mathewhe/aqua_rat huggingface dataset:
Question: The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from
(A) 5 to 7
(B) 5 to 8
(C) 5 to 9
(D) 6 to 8
(E) 6 to 9
Rationale: The sum of the length of the remaining sides must be 45 - (5 + 10) = 30.
We can have 5-sided polygon {5,10, 10, 10,10} (we cannot increase the length of any side to reduce the number of sides);
We can have 6-sided polygon {5,5, 5, 10, 10,10};
We can have 7-sided polygon {5,5, 5, 5, 5, 10,10};
We can have 8-sided polygon {5,5, 5, 5, 5, 5, 5,10} (we cannot decrease the length of any side to increase the number of sides).
Answer: B.
Answer: (B) 5 to 8
Question: A train 75m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 35kmph
(B) 40kmph
(C) 45kmph
(D) 50kmph
(E) 55kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
75/[(x+5)*5/18] = 6
30(x+5) = 1350
x = 40kmph
Answer is B
Answer: (B) 40kmph
Question: If shares of two persons in profits are Rs.400 and Rs.1200 then ratio of their capitals is
(A) 3:4
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:2
Rationale: profit=time*capital
so 400:1200=1:3
ANSWER:D
Answer: (D) 1:3
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 9 a.m
(B) 8 a.m
(C) 7 a.m
(D) 6 a.m
(E) 5 a.m
Rationale: A
9 a.m.
Answer: (A) 9 a.m
Question: A,B,C together can do a work in 16 days. A alone can do the work in 64 days and B alone can do the same work in 80 days. Find in what time C alone can do that work?
(A) 24days
(B) 29.50days
(C) 33.59days
(D) 29.09days
(E) 38.80days
Rationale: The required answer is = 16*64*80 / 64*80-16(64+80)
= 81920/2816 = 29.09days
Answer is D
Answer: (D) 29.09days
Question: A baseball card decreased in value 20% in its first year and 20% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32%
(D) 36%
(E) 72%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.8 = 80
After second year price = 80 *0.8 = 64
final decrease = [(100 - 64)/100] * 100 = 36%
correct answer - D
Answer: (D) 36%
Question: Dividing by 3⁄8 and then multiplying by 5⁄9 is the same as dividing by what number?
(A) 31⁄5
(B) 16⁄5
(C) 20⁄9
(D) 40/27
(E) 5⁄16
Rationale: say X/3/8*5/9 = x*8/3*5/9 = x*40/27
D
Answer: (D) 40/27
Question: Look at this series: 80, 10, 70, 15, 60, ... What number should come next?
(A) 20
(B) 25
(C) 30
(D) 50
(E) None
Rationale: Explanation: This is an alternating addition and subtraction series. In the first pattern, 10 is subtracted from each number to arrive at the next. In the second, 5 is added to each number to arrive at the next.
Answer: Option A
Answer: (A) 20
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
(A) 7:2
(B) 7:8
(C) 7:4
(D) 7:6
(E) 7:1
Rationale: Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7:6
Answer: D
Answer: (D) 7:6
Question: When the integer z is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2z
II. 6z
III. 4z + 6
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I, II, and III
Rationale: is it E.
z= 12*a + 3
2z = 12*2*a + 6
6z = 12*6*a + 18 ( 18 = 12+6)
4z + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: (E)  I, II, and III
Question: A certain lab experiments with white and brown mice only. In one experiment, 4/9 of the mice are brown. If there are 20 brown mice in the experiment, how many mice in total are in the experiment?
(A) 32
(B) 26
(C) 36
(D) 28
(E) 24
Rationale: Let total number of mice = M
Number of brown mice = 4/9 M
Number of white mice = 5/9 M = 20
=> M = 36
Answer C
Answer: (C) 36
Question: The sides of a rectangular region measured to the nearest centimeter are 9 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ?
(A) 48
(B) 55.25
(C) 52.29
(D) 59.66
(E) 41.25
Rationale: acan be anywhere between 8.5 and 9.4 andbcan be anywhere between 5.5 and 6.4.
Hence max area can be 9.4*6.4 eq 60.16.
largest value which is near to 60.16 is 59.66.
Hence D.
Answer: (D) 59.66
Question: How many halves are there in six-fourth?
(A) 8
(B) 12
(C) 32
(D) 7
(E) 3
Rationale: divide 6/4 by 1/2
=6/4÷1/2
=6/4*2/1
=12/4
=3.
Answer is E.
Answer: (E) 3
Question: Mudit's age 26 years hence will be thrice his age four years ago. Find Mudit's present age?
(A) 12
(B) 22
(C) 19
(D) 18
(E) 15
Rationale: Explanation:
Let Mudit's present age be 'm' years.
m + 26 = 3(m - 4)
=> 2m = 38 => m = 19 years.
Answer:C
Answer: (C) 19
Question: What is the unit digit of (6!*6! / 6!*3!)?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (6!*6! /6!*3!)
=(6! / 3!)
=720/6
=120
Units digit of the above product will be equal to 0
Answer A
Answer: (A) 0
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 350 more than A :
(A) 10150
(B) 7250
(C) 2767
(D) 1998
(E) 2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 350
Total earning = \inline \frac{58xy}{100} = 10150
Answer: A) Rs.10150
Answer: (A) 10150
Question: What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks ?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 1
Rationale: 3 Ducks
ANSWER:A
Answer: (A) 3
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 1/1%
(C) 33 1/3%
(D) 33 2/3%
(E) 32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: One boy forgot the last digit of a 7 digit no. If he randomly dialthe final 3 digits aftercorrectly dialing the 1st 4, then what is the chance of dialing the correct no.?
(A) 1/890
(B) 2/465
(C) 1/1000
(D) 1/3453
(E) 2/1454
Rationale: it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C
Answer: (C) 1/1000
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 76
(B) 88
(C) 66
(D) 55
(E) 35
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E
Answer: (E) 35
Question: The average length of 6 bars is 80 cm. If the average length of one third of the barsis 70 cm, what is the average of the other bars?
(A) 75.
(B) 85.
(C) 90.
(D) 94.
(E) 100.
Rationale: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third barsis 70. That means out 6 / 3 = 2 bars.
let the avg length of two barsbe ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining bars.
IMO correct option is B.
Answer: (B) 85.
Question: Two boys started running simultaneously around a circular track of length 4800 m from the same point at speeds of 60 km/hr and 100 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 105
(B) 106
(C) 107
(D) 108
(E) 109
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 4800 / (60 + 100)5/18 = 4800* 18 / 160 * 5 = 108 seconds.
Answer:D
Answer: (D) 108
Question: A person has in is bag 14 notes of Rs. 10 each, 9 notes of Rs. 5 each, 4 notes of Rs. 2 each and 7 notes of Re 1 each. In how many different ways can be contribute to a charitable find?
(A) 599
(B) 5999
(C) 3528
(D) 600
(E) 700
Rationale: As per the questions,
14 notes of Rs10...so person can contribute
Rs10 note in 14 ways.if person dont give Rs
10 note then number of ways of
contribution are 14+1=15.
9 notes of Rs 5...so person can contribute
Rs5 note in 9 ways.if person dont give Rs
10 note then number of ways of
contribution are 9+1=10.
and so on..
SO the number of ways can be contribute
to a charitable fund
15*10*5*8-1=5999
ANSWER:B
Answer: (B) 5999
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.14 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1276
(B) 1680
(C) 2832
(D) 1299
(E) 1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 14 = 1680
Answer: Option B
Answer: (B) 1680
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/6
(B) 17 1/9
(C) 17 1/7
(D) 17 1/5
(E) 17 1/1
Rationale: 1/20 + 1/30 - 1/40 = 7/120
120/7
= 17 1/7
Answer:C
Answer: (C) 17 1/7
Question: In a forest 250 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
(A) 150
(B) 750
(C) 1,250
(D) 1,500
(E) 2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 250 tagged deers comprise 10% of total # of deers --> total # of deers =250*10 = 2,500.
Answer: E
Answer: (E) 2,500
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p?
(A) p
(B) 2p
(C) 5p
(D) 7p
(E) p^2
Rationale: Y=30p
other number is 5p
then GCF(30p,5P)=5P; C is the correct answer
Answer: (C) 5p
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.57. How much did the meal cost without the tip?
(A) $31.80
(B) $29.91
(C) $30.15
(D) $30.60
(E) $30.85
Rationale: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $36.57:
1.15x = 36.57
Divide both sides by 1.15:=>x=36.57/1.15=31.80
correct answer A)$31.80
Answer: (A) $31.80
Question: A, B and C started a partnership business by investing Rs.27000, Rs.72000, Rs.81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
(A) 70000
(B) 60000
(C) 80000
(D) 90000
(E) 50000
Rationale: A:B:C =27000:72000:81000
=3:8:9
Let total profit =p
Then p×9/20=36000
p=(36000×20)/9=80000
Answer is C.
Answer: (C) 80000
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 115
(B) 135
(C) 155
(D) 175
(E) 195
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 645.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 645 - (P + Q + R) = 350
Average of the last two numbers = (S + T)/2 = 175.
ANSWER:D
Answer: (D) 175
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 10 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 15 litres
(B) 10 litres
(C) 30 litres
(D) 20 litres
(E) 8 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+10)=4/5
20x=4(3x+10)
8x=40
x=5
Quantity of alcohol = (4 x 5) litres = 20 litres.
Answer is D.
Answer: (D) 20 litres
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and white. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
(A) 12
(B) 14
(C) 18
(D) 19
(E) 20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, white) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: (D) 19
Question: When a certain shoe store reduces the price of its best-selling style of shoe by 10 percent, the weekly sales of this style increase by 30 percent. Which of the following best describes the resulting change in the store's weekly revenue from sales of this style of shoe?
(A) Revenue decreases by 10%
(B) Revenue decreases by 1%
(C) There is no change in revenue
(D) Revenue increases by 17%
(E) Revenue increases by 10%
Rationale: Old price = 10, old sales = 10 --> old revenue = 100;
New price = 9, new sales = 13 --> new revenue = 117.
Revenue increased by 17%.
Answer: D.
Answer: (D) Revenue increases by 17%
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 28% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
(A) 25%
(B) 30%
(C) 50%
(D) 55%
(E) 75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.28N
x = 0.7N
The percentage of rooms which permit smoking is 1 - 0.7 = 30%
The answer is B.
Answer: (B) 30%
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 6 buckles is how many times that of 5 buckles and 6 buttons?
(A) 7/15
(B) 2/5
(C) 8/15
(D) 3/5
(E) 11/15
Rationale: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 6y = a(6x+5y)
11y = a(15y)
a = 11/15
The answer is E.
Answer: (E) 11/15
Question: Calculate the ratio between x and y if 80% of x equal to 20% of y?
(A) 1 : 1
(B) 3 : 1
(C) 4 : 5
(D) 4 : 3
(E) 4 : 1
Rationale: Explanation:
80 x = 20 y
x: y = 80: 20 = 4 : 1
Answer:E
Answer: (E) 4 : 1
Question: The number of ways in which a couple can sit around a table with 6 guests if the couple take consecutive seat is
(A) 1440
(B) 720
(C) 5040
(D) None of these
(E) Cannot be determined
Rationale: Solution
A couple and 6 guests can be arranged in (7 – 1) ways. But in two people forming the couple can be arranged among themselves in 2! ways.
∴ the required number of ways = 6! × 2! = 1440
Answer A
Answer: (A) 1440
Question: A clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?
(A) 9 p.m
(B) 10 p.m
(C) 11 p.m
(D) 12 p.m
(E) none
Rationale: Solution
Time from 5 a.m on a day to 10 p.m.on 4th day	= 89 hours.
Now 23 hrs 44 min. of this clock	= 24 hours of correct clock.
Therefore 356 / 15 hrs of this clock	= 24 hours of correct clock.
89 hrs of this clock	= (24 x 15/356 x 89) hrs
= 90 hrs
So, the correct time is	11 p.m.
Answer C
Answer: (C) 11 p.m
Question: There are 8 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
(A) 15
(B) 16
(C) 28
(D) 56
(E) 64
Rationale: Every team plays with 7 teams...so total no of matches = 8 x 7 = 56.
Now, each match is played twice => 56 x 2
But 2 teams play a match => 56 x 2 /2 = 56.
ANS:D
Answer: (D) 56
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
(A) 380
(B) 395
(C) 400
(D) 425
(E) 482
Rationale: Let the numbers be x and y.
Then, xy = 9375 and	x	= 15.
y
xy	=	9375
(x/y)	15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
Answer:C
Answer: (C) 400
Question: Last year, sales at Company Zora were 10% greater in February than in January, 10% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?
(A) March
(B) April
(C) May
(D) June
(E) February
Rationale: Jan = $100
10% greater in February than in January ---> Feb = $110
10% less in March than in Feb ---> Mar = $99
20% greater in April than in March ---> Apr = $118.80
10% less in May than in April ---> May $106.92
10% greater in June than in May --->Jun = $117.61
Answer : A
Answer: (A) March
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 80%
(B) 49%
(C) 40%
(D) 70%
(E) 90%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer:C
Answer: (C) 40%
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 2,40,000 earned at the end of 3 years from the start of the business in 2010?
(A) Rs.45000
(B) Rs.50000
(C) Rs.60000
(D) Rs.80000
(E) None of these
Rationale: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 240000 x 2/6
= Rs. 80000.
Answer : D
Answer: (D) Rs.80000
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a seven-percent vinegar solution, what was the concentration of the original solution?
(A) 19.3%
(B) 17%
(C) 36.17%
(D) 15.5%
(E) 12.5%
Rationale: 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 7%, thus (12 - X)/62 = 7/100
From this equation X = 7.66
Answer (12-7.66)/12 = 36.17%
ANSWER:C
Answer: (C) 36.17%
Question: In what time will a train 175 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.58 sec
(B) 2.91 sec
(C) 4.37 sec
(D) 2.9 sec
(E) 1.8 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 175/40
= 4.37 sec.
Answer:C
Answer: (C) 4.37 sec
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 1/2
(B) 16/19
(C) 4/5
(D) 17/20
(E) 3/5
Rationale: Explanation:
n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(Eá´œP) = 10/20 + 8/20 - 1/20 = 17/20
ANSWER IS D
Answer: (D) 17/20
Question: What is the equation of the line that goes through (–2, 3) and (5, –4)?
(A) y = –x + 1
(B) y = x + 5
(C) y = –3x/7 + 15/7
(D) y = –4x/3 + 1/3
(E) y = 9x/5 + 33/5
Rationale: Here, we will follow the procedure we demonstrated in the last section. Call (–2, 3) the “first” point and (5, –4), the “second.” Rise = –4 – 3 = –7. Run = 5 – (–2) = 7. Slope = rise/run = –7/7 = –1.
Yes, it makes sense that the slope is negative. We have the slope, so plug m = –1 and (x, y) = (–2, 3) into y = mx + b:
3 = (–1)*(–2) + b
3 = 2 + b
1 = b
So, plugging in m = –1 and b = 1, we get an equation y = –x + 1. Answer = A
Answer: (A) y = –x + 1
Question: In a certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?
(A) 15/18
(B) 7/18
(C) 17/18
(D) 6/18
(E) 11/18
Rationale: Let the total no of workers be x
No of women =x/3
No of men =x-(x/3)=2x/3
No of women having children =1/3 of ½ ofx/3=x/18
No of men having children=2/3 of ¾ of2x/3=x/3
No of workers having children = x/8 +x/3=7x/18
Workers having no children=x-7x/18=11x/18=11/18 of all workers
Answer is E.
Answer: (E) 11/18
Question: If g > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - g) =
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4
(E) 1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have g-x=2t. So y-x=-t, y-g=-3t. ---> (y - x)/(y - g) = 1/3.
The answer is (B).
Answer: (B) 1/3
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 45 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
(A) 80
(B) 360
(C) 120
(D) 144
(E) 240
Rationale: A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.
If 2x = 45 then 16x = 360;
If 3x = 45 then 16x = 240;
If 5x = 45 then 16x = 144;
If 6x = 45 then 16x = 120;
Only answer choices which is not obtained is 80.
Answer: A.
Answer: (A) 80
Question: One hour after Yolanda started walking from X to Y, a distance of 24 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 12
Rationale: When B started walking Y already has covered 3 miles out of 24, hence the distance at that time between them was 24-3=21 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 21/7=3 hours. In 6 hours B walked 3*4=12 miles.
Answer: E.
Answer: (E) 12
Question: If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - x - w ?
(A) -4
(B) -2
(C) -1
(D) 0
(E) 3
Rationale: Given:w, x, and y are consecutive odd positive integers and w < x < y
Let take value of X as a ; value of y=x+2(consecutive odd integer) ; and w=x-2
So;
y-x-w = x+2 - x - (X+2)
therefore , y-x-w = 4-x
Now,
X is odd and x>= 3
so x can assume values= 3,5,7 ...
therefore when x=5
4-5= -1
ANSWER:C
Answer: (C) -1
Question: The population of a town is 189400. If it increase at the rate of 6% per annum. What will be its population for 2years hence?
(A) 200000
(B) 215600
(C) 194582
(D) 212809
(E) 215460
Rationale: population after 2years = 189400*(1+ 6/100)^2 = 212809
Answer is D
Answer: (D) 212809
Question: a,b,c,d,e,f,g,h sitting in a row what is the probability that a,b,c sitting together?
(A) 3/14
(B) 5/28
(C) 3/28
(D) 1/7
(E) 9/28
Rationale: total number of arrangement is= 8!= 40320
Favorable event i.e)a,b and c can be arranged in 3! and the remaining can be arranged in 6! since ab can be in any of the four positions.
so 3!*6!/8! = 3/28
ANSWER:C
Answer: (C) 3/28
Question: It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 2.5 cms, How much did it rain on Wednesday?
(A) 10.9
(B) 10.5
(C) 8.75
(D) 10.1
(E) 10.6
Rationale: Explanation:
Let the rainfall on wednesday = 6x.
âˆ´ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 2.5
â‡’12x = 17.5
â‡’6x = 8.75
Answer: C
Answer: (C) 8.75