	D	18	Since A and E must be among 3 letters then the third letter must be out of B, C and D. 3C1 = 3 ways to choose which one it'll be. Now, 3 different letters (A, E and the third one) can be arranged in 3!=6 ways, so the final answer is 3*6=18. Answer: D.	aqua_rat
An article is bought for Rs.600 and sold for Rs.500, find the loss percent?	[ "16 2/8%", "16 1/3%", "96 2/3%", "16 2/3%" ]	D	16 2/3%	600 ---- 100 100 ---- ? => 16 2/3% Answer: D	aqua_rat
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?	[ "7184 liters", "8184 liters", "6184 liters", "1184 liters" ]	D	1184 liters	Explanation: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k. Quantity of water in B = 8k - 5k = 3k. Quantity of water in container C = 8k - 3k = 5k Container: A B C Quantity of water: 8k 3k 5k It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water. 5k - 148 = 3k + 148 => 2k = 296 => k = 148 The initial quantity of water in A = 8k = 8 * 148 = 1184 liters. Answer: D	aqua_rat
In how many ways can 6 apples (identical) be distributed among 4 children? (Some children may get no apples.)	[ "84", "54", "94", "104" ]	A	84	Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1. n=6 r= 4 9C3 =84 Answer : A	aqua_rat
The largest 5 digit number exactly divisible by 91 is?	[ "99918", "99919", "99921", "99923" ]	A	99918	Largest 5-digit number = 99999 91) 99999 (1098 91 --- 899 819 ---- 809 728 --- 81 --- Required number = (99999 - 81) = 99918. Option A	aqua_rat
What can fungi do?	[ "protect them", "survive", "Spread disease", "migrate" ]	C	Spread disease	Fungi can cause disease	qasc
A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?	[ "39:40", "39:30", "39:47", "39:45" ]	A	39:40	3: 4 A = 3/7*210 = 90 390: 400 39:40 Answer: A	aqua_rat
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?	[ "$1.75", "$1.85", "$2.00", "$2.15" ]	A	$1.75	This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS. We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot. Since the total price is $8.25 (a 15-cent increment) and the the difference in sequential prices of the pots is 15 cents, the largest pot PROBABLY has a price that is a 15-cent increment. From the answer choices, I would then TEST Answer A first IF.... The largest pot = $1.75 1 1.15 1.3 1.45 1.6 1.75 Total = $8.25 So this MUST be the answer. A	aqua_rat
The speed of light is approximately 1,86 * 10^4 miles per second. This approximate speed is how many miles per hour?	[ "1,11 * 10^7", "6,70 * 10^7", "1,11 * 10^8", "1,86 * 10^8" ]	B	6,70 * 10^7	The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be. (1.8610^4)3600 = (1.8610^4)(3.610^3) = some number10^7... The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is B	aqua_rat
A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?	[ "5", "6", "7", "8" ]	D	8	Speed = 180/3 = 60 m/sec. Required time = (180 + 300)/60 = 8 sec. Answer:D	aqua_rat
How long will it take a sum of money invested at 6 % p.a. S.I. to increase its value by 60%?	[ "11 years", "12 years", "10 years", "15 years" ]	C	10 years	Sol. Let the sum be x. Then, S.I. = 60% of x = 3x/5; Rate = 6%. âˆ´ Time = [100 * 3x/5 * 1/x*6] = 10 years Answer C	aqua_rat
What number is obtained by adding the units digits of 734^98 and 347^81?	[ "10", "11", "12", "13" ]	D	13	The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6. The units digit of 347^81 is 7 because powers of 7 end in 7, 9, 3 or 1 cyclically. Since 81 is in the form 4n+1, the units digit is 7. Then 6+7 = 13. The answer is D.	aqua_rat
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?	[ "176 km/hr", "189 km/hr", "175 km/hr", "197 km/hr" ]	C	175 km/hr	Let speed of the car be x km/hr. Then, speed of the train = 150/100 x = 3/2 x km/hr. 75/x - 75/(3/2 x) = 125/(10 * 60) 75/x - 50/x = 5/24 = 120 km/hr. Answer:C	aqua_rat
Which of the following is divisible by the first five positive integer multiples of 23? (i) 11110 (ii) 102120 (iii) 307740	[ "None", "iii only", "i and iii only", "ii and iii only" ]	D	ii and iii only	A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 34523=6023=1380. The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380. 102=176 and 120=206, so 102120=60(1700+2)=601702=602851. Now, 851-3023=851-690=161=723, so 102120 is divisibly by 6023=1380. Finally, 1021203=306360, and 306360+1380=307740, so (iii) is also divisible by 1380. Answer D.	aqua_rat

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability G that the sum of the three numbers on the balls selected from the box will be odd?

[ "1/4", "3/8", "1/2", "5/8" ]

C

1/2

The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd); P(OOO)=(1/2)^3; P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE); So finally G=1/8+3/8=1/2. Answer: C.

aqua_rat

A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?

[ "340 yr", "330 yr", "350 yr", "360 yr" ]

D

360 yr

nepo's age=x yr nepo's son's age=x/3 yr nepo's father's age=2x+40 yr total age=1240 x+x/3+2x+40=1240 3x+x+6x+120=1240*3 10x=3720-120 x=360 Hence nepo's age is 360 yr ANSWER:D

aqua_rat

One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

[ "Rs. 14", "Rs. 5", "Rs 20", "Rs 7" ]

D

Rs 7

Explanation : Let work done by a man in one day = x Then, work done by a woman in 1 day = x/2. work done by a child in 1 day = x/6. estate owner hires total 39 persons men : women : children = 6:5:2 Number of men = 39 × 6 / 13 = 18 Number of women = 39 × 5 / 13 = 15. Number of children = 39 × 2 / 13 = 6. Work done by 18 men in 1 day = 18x Work done by 15 women in 1 day = 15x/2 Work done by 6 children in 1 day = 6x/6 = x. Total amount given to 6 children = 1113 × x / ( 18x + 15x/2 + x) = 2226 / (36 + 15 + 2 ) = 42. Daily wage of a child = 42 / 6 = Rs. 7. Answer : D

aqua_rat

How many three letter words are formed using the letters of the word TIME?

[ "12", "20", "16", "24" ]

D

24

Explanation: The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2 = 24. ANSWER IS D

aqua_rat

A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B

[ "Rs. 3400", "Rs. 2700", "Rs. 1720", "Rs. 7200" ]

D

Rs. 7200

Explanation: Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y Then, savings of A = 5x-3y = 1800—?(1) Savings of B = 6x-4y = 1600—?(2) By solving equations (1) and (2) y = 1400 Monthly income of B = Expenses of B + savings of B = 4y+1600 = 4(1400) + 1600 = Rs. 7200 Answer: D

aqua_rat

If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a six-percent vinegar solution, what was the concentration of the original solution?

[ "19.3%", "31%", "16.67%", "15.5%" ]

B

31%

Let X be the quantity of non-vinegar in the strong vinegar solution Thus vinegar quantity will be 12 - X When 50 ounces of water were added the percentage of vinegar becomes 6%, thus (12 - X)/62 = 6/100 From this equation X = 8.28 Answer (12-8.28)/12 = 31% ANSWER:B

aqua_rat

A and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?

[ "30days", "35days", "40days", "45days" ]

A

30days

Explanation: (A+B)’s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2 A complete remaining work in 1/2*40 = 20 Total work = 10+20 = 30days Answer: Option A

aqua_rat

The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

[ "0.4", "0.004", "0.04", "0.0004" ]

C

0.04

Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x. For the given expression to be a perfect square, we must have 11.98 x (x) = 2 x 11.98 x 0.02 or x = 0.04 Answer is C.

aqua_rat

Evolution changes the characteristics of what over time?

[ "the Moon", "Man", "life", "trees" ]

D

trees

evolution changes the characteristics of trees over time

qasc

If a = 105 and a^3= 21 * 25 * 15 * b, what is the value of b?

[ "35", "42", "45", "147" ]

D

147

First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so, (105)^3 = 3 * 7 * 5 * 5 *3 *5 *b Therefore (3 * 5 * 7) ^ 3 = 3^2 * 5^3 * 7 *b Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^2 * 5 ^3 * 7 b = 3*7^2 =3* 49=147 Correct answer D.

aqua_rat

What is one way dogs learn to behave?

[ "exercise", "mating", "ligt", "playing" ]

D

playing

Playing is one way dogs learn to behave.

qasc

A coin is tossed four times. What is the probability that there is at the least one tail?

[ "15/16", "15/37", "15/67", "15/17" ]

A

15/16

Let P(T) be the probability of getting least one tail when the coin is tossed four times. = There is not even a single tail. i.e. all the outcomes are heads. = 1/16 ; P(T) = 1 - 1/16 = 15/16 Answer: A

aqua_rat

If the average (arithmetic mean) of five consecutive negative integers is 8k – 1, what is the difference between the greatest and least of the five integers?

[ "4K", "4k^2 -4k", "4-4k", "4" ]

D

4

(n-2 + n - 1 + n + n + 1 + n + 2)/5 = 8k - 1 => n = 40k - 5 Greatest = n + 2 = 40k - 5 + 2 = 40k - 3 Least = n - 2 = 40k - 5 - 2 => Difference = 40k - 3 - (40k - 7) = 4 Answer - D

aqua_rat

The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.

[ "121", "123", "125", "122" ]

A

121

Let 6x and 5x be sides of the rectangle 6x × 5x = 1331 11xpower2 = 1331 xpower2 = 1331/11 = 121 => x = 11 Length = 6x = 6 × 11 = 66 Breadth = 5x => 5 × 11 = 55 Perimeter = 2 (l+b) => 2 (66+55) = 121 m Answer is A.

aqua_rat

10, 14, 16, 18, 21, 24, 26

[ "17", "20", "21", "25" ]

C

21

Each of the numbers except 21 is an even number ANSWER :C

aqua_rat

Arun and Amit started walking from two different points 'A' and 'B' respectively.Arun walks 2 kms North and turns to the East and walks 3 kms and again turns to North walks 4 kms and finally turns to East and Walks 5kms to reach point 'C'. Similarly, Amit walks 2 kms North and turns to west and walks 3 kms and finally turns to North, walks 4 kms and meets Arun at point 'C'. What is the distance between Arun and Amit's starting points?

[ "5 km", "8 km", "11 km", "13 km" ]

C

11 km

Explanation: Where A= Arun's starting point; B = Amit's starting point; C = The point where Arun and Amit meet PQ + RC + ST = 3 + 5 + 3 = 11 kms. ANSWER IS C

aqua_rat

A person want to give his money of $1800 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?

[ "$700", "$600", "$900", "$500" ]

B

$600

B's share = 1800*3/9 = $600 Answer is B

aqua_rat

At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score D of team B?

[ "1)8", "2)10", "3)20", "4)40" ]

A

1)8

A to B = 3 : 4 So, on doubling we get 6 : 4 A to C = 3 : 5 So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20 So final ratio = 6 : 4 : 20. If 20x = 40 4x = 8 Hence, answer is A

aqua_rat

I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?

[ "298", "280", "279", "267" ]

B

280

x*(85/100) = (480 - x)119/100 x = 280 Answer:B

aqua_rat

he ratio between the sale price and the cost price of an article is 3:1. What is the ratio between the profit and the cost price of that article?

[ "2:1", "2:9", "2:4", "2:1" ]

A

2:1

Let C.P. = Rs. x and S.P. = Rs. 3x. Then, Gain = Rs. 2x Required ratio = 2x : x = 2:1. Answer:A

aqua_rat

At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number E of different possible seating arrangements for the group?

[ "5", "10", "24", "32" ]

C

24

Circular arrangements= (n-1)! Hence (4!) = 24=E Answer is C

aqua_rat

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?

[ "$150", "$175", "$200", "$210" ]

C

$200

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 C

aqua_rat

The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :

[ "4", "8", "12", "16" ]

B

8

Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8 Answer : B

aqua_rat

Several people are sitting around a round table playing a card game with a deck of 49 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

[ "4", "5", "7", "11" ]

A

4

Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 49/n has a remainder of 1 and so 49-1 = 48 is a multiple of n. The answer is A.

aqua_rat

John purchased a fridge and a mobile for Rs.5000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.

[ "Rs. 100", "Rs. 150", "Rs. 200", "Rs. 260" ]

C

Rs. 200

Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively. r = 15000(1 - 4/100) = 15000 - 600 m = 8000(1 + 10/100) = 8000 + 800 Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200 As this is positive, an overall profit of Rs. 200 was made. C

aqua_rat

A car takes 6 hours to cover a distance of 450 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?

[ "60", "50", "40", "70" ]

B

50

Time = 6 Distance = 450 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 450/9 = 50 Kmph Answer B.

aqua_rat

The duplicate ratio of 1:4 is?

[ "1:2", "1:4", "1:8", "1:18" ]

C

1:8

1^2: 4^2 = 2:16=1:8 ANSWER:C

aqua_rat

Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $195 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?

[ "17,010", "2,100", "1,890", "1,950" ]

D

1,950

10% ---- 195 millions for 100% => ( 195 * 100% )/10% = 1950. Option D.

aqua_rat

A family made a down payment of $100 and borrowed the balance on a set of encyclopedias that cost $400. The balance with interest was paid in 20 monthly payments of $17.2 each and a final payment of $3. The amount of interest paid was what percent of the amount borrowed?

[ "6%", "12%", "14%", "15.6%" ]

D

15.6%

interest paid = 17.2*20+3 - 300=47 % off the balance = (47/300) * 100 = 15.67% Answer is D.

aqua_rat

If n ≠ 0, which of the following must be greater than n? I. n^4 II. 2n III. 2 - n

[ "I only", "II only", "I and II only", "II and III only" ]

A

I only

n ≠ 0 => n = negative or n = positive if n = negative: 2n < n (n = -1 then 2n = -2 => -2 < -1) n^2 > n (n =-1 then n^2 = 1 => n^2 > n) 2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n) but if n = positive: n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II 2 - n < n(n =2 then 2-2 = 0) => only I =>answer is A

aqua_rat

The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?

[ "2480", "3490", "6785", "8215" ]

D

8215

sum of square of n numbers is found using the formula [n (n+1) (2n+1)]/6 we have sum of 1st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1st 30 +ve integers - sum of squares of 1st 15 +ve integers. we will get D - 8215;ANSWER:D

aqua_rat

Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is

[ "Rs 429", "Rs 412", "Rs 400", "Rs 129" ]

C

Rs 400

Let C = x. Then B = x/2 and A = x/4 A:B:C = 1:2:4. C's share Rs.[(4/7)*700) = 400 Answer: C

aqua_rat

The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?

[ "12300", "12350", "12100", "12500" ]

C

12100

Formula : ( After =100 denominator Ago = 100 numerator) 10000 Ã— 110/100 Ã— 110/100 = 12100 C

aqua_rat

Positive integer n leaves a remainder of 4 after division by 5 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

[ "3", "12", "18", "22" ]

D

22

The theory says: if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder. e.g: 9 when devided by 5 leves the remainder 4 : 9=5*1+4 it can also leave the remainder 4-5 = -1 : 9=5*2 -1 back to the original qtn: n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5 ==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5 ==> n when devided by 5 and 6 leaves the same remainder -2. what is n? LCM (5,6)-2 = 30-2 = 28 CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3 However, the qtn says n > 30 so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5 nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders. hence n could be anything that is in the form 28 + (some multiple of 6 and 5) observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30. hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 22. D

aqua_rat

What can cause a rainbow?

[ "sunlight", "cold fronts", "heating liquids", "earthquakes" ]

B

cold fronts

Cold fronts can cause a rainbow.

qasc

A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?

[ "11 days", "14 days", "13 days", "10 days" ]

A

11 days

x/24 + x/30 + x/40 = 1 x = 11 days ANSWER A

aqua_rat

A table is bought for Rs.400/- and sold at Rs.250/- find gain or loss percentage

[ "5%loss", "10%gain", "20%gain", "37.5%loss" ]

D

37.5%loss

Formula = (Selling price ~ Cost price)/Cost price * 100 = (250 - 400)/400 = 37.5% loss D

aqua_rat

The average age of 20 students in a class is 5years. If teacher's age is also included then average increases 1year then find the teacher's age?

[ "28", "24", "20", "22" ]

C

20

Total age of 50 students = 20*5 = 100 Total age of 51 persons = 20*6 = 120 Age of teacher = 120-100 = 20years Answer is C

aqua_rat

Which of the following is a prime number ?

[ "81", "90", "97", "99" ]

C

97

Explanation: Clearly, 97 is a prime number. C)

aqua_rat

The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?

[ "288", "270", "289", "480" ]

D

480

Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer: D

aqua_rat

if each of its sides of a rectangle is increased by 18%, what is the percentage increase in the area of the rectangle, ?

[ "39.24%", "38.24%", "36.24%", "37.24%" ]

A

39.24%

Assume original length = 100m by 50m original area = 100*50= 5000 18% increase on each side l = 100 + 18= 118 w = 50 + 9 = 59 new area = 118*59= 6962 increase in area = 6962 - 5000 = 1962 %increase =39.24% Answer A

aqua_rat

The bankers discount of a certain sum of money is Rs. 144 and the true discount on the same sum for the same time is Rs. 120. The sum due is:

[ "715", "716", "718", "720" ]

D

720

Sum = (B.D*T.D)/(B.D-T.D) (144*120)/144-120; 720 ANSWER: D

aqua_rat

At a blind taste competition a contestant is offered 3 cups of each of the 3 samples of tea in a random arrangement of 9 marked cups. If each contestant tastes 4 different cups of tea, what is the probability that a contestant does not taste all of the samples?

[ "1/12", "5/14", "4/9", "1/2" ]

B

5/14

"The probability that a contestant does not taste all of the samples" means that contestant tastes only 2 samples of tea (one sample is not possible as contestant tastes 4 cups>3 of each kind). C23∗C46C49=514C32∗C64C94=514. C23C32 - # of ways to choose which 2 samples will be tasted; C46C64 - # of ways to choose 4 cups out of 6 cups of two samples (2 samples*3 cups each = 6 cups); C49C94 - total # of ways to choose 4 cups out of 9. Answer: B

aqua_rat

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

[ "Rs. 3500", "Rs. 3600", "Rs. 3900", "Rs. 4000" ]

C

Rs. 3900

Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y or y = 5 x. 2 15x + 2y = 4000 15x + 2 x 5 x = 4000 2 20x = 4000 x = 200. So, y = 5 x 200 = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. C

aqua_rat

A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?

[ "230", "9927", "267", "1268" ]

A

230

Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A

aqua_rat

A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/5 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?

[ "x/3", "x/2", "2x/3", "3x/2" ]

D

3x/2

x/(x+y) = 2/5 5x = 2x+2y 3x = 2y y = 3x/2 Answer D

aqua_rat

Average of six numbers is 30, and the sum of three of the numbers is 99, wat is the average of the other 3 numbers?

[ "27", "34", "29", "35" ]

A

27

Let the six numbers be a, b, c, d, e,f. Then their average is (a+b+c+d+e+f)/6=30 a+b+c=99 (99+d+e+f)/6=30 99+d+e+f=180 d+e+f=81 average=81/3=27 Ans A

aqua_rat

a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c

[ "8/30", "9/30", "10/30", "11/30" ]

D

11/30

c/(a+b)-(a+b)/c = (c/(a+b))-((a+b)/c) = (6/(2+3))-((2+3)/6) = (6/5)-(5/6) = 11/30 ANSWER:D

aqua_rat

Combine terms: 10a + 26b -4b – 16a.

[ "4a + 22b", "-28a + 30b", "-6a + 22b", "28a + 30b" ]

C

-6a + 22b

Solution: 10a + 26b -4b – 16a. = 10a – 16a + 26b – 4b. = -6a + 22b. Answer: (C)

aqua_rat

How many numbers from 29 to 119 are exactly divisible by 11?

[ "5", "7", "9", "8" ]

D

8

29/11 = 2 and 119/11 = 10 ==> 10 - 2 = 8 Numbers Answer : D

aqua_rat

A work as fast as B. If B can complete a work in 12days independently,the number of days in which A and B can together finish the work in?

[ "2days", "3days", "4days", "5days" ]

C

4days

Ratio of rates of working of A and B = 2:1 ratio of times taken = 1:2 A's 1day work = 1/6 B's 1day work = 1/12 A+B 1day work = 1/6 + 1/12 = 3/12 = 1/4 A and B can finish the work in 4days Answer is C

aqua_rat

The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?

[ "101!", "100!", "99^2(98!)", "100^2(99!)" ]

D

100^2(99!)

According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out: 101! - 100! Both these terms have something in common: 100! so we can factor that out of each piece... 101! - 100! 100!(101 - 1) Simplifying the parentheses, we get... 100!(100) Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices... 100! = (100)(99!) so our answer can be rewritten as... (100)(99!)(100) Or.... (100^2)(99!) ANSWER:D

aqua_rat

The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?

[ "30, 40", "30, 46", "30, 29", "31, 40" ]

A

30, 40

Their present ages be 3X and 4X. 5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7 X = 35 - 25 => X = 10. Their present ages are: 30, 40. Answer: A

aqua_rat

If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added?

[ "1", "2", "3", "4" ]

A

1

Given there are 20 apples.If 1 extra apple is added, then it becomes 21 which can be divided equally that is 7 apples to each baby. Option A is correct.

aqua_rat

It is known that no more than 5 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?

[ "35", "105", "60", "210" ]

C

60

The question states that there are no more than 5 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4 or 5 children. If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally. similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally. or if there were 210 cookies, and 4 children, cookies cannot be distributed equally. Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 5). And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5), i.e., 60. Answer (C)

aqua_rat

If taxi fares were $1.00 for the first 1/5 mile and $0.25 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was

[ "$1.56", "$2.40", "$3.80", "$4.50" ]

D

$4.50

In 3 miles , initial 1/5 mile charge is $1 rest of the distance = 3 - (1/5) = 14/5 rest of the distance charge = 14(0.25) = $3.5 (as the charge is 0.25 for every 1/5 mile) => total charge for 3 miles = 1+3.5 = 4.5 Answer is D.

aqua_rat

A class has 10 students.Teacher decided to go the tour.But the seats are available only 7.What is the probability that 7 students have to go out of 10 students?

[ "150", "125", "120", "105" ]

C

120

out of 10 students, 7 students must be go to tour. The probablity is 10C7=120 120 possible ways to go to tour

aqua_rat

In a sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?

[ "3/5", "5/8", "8/5", "5/3" ]

C

8/5

First term = 1 Second term = (1/1)+1 = 2 Third Term = (1/2)+1 = 3/2 Forth Term = [1/(3/2)]+1 = 5/3 Fifth Term = [1/(5/3)]+1 = 8/5 Answer: Option C

aqua_rat

Jessica can text 85 words per minute, while Maurice can text 25 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?

[ "0.3", "1.3", "3", "2.6" ]

D

2.6

Since the answer choices are reasonably spaced out, we can approximate and save time Combined words per day = 110*60*24 410400/158400 will be closest to only 2.6 So, Answer should be D.

aqua_rat

A jar contains 16 marbles, of which 4 are red, 3 are blue, and the rest are yellow. If 2 marbles are to be selected at random from the jar, one at a time without being replaced, what is the probability that the first marble selected will be red and the second marble selected will be blue?

[ "3/64", "1/20", "1/16", "1/12" ]

B

1/20

Note that we want the first marble selected to be red and the second marble selected to be blue. P=4/16*3/15=1/20. Answer: B.

aqua_rat

Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

[ "12", "36", "72", "240" ]

C

72

in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B). Total ways = 2C1*3!*3! =2*6*6 =72 Ans - C

aqua_rat

The ratio between the number of sheep and the number of horses at the Stewart farm is 5 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?

[ "18", "28", "40", "56" ]

C

40

Let the number of sheeps and horses be 4x and 7x. Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8 Sheeps = 5x = 5*8 = 40. Hence C.

aqua_rat

At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.6 minutes per mile and then turn around and drive at 0.6 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?

[ "a) 10", "b) 11", "c) 55/3", "d) 13" ]

C

c) 55/3

0.8 minutes --> 1 mile 1 minute --> 1/0.6 = 10/6 = 5/3 miles/minute Distance covered in 40 minutes = 5/3 * 40 = 200/3 miles Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point) Let x be the miles driven before turning 30 + x = 200/3 - x 2x = 200/3 -30 x = 55/3 Answer: C

aqua_rat

In order to obtain an income of Rs. 900 from 20% stock at Rs. 102, one must make an investment of

[ "Rs.6000", "Rs.4590", "Rs.4560", "Rs.4500" ]

B

Rs.4590

Explanation : Market Value = Rs. 102. Required Income = Rs. 900. Here face value is not given. Take face value as Rs.100 if it is not given in the question To obtain Rs.20(ie,20% of the face value 100), investment = Rs.102 To obtain Rs.900, investment = 102/20Ã—900=Rs.4590 Answer : Option B

aqua_rat

A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?

[ "79.5", "79.0", "79.4", "79.2" ]

D

79.2

Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr. Answer: D

aqua_rat

Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?

[ "8% p.a.", "6% p.a.", "4% p.a.", "5% p.a." ]

D

5% p.a.

Let the rate of interest be R% p.a. 17400[1 + R/100]2 = 17400 + 1783.50 [1 + R/100]2 = (17400 + 1783.50)/17400 = 1 + 1025/10000 = 1 + 41/400 = 441/400 = [21/20]2 [1 + R/100] = 21/20 R/100 = 1/20 Therefore R = 5 ANSWER:D

aqua_rat

A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?

[ "200", "250", "350", "800" ]

D

800

science books sold = 2x × 0.2 = 0.4x science books unsold = 2x – 0.4x = 1.6x art books sold = 5x × 0.2 = x art books unsold = 5x – x = 4x total books unsold = 1.6x + 4x = 5.6x 5.6x = 2240 x = 400 2x science = 800 D

aqua_rat

The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 220 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?

[ "44", "64", "70", "80" ]

A

44

Let x be the number of new boarders. The ratio changed from 5:12 up to 1:2 = 6:12. 220 / (220+x) = 5/6 x = 44 The answer is A.

aqua_rat

What number should replace the question mark? 105, 87, 70, 52, ?

[ "49", "35", "70", "55" ]

B

35

B 35 The sequence progresses -18, -17, -18, -17.

aqua_rat

The percentage increase in the area of rectangle , if each of its side is increased by 20% is?

[ "30%", "44%", "50%", "55%" ]

B

44%

Let original length = x meters original breadth = y meters original area = xy m^2 New length = 120x/100 New breadth = 120y/100 = 6y/5 New area = 6x/5 * 6y/5 = 36xy/25 m^2 Increase percent = 11xy/25 * 1/xy *100 = 44% Answer is B

aqua_rat

There are 3 teams each with 8 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?

[ "50", "23", "192", "28" ]

C

192

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 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand.

aqua_rat

If a2 + b2 + c2 = 390 and ab + bc + ca = 5, then a + b + c is

[ "19", "20", "25", "30" ]

B

20

by formula , (a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca), since, a^2 + b^2 + c^2 = 390 and ab + bc + ca = 5, (a + b + c)^2 = 390 + 2(5) = 400 = 20^2 therefore: a + b + c = 20 ANSWER:B

aqua_rat

the movement what over Earth 's surface causes local weather changes

[ "lava", "Temperature", "moon", "frontal zones" ]

D

frontal zones

the movement frontal zones over Earth 's surface causes local weather changes

qasc

Mike earns $12per hour and Phil earns $6 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?

[ "50%", "32.5%", "37%", "37.5%" ]

A

50%

What % less of 12 is 6 let it be x % less ,then =12(1-x/100)=6 1-x/100=6/12 x=100/2 x=50% Ans A

aqua_rat

John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?

[ "1/5", "1/3", "2/5", "1/2" ]

B

1/3

John = (1/2)Karen --> Karen = 2(John) John = 1/3(Luke) --> Luke = 3(John) Total = 6(John) Karen/Total = 2/6 = 1/3 Answer: B

aqua_rat

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

[ "251", "253", "255", "257" ]

B

253

Let the middle digit be x. Then, 2x = 10 or x = 5. So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit. Hence, required number = 253. Option B

aqua_rat

A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.

[ "4 hours", "5 hours", "6 hours", "7 hours" ]

A

4 hours

Explanation: It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only. Lets see the question now. Speed downstream = (16 + 5) = 21 kmph Time = distance/speed = 84/21 = 4 hours ANSWER IS A

aqua_rat

A charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?

[ "60", "64", "66", "68" ]

B

64

Min fund = 20 Total = 1299 The closest multiple of 20 to 1299 is : 63 Which implies 63 people gave 20 and 1 person gave 39 Ans. B

aqua_rat

Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 4x + 2 = 0?

[ "8", "10", "2", "16" ]

C

2

a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab = [(a + b)2 - 2ab]/ab a + b = -4/1 = -4 ab = 2/1 = 2 Hence a/b + b/a = [(-4)2 - 2(2)]/2 = 4/2= 2. C)

aqua_rat

How many bricks, each measuring 25 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 1 m x 5 cm?

[ "5600", "6000", "242", "7200" ]

C

242

Number of bricks =Volume of the wall/Volume of 1 brick = (800 x 100 x 5)/(25 x 11 x 6) = 242. Answer: Option C

aqua_rat

Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?

[ "432", "444", "2881", "287" ]

A

432

1h ----- 5 ? ------ 60 12 h RS = 15 + 21 = 36 T = 12 D = 36 * 12 = 432 Answer:A

aqua_rat

n a certain flower shop, which stocks four types of flowers, there are 1/3 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?

[ "62", "63", "64", "66.66" ]

D

66.66

Given :- Violets - C/3 Carnations - C Tulip - C/12 Rose - C/12 Total flowers in terms of C = C/3+C+C/12+C/12 = 18C/12 Percentage of Carnations = C/3C/2 *100 =66.66% Answer D

aqua_rat

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?

[ "79.0", "79:9", "79.1", "79.2" ]

D

79.2

Let the length of the train be x metres and its speed by y m/sec. Then, Now, 8y + 264 = 20y y = 22. Speed = 22 m/sec =km/hr = 79.2 km/hr. Answer: D) 79.2 km/hr

aqua_rat

If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 40 minutes?

[ "80", "100", "160", "240" ]

C

160

Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 40 minutes the population increases by 40 x 4 = 160 people. Answer. C.

aqua_rat

A train 500m long takes 10 sec to cross a man walking at 6 kmph in a direction opposite to that of the train. Find the speed of the train?

[ "A)175kmph", "B)150kmph", "C)162kmph", "D)176kmph" ]

D

D)176kmph

Let the speed of the train be x kmph Speed of the train relative to man = x+6 = (x+6)*5/18 m/sec 500/[(x+6)*5/18] = 10 10(x+6) = 1800 x = 176kmph Answer is D

aqua_rat

what are light bulbs powered by?

[ "heat", "metal", "wind", "sun" ]

A

heat

light bulbs are powered by heat

qasc

How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

[ "72", "64", "36", "18" ]

D

18

Since A and E must be among 3 letters then the third letter must be out of B, C and D. 3C1 = 3 ways to choose which one it'll be. Now, 3 different letters (A, E and the third one) can be arranged in 3!=6 ways, so the final answer is 3*6=18. Answer: D.

aqua_rat

An article is bought for Rs.600 and sold for Rs.500, find the loss percent?

[ "16 2/8%", "16 1/3%", "96 2/3%", "16 2/3%" ]

D

16 2/3%

600 ---- 100 100 ---- ? => 16 2/3% Answer: D

aqua_rat

All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?

[ "7184 liters", "8184 liters", "6184 liters", "1184 liters" ]

D

1184 liters

Explanation: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k. Quantity of water in B = 8k - 5k = 3k. Quantity of water in container C = 8k - 3k = 5k Container: A B C Quantity of water: 8k 3k 5k It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water. 5k - 148 = 3k + 148 => 2k = 296 => k = 148 The initial quantity of water in A = 8k = 8 * 148 = 1184 liters. Answer: D

aqua_rat

In how many ways can 6 apples (identical) be distributed among 4 children? (Some children may get no apples.)

[ "84", "54", "94", "104" ]

A

84

Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1. n=6 r= 4 9C3 =84 Answer : A

aqua_rat

The largest 5 digit number exactly divisible by 91 is?

[ "99918", "99919", "99921", "99923" ]

A

99918

Largest 5-digit number = 99999 91) 99999 (1098 91 --- 899 819 ---- 809 728 --- 81 --- Required number = (99999 - 81) = 99918. Option A

aqua_rat

What can fungi do?

[ "protect them", "survive", "Spread disease", "migrate" ]

C

Spread disease

Fungi can cause disease

qasc

A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?

[ "39:40", "39:30", "39:47", "39:45" ]

A

39:40

3: 4 A = 3/7*210 = 90 390: 400 39:40 Answer: A

aqua_rat

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

[ "$1.75", "$1.85", "$2.00", "$2.15" ]

A

$1.75

This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS. We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot. Since the total price is $8.25 (a 15-cent increment) and the the difference in sequential prices of the pots is 15 cents, the largest pot PROBABLY has a price that is a 15-cent increment. From the answer choices, I would then TEST Answer A first IF.... The largest pot = $1.75 1 1.15 1.3 1.45 1.6 1.75 Total = $8.25 So this MUST be the answer. A

aqua_rat

The speed of light is approximately 1,86 * 10^4 miles per second. This approximate speed is how many miles per hour?

[ "1,11 * 10^7", "6,70 * 10^7", "1,11 * 10^8", "1,86 * 10^8" ]

B

6,70 * 10^7

The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be. (1.86*10^4)*3600 = (1.86*10^4)*(3.6*10^3) = some number*10^7... The key is realizing that thesome numberhas to be bigger thatn 1.86 (because 1.86*3.6), and the only answer that fits that is B

aqua_rat

A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?

[ "5", "6", "7", "8" ]

D

8

Speed = 180/3 = 60 m/sec. Required time = (180 + 300)/60 = 8 sec. Answer:D

aqua_rat

How long will it take a sum of money invested at 6 % p.a. S.I. to increase its value by 60%?

[ "11 years", "12 years", "10 years", "15 years" ]

C

10 years

Sol. Let the sum be x. Then, S.I. = 60% of x = 3x/5; Rate = 6%. âˆ´ Time = [100 * 3x/5 * 1/x*6] = 10 years Answer C

aqua_rat

What number is obtained by adding the units digits of 734^98 and 347^81?

[ "10", "11", "12", "13" ]

D

13

The units digit of 734^98 is 6 because 4 raised to the power of an even integer ends in 6. The units digit of 347^81 is 7 because powers of 7 end in 7, 9, 3 or 1 cyclically. Since 81 is in the form 4n+1, the units digit is 7. Then 6+7 = 13. The answer is D.

aqua_rat

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?

[ "176 km/hr", "189 km/hr", "175 km/hr", "197 km/hr" ]

C

175 km/hr

Let speed of the car be x km/hr. Then, speed of the train = 150/100 x = 3/2 x km/hr. 75/x - 75/(3/2 x) = 125/(10 * 60) 75/x - 50/x = 5/24 = 120 km/hr. Answer:C

aqua_rat

Which of the following is divisible by the first five positive integer multiples of 23? (i) 11110 (ii) 102120 (iii) 307740

[ "None", "iii only", "i and iii only", "ii and iii only" ]

D

ii and iii only

A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 3*4*5*23=60*23=1380. The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380. 102=17*6 and 120=20*6, so 102120=60*(1700+2)=60*1702=60*2*851. Now, 851-30*23=851-690=161=7*23, so 102120 is divisibly by 60*23=1380. Finally, 102120*3=306360, and 306360+1380=307740, so (iii) is also divisible by 1380. Answer D.

aqua_rat