mathewhe/aqua_rat huggingface dataset:
Question: At the Widget factory, 20 percent of the employees are engineers and 50 percent are builders. If there are 57 other employees at the Widget factory, how many total employees work there?
(A)  190
(B)  180
(C)  160
(D)  200
(E)  400
Rationale: Let the total number of employees in the factory be x
% of engineers = 20%
% of builders = 50%
% of other employees = 100% - 70% = 30%
But this number is given as 57
so 30% of x = 57
x = (57)(100/30) = 570/3 = 190
Therefore there a total of 190 employees in the Widget factory.
Correct answer - A
Answer: (A)  190
Question: The value of P, when 4864 x 9P2 is divisible by 12, is:
(A) 2
(B) 5
(C) 8
(D) 9
(E) None of these
Rationale: Since 4864 is divisible by 4, so 9P2 must be divisible by 3.
Therefore (11+P) must be divisible by 3.
Therefore least value of P is 1
Answer: E
Answer: (E) None of these
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone
finishes the remaining work in 42 days. In how much time will A and B, working
together, finish the work?
(A) 30
(B) 120
(C) 150
(D) 41
(E) 50
Rationale: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
ANSWER A
Answer: (A) 30
Question: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?
I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.
I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers
Answer (E).
E is the correct answer
Answer: (E) I and III only
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?
(A) 884
(B) 890
(C) 892
(D) 910
(E) 945
Rationale: Number divisible by 11:-
1000/11= 90
numbers divisible by 35:-
1000/35= 28
Numbers divisible by both 11 and 35= 2
Total numbers divisible by both 11 and 28= 90+28-2= 116 (because we counted 2 in both 90 and 28)
Total numbers not divisible by 11 or 35= 1000-116= 884
Answer : A
Answer: (A) 884
Question: If 8 men or 12 women can do a piece of work in 30 days, in how many days can the same work be done by 6 men and 11 women?
(A) 10 days
(B) 11 days
(C) 13 days
(D) 15 days
(E) 18 days
Rationale: 8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/30
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*30= 1/360
so, 20 women work= 20/360=1/18
ans: 18 days
ANSWER:E
Answer: (E) 18 days
Question: Of a set of 30 numbers, average of 1st 10 numbers is equal to average of last 20 numbers. The sum of last 20 numbers is?
(A) 2 x sum of 1st 60 numbers
(B) 2 x sum of 1st 10 numbers
(C) 2 x sum of 1st 30 numbers
(D) 2 x sum of 1st 20 numbers
(E) 6 x sum of 1st 10 numbers
Rationale: Let average of first 10 numbers is a. Then sum = 10a
Average of last 10 nmbers also a. Then their sum = 20a
From the options B correct
Answer:B
Answer: (B) 2 x sum of 1st 10 numbers
Question: The product of the squares of two positive integers is 100. How many pairs of positive integers satisfy this condition?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Ans: C - 2 pairs
(xˆ2)(yˆ2) = 100 [square root both sides]
xy = 10
10 = 1x10, 10x1, 2x5, 5x2
Cancel the repeats
This leaves us with exactly 2 options.
Hence, C
Answer: (C) 2
Question: What is the sum of 60 consecutive integers from -30 inclusive, in a increasing order?
(A) -29
(B) 29
(C) -30
(D) 30
(E) 60
Rationale: From -39 to -1 --> 30 nos.
zero --> 1 number
from +1 to +29 --> 29 nos.
When we add up nos. from -30 to +29 sum will be -30 for total 60 numbers.
C is the answer.
Answer: (C) -30
Question: A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 156 pounds?
(A) 18
(B) 7
(C) 12
(D) 9
(E) none of the above
Rationale: Ans is A:
39 pounds --> 6 days
91 pounds --> x days
x = 156*6/39 = 24
the animal has already consumed food in 6 days so the the number of
days for it's total consumption be 156 pounds is 24-6 = 18
Answer: (A) 18
Question: John makes $50 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 18%
(D) 21%
(E) 40%
Rationale: Increase = (20/50)*100 = 40%.
E
Answer: (E) 40%
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
(A) 1/20
(B) 7/30
(C) 1/45
(D) 13/56
(E) 12/72
Rationale: Difference of reciprocals means 1 has to be in the numerator;
So option BD can be ignored
For option A, BE, we require to search two consecutive numbers whose product is the denominator
20= 4 * 5 ......... Answer
Answer = A
Answer: (A) 1/20
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
(A) 196
(B) 630
(C) 680
(D) 780
(E) 960
Rationale: L.C.M. of 12, 18, 21 30 2 | 12 - 18 - 21 - 30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3 | 6 - 9 - 21 - 15
----------------------------
Required number = (1260 ÷ 2) | 2 - 3 - 7 - 5
= 630.
Answer: Option B
Answer: (B) 630
Question: The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.
(A) 60 degrees
(B) 120 degrees
(C) 45 degrees
(D) 50 degrees
(E) None of these
Rationale: Solution:
Time is 2:20. Position of the hands: Hour hand at 2 (nearly).
Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees
Answer D
Answer: (D) 50 degrees
Question: A pet groomer has 7 animals to groom for the day (2 cats and 5 dogs). If she randomly selects 4 animals to groom before lunch, what is the probability she will finish all the cats before lunch?
(A) 3/7
(B) 2/7
(C) 12/13
(D) 5/11
(E) 4/7
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 4 animals from 7 animals = 7C4 = 7!/[4!(7 - 4)!] = 35.
To finish all 2 cats there must be 2 dogs, select 2 dogs from 5 = 5C2 = 10.
And, select 2 cats from 2 = 2C2 = 1.
2 cats and 2 dogs = (1)(10) = 10
Probability = (number outcomes favorable)/(total number outcomes) = 10/735 = 2/7
Answer: B
Answer: (B) 2/7
Question: A river 5m deep and 19 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
(A) 4500
(B) 6333
(C) 6576
(D) 6345
(E) 2882
Rationale: (4000 * 5 * 19)/60
= 6333 M3
Answer:B
Answer: (B) 6333
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,000 - 52,800 = 13,200.
Answer: E.
Answer: (E) $13,200
Question: What is the are of an equilateral triangle of side 10 cm?
(A) 25√3
(B) 20√3
(C) 15√3
(D) 30√3
(E) 35√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 10, Area of triangle = √3/4 * 10 * 10
= 25√3 cm2;
Answer:A
Answer: (A) 25√3
Question: Two trains are traveling from point A to point B such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph. Where is the distance b/w A and B such that the slower train reached 5 hrs late compared to the faster?
(A) 3
(B) 65
(C) 9
(D) 5
(E) 31
Rationale: Answer:B
Answer: (B) 65
Question: If m is the average (arithmetic mean) of the first 10 positive multiples of 3 and if M is the median of the first 10 positive multiples of 3, what is the value of M – m ?
(A)  –5
(B)  5
(C)  0
(D)  25
(E)  27.5
Rationale: The first 10 positive multiples of 3 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.
Hence M=m --> M-m=0.
Answer: C.
Answer: (C)  0
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
(A) 15 hours
(B) 16hours
(C) 17 hours
(D) 18 hours
(E) None of these
Rationale: Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
Answer: C
Answer: (C) 17 hours
Question: If 625^(-x) + 25^(-2x) + 5^(-4x) = 10, what is the value of x?
(A) -4
(B) -1/4
(C) 0
(D) 1/4
(E) 4
Rationale: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.
With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.
With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.
With Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.
C
Answer: (C) 0
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 9/8 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 17/35
(E) (e) 3/7
Rationale: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $8. so the large ones would cost $9.
So,
3*8=24 and 2*9=18.
Total revenue was 24+18=42
and Large cup sales as found above is 18
Therefore answer is 18/42 i.e 3/7
E
Answer: (E) (e) 3/7
Question: If a new town has 200 residents, and the population doubles every 10 years, what will be its population after 75 years?
(A) 6034 residents
(B) 9051 residents
(C) 12068 residents
(D) 36204 residents
(E) 18102 residents
Rationale: 200*2^(75/10)=100*2^7.5=200*181.02=36204
The answer is D.
Answer: (D) 36204 residents
Question: Susan weighs 7 pounds more than Anna does, and together they weigh a total of 127 pounds. Which of the following represents Anna’s weight in pounds?
(A) 55
(B) 58
(C) 62
(D) 63
(E) 60
Rationale: Total weight = 127
Anna's weight = 127-7 /2 = 60
Answer : E
Answer: (E) 60
Question: Jim drove 923 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 113 miles
(B) 277 miles
(C) 456miles
(D) 887 miles
(E) 767 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 923 = 277 miles
correct answer B
Answer: (B) 277 miles
Question: An uneducated retailer marks all his goods at 65% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
(A) 12.50 %
(B) 13.50 %
(C) 14 %
(D) 23.75%
(E) None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 165.
S.P. = 75% of Rs. 165 = Rs. 123.75.
∴ Gain% = 23.75%.
Answer D
Answer: (D) 23.75%
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 210 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?
(A) $ 1.50
(B) $ 1.64
(C) $ 2.25
(D) $ 2.50
(E) $ 3.25
Rationale: 7 regular days --> sales = 7*32*x = 224x;
3 hot days --> sales = 3*32*(1.25x) = 120x;
Total sales = 224x+120x = 344x.
Total cost = 10*32*0.75 = 240.
Profit = 344x - 240 = 210 --> x=1.308.
1.25x=~1.64.
Answer: B.
Answer: (B) $ 1.64
Question: A man gains 10% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.
(A) 130%
(B) 120%
(C) 150%
(D) 160%
(E) 170%
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (110/100)x = 11x/10
New S.P. = 2(11x/10) = 22x/10
Profit = 22x/10 - x = 12x/10
Profit% = (Profit/C.P.) * 100
=> (12x/10) * (1/x) * 100 = 120 %
Option B
Answer: (B) 120%
Question: How many odd prime numbers are there less than 150?
(A) 24
(B) 34
(C) 44
(D) 54
(E) 64
Rationale: Odd prime number less than 150:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149
There is 34 the odd prime number
Answer is B
Answer: (B) 34
Question: A can run 4 times as fast as B and gives B a start of 69 m. How long should the race course be so that A and B might reach in the same time?
(A) 70 m
(B) 60 m
(C) 80 m
(D) 65 m
(E) 92 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 69m he gains 69*(4/3)
I.e 92m
ANSWER:E
Answer: (E) 92 m
Question: On dividing a number by 5, we get 2 as quotient and 0 as remainder. On dividing the same number by 4, what will be the remainder?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Number = 5 * 2 + 0 = 10
4) 10(2
8
--------
2
Required number = 2.
ANSWER:C
Answer: (C) 2
Question: On 8th Feb,2005 it was Tuesday.What was the day of the week on 8th Feb,2004 ?
(A) Tuesday
(B) Monday
(C) Sunday
(D) Wednesday
(E) None of these
Rationale: The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday. Option C
Answer: (C) Sunday
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
(A) 228
(B) 279
(C) 280
(D) 500
(E) 288
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer: D
Answer: (D) 500
Question: In a certain book club, the members are voting between two books – a mystery novel and a biography – to decide which book the group will read next. There are 2 times as many votes for the mystery novel as there are votes for the biography. The ratio of biography votes to the mystery votes is
(A) 3 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 1 to 2
Rationale: IMO : Answer E 1 to 4
Answer: (E) 1 to 2
Question: A certain bridge is 3,124 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 5 miles per hour? (1 mile = 5,280 feet)
(A)  1
(B)  2
(C)  4
(D)  6
(E)  7
Rationale: Distance: 3124 feet. This is (3124/5280) miles = 0.59 miles
Speed: 5 miles per hour
Time: (Distance / Speed) (0.59/5) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 7.08 minutes.
Answer to be 7 minutes.
ANS E
Answer: (E)  7
Question: Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
(A) 670
(B) 664
(C) 698
(D) 744
(E) 700
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 854 - 815 = 39
Interest earned for 3 years = 39*3 = 117
Amount invested = 815 - 117 = 698
Answer: C
Answer: (C) 698
Question: P is four times as old as Q, and Q is four years older than R. If R is z years old, what is P’s age in terms of z?
(A) 4z + 16
(B) 4z + 4
(C) (z+4) / 4
(D) 4z - 4
(E) 4z - 16
Rationale: P = 4Q
Q = R+4 = z+4
P = 4(z+4) = 4z + 16
The answer is A.
Answer: (A) 4z + 16
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 47 percent were employees. What percent were stockholders, who were not employees?
(A) 52
(B) 53
(C) 54
(D) 55
(E) 56
Rationale: 100 = 62 + 47 - n(SnE) [where n represents intersection]
=> n(SnE) = 9
=> Number who were only stockholders = n(S) - n(SnE) = 53 percent
Option (B)
Answer: (B) 53
Question: In a phase III clinical trial of Dosaxin, a new drug, patients received a progressively growing dosage of Dosaxin for a few days. On the first day, each patient received 15 milligrams of Dosaxin. On each of the following days, the daily dosage was m milligrams greater than the dosage received the day before, reaching a dosage of 43 milligram on the last day of the trial. For how many days did the trial last, if each patient received a total amount of 145 milligrams of Dosaxin during the whole trial ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: Its an arithmetic sequence where the first term is 15 and the last term is given as 43. We are also given the sum of the series as 145.
Sum of series = n*(a + l)/2
145 = n(15+43)/2
Solving for n, we get n = 5
Option B
Answer: (B) 5
Question: If n is a positive integer, which one of the following numbers must have a remainder of 1 when
divided by any of the numbers 4, 5, and 6?
(A) 12n + 1
(B) 24n + 1
(C) 80n + 1
(D) 90n + 1
(E) 120n + 1
Rationale: The numbers 4, 5, and 6 all divide 120 so they all divide 120n.
When we divide (120n + 1) by 4, 5, or 6, the remainder must be 1.
The answer is E.
Answer: (E) 120n + 1
Question: R-R-G-G-Y-Y-B-R-R-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
(A) 65
(B) 66
(C) 67
(D) 68
(E) 69
Rationale: The repeated pattern R-R-G-G-Y-Y-B has 7 beads.
But the missing section includes R-R-G-G-Y-Y at the end.
Thus the number of beads in the missing section has the form 7k + 6.
The answer is E.
Answer: (E) 69
Question: David buys 100 shares of par value Rs. 8 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
(A) 2
(B) 4
(C) 5
(D) 6
(E) 9.6
Rationale: Face value of each share = Rs.8
Total dividend received by David = 100Ã—8Ã—12/100 = Rs.96
Let market value of 100 shares = Rs.x
xÃ—10/100=96
x = 960
ie, Market value of 100 shares = Rs.960
Hence, Market value of each share = Rs.9.60
Answer is E
Answer: (E) 9.6
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 6 months
(B) 8 months
(C) 10 months
(D) 7 months
(E) 12 months
Rationale: Explanation:
7 * 8 : 9 * x = 8:9 => x= 7
ANSWER IS D
Answer: (D) 7 months
Question: A can finish a work in 4 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
(A) 1/4
(B) 1/6
(C) 1/7
(D) 3/4
(E) None of these
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/4
B's 1 day work = 1/2 [because B take half the time than A]
(A+B)'s one day work =
(1/4+1/2)=3/4
So in one day 3/4 work will be done
Answer: D
Answer: (D) 3/4
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 29
(B) 67
(C) 90
(D) 86
(E) 17
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer:C
Answer: (C) 90
Question: A bag contains 2 red, 3 green and 2 yellow balls. Two balls are drawn at random. What is the probability that none of the balls drawn is yellow?
(A) 10/15
(B) 10
(C) 11
(D) 10/21
(E) 10/23
Rationale: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7
= 7C2 `
= (7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is yellow.
n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
= (5 x 4)/(2 x 1)
= 10.
P(E) = n(E)/n(S) = 10/21
Hence answer is D
Answer: (D) 10/21
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of y?
(A)  50
(B)  100
(C)  200
(D)  1,000
(E)  2,000
Rationale: y = 50% of 50% 0f x
= x/4
and
y/100 of x = 100
y /100 *4y =100
y = 50
Answer - A
Answer: (A)  50
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 3 1/2 hours
(B) 5 1/2 hours
(C) 2 1/2 hours
(D) 7 1/2 hours
(E) 9 1/2 hours
Rationale: C
Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours
Answer: (C) 2 1/2 hours
Question: the dairy condensed milk has only 20% water while the cow milk has 90% water. How many litres of milkmaid will be obtained from 72 litres of milk?
(A) 7.2l
(B) 8.2l
(C) 9l
(D) 14.4l
(E) 15.4l
Rationale: milk in 72 liters is7.2l (10%)
now 80% of x=7.2
so answer is 9L
ANSWER:C
Answer: (C) 9l
Question: If y ≠ 3 and 2 x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None
(B) I only
(C) II only
(D) III only
(E) I and II
Rationale: Let 2 x/Y = K , Where k is a prime number > 2 ( 3, 5, 7, 11 ...etc)
so 2x = Ky --> ( 3y or 5y or 7y or 11y etc...)
Which implies always X > Y
So answer is (A)
Answer: (A) None
Question: A certain ski shop sells pairs of gloves in 16 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
(A) 1/144
(B) 1/31
(C) 1/24
(D) 1/23
(E) 1/12
Rationale: there are 16 different colours sothere are 16 pairs of gloves dropped..
first can be any of 32..so 32/32..
second has to be its pair, which will be just one out of remaining 31.. 1/31..
overall prob=32/32*1/31= 1/31..
B
Answer: (B) 1/31
Question: Seven years ago the average age of a family of 2 members was 32 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
(A) 40years
(B) 46years
(C) 50years
(D) 52years
(E) 55years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 32
= (32+ 7) * 2 = 46 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 64 = 5 years
Answer: Option B
Answer: (B) 46years