mathewhe/aqua_rat huggingface dataset:
Question: The expression (5x-2)/(x+1) is equivalent to which of the following?
(A) (5-2)/3
(B) 5 – (2/3)
(C) 5 – (x)/(x+3)
(D) 5 – (17)/(x+3)
(E) 5 - (7)/(x+3)
Rationale: Easiest way is to pick any number and put in (5x-2)/(x+3). Then check the options with the same number.
I took x=1 and got E as the answer.
Answer: (E) 5 - (7)/(x+3)
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 20% lemonade syrup?
(A) 1.5
(B) 1.75
(C) 2.14
(D) 2.34
(E) 2.64
Rationale: Let the total solution is 150 L with 80 L water70 L syrup.
To make 20% syrup solution, the result solution must have 120 L syrup and 30 L syrup.
Therefore we are taking 40 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
40 L syrup in 85.7 L solution
We started by multiplying 10
Now to get to the result we need to divide by 40 => amount of solution to be replaced with water = (85.7/40) = 2.14.
Correct option : C
Answer: (C) 2.14
Question: A certain research group plans to create computer models of x% of a list of 10,000 bacterial species known to inhabit the human body. After a budget cut, the group finds it must reduce this selection by (x − 10)%. In terms of x, how many species of bacteria will the group be able to model?
(A) x*x – 5x
(B) (x)(105 – x)
(C) (100)(105 – x)
(D) (100)(95 – x)
(E) (x)*(110 - x)
Rationale: Initial: (x/100)*10000 = 100x (bacterial species)
After reduce BY (x - 10)%, the percentage of bacterial species = 1 - (x - 10)% = 1 - (x - 10)/100 = (110 - x)/100
Note: Difference between reduce to[means: the remain] and reduce by[means: the remain = 1 -reduce by]
So, the number of bacterial species after reducing: 100x*(110 - x)/100 = (x)*(110 - x)
Ans is E.
Answer: (E) (x)*(110 - x)
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability Q that at least one will be orange?
(A) Q=7/10
(B) Q=3/5
(C) Q=2/5
(D) 3/10
(E) 1/10
Rationale: Method 1
Probability Q that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue)*P(Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: (A) Q=7/10
Question: A car covers a distance of 690 km in 6 hours. Find its speed?
(A) 104
(B) 115
(C) 266
(D) 288
(E) 121
Rationale: 690/6 = 115 kmph
Answer:B
Answer: (B) 115
Question: A sum is divided between A and B in the ratio of 1 : 2. A purchased a car from his part, which depreciates 14 2/7% per annum and B deposited his amount in a bank, which pays him 20% interest per annum compounded annually. By what percentage will the total sum of money increase after two years due to this investment pattern (approximately).
(A) 22.48%
(B) 20.48%
(C) 24.48%
(D) 25.48%
(E) 26.48%
Rationale: Let the total money=300
A's part=100
B's part=200
After 2 years A's part=73.46 (As it depreciates by 14.29% per annum)
After 2 years B's part=288 (using the compound interest formula, A=P(1+r/n)^nt), where
P=200,r=0.2,n=1,t=2)
So, After 2 years total amount=361.46
Therefore % increase in money=(361.46-300)*100/300=20.48%
ANSWER:B
Answer: (B) 20.48%
Question: A person travelled from his house to office at 40km/hr and office to house at 60km/hr. Then find the average speed?
(A) 30km/hr
(B) 40km/hr
(C) 48km/hr
(D) 50km/hr
(E) 62km/hr
Rationale: Average speed = (2*40*60)/(40+60)
= 48km/hr
Answer is C
Answer: (C) 48km/hr
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is not a face card?
(A) 4/15
(B) 5/17
(C) 9/13
(D) 3/13
(E) 7/15
Rationale: Out of 52 cards there will be 16 face cards are there.
probability of getting not a face card = 36/52 = 9/13
Answer is C
Answer: (C) 9/13
Question: Which of the following is a terminating decimal, when expressed in decimals?
(A) 17/223
(B) 13/231
(C) 41/3
(D) 41/256
(E) 35/324
Rationale: The fraction a/b is a terminating fraction only if the denominator b meets any of following conditions
(1) the denominator is a form of 2^n
(2) the denominator is a form of 5^m
(3) the denominator is a form of 2^n*5^m
If the denominator is a form of 2^n*3^m ==> The fraction is not terminating decimal.
ANSWER:D
Answer: (D) 41/256
Question: How many different ways can you select a pilot and a co pilot if you have 50 people to choose from?
(A)  199
(B)  200
(C)  2450
(D)  4950
(E)  9900
Rationale: You are not just choosing two from 50. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (50C2) x 2 = 2450.
Ans C
Answer: (C)  2450
Question: A leak at the bottom of the tank can empty the tank in 5 hours, while an inlet pipe can fill the same tank at the rate of 6 litres per minute. When the tank is full, the inlet is opened and the tank gets empty in 8 hours due to the leakage. Find the capacity of the tank.
(A) 1800 litres
(B) 3600 litres
(C) 4800 litres
(D) 5760 litres
(E) None of these
Rationale: Explanation:
The capacity of the tank is given by C = (p*q*r)/(r – p) litres
Where, p = time in which the leakage can empty the tank in hours = 5 hours
q = rate at which the inlet fills the tank in lph = 6*60 = 360 lph
r = time in which the tank gets emptied in hours = 8 hours
Hence, C = (5*360*8)/(8 – 5)
C = 4800 litres
ANSWER C
Answer: (C) 4800 litres
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,600 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
(A) 25.0
(B) 30.3
(C) 35.2
(D) 40.4
(E) 67.6
Rationale: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1600
r=67.6
Answer:E
Answer: (E) 67.6
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 250 m and they cross each other in 10 sec, then the speed of each train is?
(A) 30
(B) 31
(C) 36
(D) 25
(E) 90
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (250 + 250)/10 => x =25
Speed of each train = 25 m/sec.
= 25 * 18/5 =90 km/hr.
Answer: Option E
Answer: (E) 90
Question: A rectangular plot measuring 10 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
(A) 46m
(B) 66m
(C) 26m
(D) 24m
(E) 25m
Rationale: Perimeter of the plot = 2(10+50) = 120m
no of poles =120/5 =24m
Answer: D
Answer: (D) 24m
Question: In a certain code language, 'book' is coded as 'pencil', 'pencil' is coded as 'mirror', 'mirror' is coded as 'board'. Then what is useful to write on a paper?
(A) 2
(B) 6278
(C) 277
(D) 281
(E) 22
Rationale: We use pencil to write on a paper but here pencil is coded as mirror. So, the answer is mirror.
Answer:A
Answer: (A) 2
Question: Each side of a certain parallelogram has length 4. If the area of the parallelogram is 12. Which of the following is the measure of one of its angles?
(A) 30
(B) 48.6
(C) 60
(D) 90
(E) 120
Rationale: area of a parallelogram = b*h
b*h=12
h=12/4=3
sin theta =opp/hyp= 3/4
theta = sin inv of 3/4=48.6 deg
B
Answer: (B) 48.6
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1206. Find the number to be multiplied.
(A) 130
(B) 132
(C) 134
(D) 136
(E) 138
Rationale: Let the required number be x. Then,
43x – 34x = 1206 or 9x = 1206 or x = 134.
Required number = 134.
ANSWER:C
Answer: (C) 134
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.80 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
(A) a) $ 1.80
(B) b) $ 2.00
(C) c) $ 2.40
(D) d) $ 2.70
(E) e) $ 3.00
Rationale: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.8*1.5 = $2.7.
Answer: D.
Answer: (D) d) $ 2.70
Question: The sum of the first 50 positive even integers is 2550. What is the sum Q of even integers from 102 to 200 inclusive?
(A) 5100
(B) 7550
(C) 10100
(D) 15500
(E) 20100
Rationale: My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
Q=2550+(100*50)=7550.B
Answer: (B) 7550
Question: What is the smallest positive perfect square that is divisible by 12, 15, and 18?
(A) 900
(B) 1,600
(C) 2,500
(D) 3,600
(E) 4,900
Rationale: Take the LCM of 12,15,18 that will come 180. the smallest positive perfect square given in the option that can be divided with 180 is 900.
so the ans is (A)
Answer: (A) 900
Question: The volume of a cistern is 840 cubic meters and water is flowing into the cistern. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate, in cubic meters per minutes, at which the water is flowing into the cistern?
(A) 0.125
(B) 0.25
(C) 0.5
(D) 0.75
(E) Not enough information to determine the rate
Rationale: There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate.
The correct answer is E.
Answer: (E) Not enough information to determine the rate
Question: Calculate the amount that an investor needs to be invest to earn approximately $1076 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 10% compounded semi-annually?
(A) 10500
(B) 16576
(C) 10100
(D) 13500
(E) 11500
Rationale: the approach is substitution,
our interest requirement is $1076 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields 460 in 12 months
10500 yielded $1076
using the formula
A = P(1 + r/n)nt
hence answer is A
Answer: (A) 10500
Question: A rectangular table, kept against a wall has a three sides free and the wall along the fourth side. The side opposite the wall is twice the length of each of the other two free sides. If the area of the rectangular table is 128 square feet, what is the total length of the table free sides, in feet?
(A) 4
(B) 8
(C) 16
(D) 32
(E) 64
Rationale: two sides EACH = x the third = 2x and the wall side is thus 2x too
x*2x = 2x^2 = 128 ie x^2 = 64 ie x = 8
L = 16 W=8
TOTAL LENGHT OF table's free sides = 2*8+16 = 32
MY ANSWER IS D
Answer: (D) 32
Question: A horse has 14 apples, then he finds 7 more apples. Now how many apples does he have?
(A) A)24
(B) B)21
(C) C)7
(D) D)18
(E) E)12
Rationale: 14+7=21. Answer is B
Answer: (B) B)21
Question: Two persons start running simultaneously around a circular track of length 100 m from the same point at speeds of 10 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 20 sec
(B) 12 sec
(C) 19 sec
(D) 32 sec
(E) 28 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 100 / (10 + 20)5/18 = 100 x 18 / 30 x 5 = 12 seconds.
Answer: B
Answer: (B) 12 sec
Question: Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years.
(A) Rupees 1052
(B) Rs 1152
(C) Rs 1252
(D) Rs 1352
(E) None of these
Rationale: Explanation:
S.I. = 956 - 800 = Rs 156
R=156∗100 /800∗3
R=6 1/2%
New Rate = 6 1/2+4
=21/2%
New S.I. = 800×21/2×3100=252
Now amount will be 800 + 252 = 1052
Option A
Answer: (A) Rupees 1052
Question: The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 90 black cars in the lot, how many red cars are there in the lot?
(A) 11
(B) 33
(C) 24
(D) 31
(E) 32
Rationale: R/B = 3/8 and B =90
R = 90*3/8 = 33
Answer: (B) 33
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 30%
(B) 50%
(C) 70%
(D) 60%
(E) 80%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: If x and y are integers, what is the least positive number of 24x+18y?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: 24x+21y = 6(4x+3y) which will be a minimum positive number when 4x+3y = 1.
4(1) + 3(-1) = 1
Then 6(4x+3y) can have a minimum positive value of 6.
The answer is B.
Answer: (B) 6
Question: There are 24 students in Chadâ€™s class. He brought 28 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
(A) 1-9
(B) 1-7
(C) 2-8
(D) 1-4
(E) 3-10
Rationale: 28/24 = 1 R 4 Chad will give each student 1 cookie and there will be 4
cookies left over
correct answer D
Answer: (D) 1-4
Question: A woman complete a journey in 25 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 334 km.
(B) 216 km.
(C) 314 km.
(D) 224 km.
(E) 560 km.
Rationale: 0.5x/21 + 0.5x/24 = 25
--> x/21 + x/24 = 50
--> x = 560 km.
E
Answer: (E) 560 km.
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 39 km
(B) 76 km
(C) 25 km
(D) 15 km
(E) 30 km
Rationale: A
39 km
The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km.
Answer: (A) 39 km
Question: Find the percentage gain if a shop owner sells 39 mtr of fabric and gains Cost Price of 12 meters?
(A) 20.5%
(B) 23.5%
(C) 21.5%
(D) 13.5%
(E) 32.5%
Rationale: Let cost of each metre be Rs. 100.
Therefore, cost price of 12m cloth = 12*100 =1200
cost price of 39m cloth = 39*100 = 3900
Since the trader made the CP of 12m from the sale of 39m therefore
Profit on sale of 39m = cost price of 12 m cloth = 1200
Selling price of 39m = 3900+1200 = 5100
Profit % = 23.5%
B
Answer: (B) 23.5%
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount Y in 1996 as they paid in 1995?
(A) 33 1⁄3%
(B) 40%
(C) 50%
(D) 66 2⁄3%
(E) 100%
Rationale: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio
Y=150-> 100 means 1/3 rd= 33(1/3) %.A
Answer: (A) 33 1⁄3%
Question: At what rate percent per annum will a sum of money double in 10years?
(A) 10%
(B) 15%
(C) 18%
(D) 20%
(E) 25%
Rationale: Let principle = P
S.I. = P
T = 10yrs
Rate = 100*P/P*10 = 10%
Answer is A
Answer: (A) 10%
Question: If 3 ministers are to be seated at a round table conference, then how many different ways can they be seated?
(A) 24
(B) 60
(C) 2
(D) 720
(E) 180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (3-1)! = 2! =2=C
Answer: (C) 2
Question: If 3^x*4^y = 59,049 and x – y = 10, then x = ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since 59,049 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 10 and y = 0, then x = 10.
The answer is A.
Answer: (A) 10
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.8
(B) 12.1
(C) 12.7
(D) 12.6
(E) 12.2
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 716 cm2
(B) 176 cm2
(C) 285 cm2
(D) 751 cm2
(E) 175 cm2
Rationale: Area of a trapezium
= 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: (C) 285 cm2
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
(A) 228
(B) 276
(C) 800
(D) 288
(E) 121
Rationale: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer:C
Answer: (C) 800
Question: A train 130 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
(A) 10
(B) 6.5
(C) 7
(D) 7.13
(E) 10.2
Rationale: Speed of train relative to man = 60 +4 = 64 km/hr.
= 64* 5/18 = 160/9 m/sec.
Time taken to pass the men = 130 * 9/160 = 7.13 sec.
Answer: Option D
Answer: (D) 7.13
Question: 11, 13, 17, 19, 23, 29, 31, 37, 41, ?
(A) 43
(B) 47
(C) 51
(D) 53
(E) 43
Rationale: The series consists of prime numbers.
Answer : A.
Answer: (A) 43
Question: Calculate how many days it will take for 8 boys to paint a 50 m long wall if 6 boys can paint a 60 m long wall in 5 days,
(A) 4.13 days
(B) 3.13 days
(C) 513 days
(D) 9.13 days
(E) 2 days
Rationale: The length of wall painted by one boy in one day = 60 / 6 * 1/5 = 2 m
No. of days required to paint 50 m cloth by 8 boys = 50/ 8 *1/ 2 = 3.13 days.
B
Answer: (B) 3.13 days
Question: If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 0
(B) 1
(C) 2
(D) None of these
(E) Cannot be determined
Rationale: Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
Answer: Option C
Answer: (C) 2
Question: If 5log(4*5^2) = x, find x
(A) 8
(B) 6
(C) 7
(D) 10
(E) 9
Rationale: 5(log2^2*5^2)=x
5log(5*2)^2=x
5*2log(5*2)=x
10log10=x
log10 base 10=1
so
10*1=x
x=10
ANSWER:D
Answer: (D) 10
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 14 days
(E) 30/4 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 30/40 = 30/4 days
E)
Answer: (E) 30/4 days
Question: How much interest can a person get on Rs. 8100 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3543.75
(B) 3587.59
(C) 3587.5
(D) 3587.52
(E) 3587.56
Rationale: I = (8100 * 2.5 * 17.5)/100 = (8100 * 5 * 35)/(100 * 2 * 2) = Rs. 3543.75.Answer: A
Answer: (A) 3543.75
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 22%
(B) 25%
(C) 28%
(D) 87%
(E) 16%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
(A) 5
(B) 7
(C) 6
(D) 8
(E) 9
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
B
Answer: (B) 7
Question: If the denominator of a fraction is increased by 4, then the fraction becomes 5/8. If the numerator is 11 less than the denominator, find the numerator.
(A) 25
(B) 20
(C) 30
(D) 15
(E) 35
Rationale: iniatial fraction=x/y;
after increasing deno..by 4=> x/(y+4)=5/8;
given x = y - 11;
then (y-11)/(y+4)=5/8=>y=36;
x = 36-11 = 25
ANSWER:A
Answer: (A) 25
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 155600 m
(B) 123600 m
(C) 153600 m
(D) 123344 m
(E) 124556 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: Ayesha's father was 28 years of age when she was born while her mother was 10 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 22 years
(B) 44 years
(C) 46 years
(D) 88 years
(E) 10 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 10 years.
Father's age when Ayesha's brother was born = (28 + 4) years = 32 years.
Required difference = (32 - 10) years = 22 years.
Answer: A
Answer: (A) 22 years
Question: In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If one-sevenths of the male students are married, what fraction of the female students is single?
(A) 1/3
(B) 1/7
(C) 1/2
(D) 2/3
(E) 5/7
Rationale: let assume there are 100 students of which 70 are male and 30 are females
if 30 are married then 70 will be single.
now its given that two-sevenths of the male students are married that means 1/7 of 70 = 10 males are married
if 30 is the total number of students who are married and out of that 10 are males then the remaining 20 will be females who are married.
total females = 30
married females = 20
then single females = 30-20 = 10
we need to find the fraction of female students who are single i.e single female students / total female student
= 10/30 = 1/3 [A]
Answer: (A) 1/3
Question: When x is multiplied by 2, the result is 19 more than the result of subtracting x from 26. What is the value of x?
(A) -4
(B) -2
(C) 15
(D) 13
(E) 22
Rationale: The equation that can be formed is:
2x-19=26-x
or, 3x=45
or, x=15.
C answer.
Answer: (C) 15
Question: A certain number X when divided by 243 leaves a remainder of 83. Which of the following can be subtracted from X to make X divisible by 82?
(A) 17
(B) 27
(C) 37
(D) 80
(E) 57
Rationale: Least possible value of the number is 243 + 83 = 326
Further it is given the number must be divisible by 82 .
326/82 = Gives remainder as 80
So, 80 must be subtracted from the number , answer is (C)
Answer: (C) 37
Question: When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
(A) 233
(B) 671
(C) 287
(D) 279
(E) 171
Rationale: Explanation:
When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671
Answer: B) 671
Answer: (B) 671
Question: There are 100 employees in a room. 99% are President. How many managers must leave the room to bring down the percentage of President to 98%?
(A)  1
(B)  2
(C)  46
(D)  50
(E)  97
Rationale: We have 99 Presidents and 1 director. That 1 director to compose 2% of the total number of people, there must be 50 people in the room, hence 50 Presidents must leave.
Answer: B.
Answer: (B)  2