mathewhe/aqua_rat huggingface dataset:
Question: In a school of 850 boys, 44% of Muslims, 32% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) A)125
(B) B)119
(C) C)153
(D) D)721
(E) E)159
Rationale: 44 + 32 + 10 = 86%
100 – 84 = 14%
850 * 14/100 = 119
Answer:B
Answer: (B) B)119
Question: An office supply store stocks two sizes of notebooks, each in six colors: orange, blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 20
(B) 24
(C) 32
(D) 36
(E) 42
Rationale: First let's consider the small notebooks.
There are 6 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 6C4=15.
There are 21 different packages we can make with the small notebooks.
We can use the same process to find 21 different packages with large notebooks.
The total number of different packages is 42.
The answer is E.
Answer: (E) 42
Question: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 1) II. (4, 4) III. (6, 6)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 5 lies on the parabola, so (1, 1) will be enclosed by the parabola and x axis.
When x = 4, y = 8 lies on the parabola, so (4, 4) will be enclosed by the parabola and x axis.
When x = 6, y = 0 lies on the parabola, so (6, 6) will not be enclosed by the parabola and x axis.
The answer is D.
Answer: (D) I and II
Question: Bradley owns b video game cartridges. If Bradley’s total is one-fifth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 16b / 3
(B) 17b / 4
(C) 13b / 4
(D) 19b / 12
(E) 25b / 4
Rationale: b = Bradley’s total
5b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 5b+ b/4 = (4b + 20b + b) / 4 = 25b / 4
The answer is E.
Answer: (E) 25b / 4
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 65%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.098 - ♠1.125 =
(A) -1.1
(B) 1.04
(C) -1.05
(D) -1.0
(E) -0.1
Rationale: ♠0.098 - ♠1.125 =
0.1 - 1.1 = -1.1
Answer : A
Answer: (A) -1.1
Question: A customer pays 20 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffee maker?
(A) 50
(B) 40
(C) 70
(D) 60
(E) 20
Rationale: Let x be the original price.
x - 20 = 20
x - 20 + 20 = 20 + 20
x + 0 = 40
x = 40
Answer is B
Answer: (B) 40
Question: John makes $60 a week from his job. He earns a raise and now makes $90 a week. What is the % increase?
(A) 16%
(B) 50%
(C) 17%
(D) 17.61%
(E) 17.56%
Rationale: Increase = (30/60)*100 = (3/6)*100 = 50%.
B
Answer: (B) 50%
Question: How much space, in cubic units, is left vacant when maximum number of 4x4x4 cubes are fitted in a rectangular box measuring 10x12x16 ?
(A) 0
(B) 36
(C) 180
(D) 216
(E) 384
Rationale: No of cubes that can be accommodated in box = (10*12*16)/(4*4*4)
12*16 in numerator can be perfectly divided by 4*4 in denominator.
side with length 10 can't be perfectly divided by 4 and hence is the limiting factor. Closet multiple of 4 less that 10 is 8. so vacant area in cube =
=12*16*(10-8)
=12*16*2
=384
ANSWER:E
Answer: (E) 384
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 30 and n is not prime, what is the greatest possible value of f(n)?
(A) 28
(B) 26
(C) 20
(D) 18
(E) 15
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 28 = 2*2*7. This is not a product of distinct prime numbers. Hence incorrect
Option B: 26 = 2*13. This is a product of distinct prime numbers.
Rest all the options are smaller that 26.
Correct Option: B
Answer: (B) 26
Question: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders Q will be:[/b]
(A) Q=3, 3, 2
(B) Q=3, 4, 2
(C) Q=5, 4, 3
(D) Q=5, 5, 2
(E) 6, 4, 3
Rationale: Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.
So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.
Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.
The remainders are, therefore, 5, 5, 2.
The answer is (D).
Answer: (D) Q=5, 5, 2
Question: One-fourth of a tank holds 135 litres of water. What part of the tank is full if it contains 180 litres of water?
(A) 1/2
(B) 1/3
(C) 1/5
(D) 1/6
(E) 1/4
Rationale: 135 litres = 1/4 of tank
180 litres = 1/4 x 180/135 = 1/3
Answer B.
Answer: (B) 1/3
Question: ?⁄50 = 60.5⁄?
(A) 55
(B) 1512.5
(C) 52.5
(D) 57.5
(E) None of these
Rationale: ?⁄50 = 60.5⁄?
or,?2 = 50 × 60.5 or, ?2 = 3025
or, ? = √3025 = 55
Answer A
Answer: (A) 55
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
(A) 87 years
(B) 40 years
(C) 19 years
(D) 16 years
(E) 18 years
Rationale: Sum of the present ages of husband, wife and child
= (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child
= (20 * 2 + 5 * 2) = 50 years.
Husband's present age
= (90 - 50) = 40 years.
Answer: B
Answer: (B) 40 years
Question: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 33
(B) 77
(C) 30
(D) 88
(E) 12
Rationale: 3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30
Answer: C
Answer: (C) 30
Question: The average of 35 students in a class is 18 years. The average age of 25 students is 16. What is the average age of remaining 10 students?
(A) 21 years
(B) 23 years
(C) 22 years
(D) 20 years
(E) 24 years
Rationale: Sum of the ages of 14 students
= (18 * 35) - (16 * 25) = 630 - 400 = 230
Required average = (230/10) = 23 years.
Answer:B
Answer: (B) 23 years
Question: What is the median from the below series 93, 88, 95, 88, 97, 87, and 98
(A) 80
(B) 82
(C) 92.14
(D) 98
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 93, 95, 96, 98
The median quiz score was 92.14 (Four quiz scores were higher than 92.14 and four were lower.)
C
Answer: (C) 92.14
Question: There are 380 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
(A) 152
(B) 209
(C) 57
(D) 171
(E) 220
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 380 = 220
ANSWER:E
Answer: (E) 220
Question: What is the greatest 6-digit number when divided by 7 ,8 , 9, and 10 leaves a remainder of 5, 6, 7, and 8 respectively?
(A) 456788
(B) 678910
(C) 997479
(D) 997919
(E) 997920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so A is the only possible answer.
Answer: (A) 456788
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed R of the train.
(A) a) 45
(B) b) 33
(C) c) 48
(D) d) 55
(E) e) 61
Rationale: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=R
Ans = C
Answer: (C) c) 48
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5
(A) 18
(B) 20
(C) 24
(D) 30
(E) 40
Rationale: Exp. Multiples of 5 between 6 and 34 are 10,15,20,25,30
Average = (10+15+20+25+30)/5 =5(10+30)/2*5 = 40/2 =20
Answer:B
Answer: (B) 20
Question: In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at T mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]
(A) { (6T)^2 + (5000-5y)^2 }^1/2
(B) { (36x)^2 + (5000-7y)^2 }^1/2
(C) { (16x)^2 + (5000-7y)^2 }^1/2
(D) { (7x)^2 + (5200-7y)^2 }^1/2
(E) { (2x)^2 + (300-7y)^2 }^1/2
Rationale: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Answer: (A) { (6T)^2 + (5000-5y)^2 }^1/2
Question: After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm?
(A) 45%
(B) 48%
(C) 50%
(D) 58%
(E) 65%
Rationale: When the storm deposited 120 billion gallons, volume of water in the reservoir = 200 + 120 = 320 billion gallons
If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 320/0.8 = 400 billion gallons
Therefore percentage of reservoir that was full before the storm = (200/400)*100 = 50%
Option C
Answer: (C) 50%
Question: A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
(A) 2
(B) 8
(C) 6
(D) 3
(E) 4
Rationale: A
2
Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
Answer: (A) 2
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
(A) 32 Yrs
(B) 36 Yrs
(C) 40 Yrs
(D) 48 Yrs
(E) None
Rationale: Explanation:
Let the mother's present age be x years.
Then, the person's present age = (2/5)*x years.
((2/5)*x)+8 = (1/2)(x+8)
2(2x + 40) = 5(x + 8)
x = 40.
Answer: C
Answer: (C) 40 Yrs
Question: By selling 15 pens for a rupee a woman loses 25%. How many for a rupee should he sell in order to gain 25%?
(A) 12
(B) 14
(C) 45
(D) 10
(E) 65
Rationale: D
85% --- 15
125% --- ?
85/125 * 15 = 10
Answer: (D) 10
Question: James started from his house headed North. After walking a distance of 50 m. He turned to the left and walked 60 m. He then made a right turn and walked 30 m. After this he is to turn left at 90o degrees and to cover another 40 m. How many meters did James walk in total and what direction was he headed in when he left his house?
(A) 158/South
(B) 10/East
(C) South-West
(D) 180/North
(E) 180/North-West
Rationale: Answer: E
Answer: (E) 180/North-West
Question: By selling an article for 96, double profit is obtained than the profit that would have been obtained by selling it for 84. What is the cost price of the article?
(A) 72.0
(B) 75.0
(C) 70.00
(D) 68.00
(E) None of these
Rationale: Let the cost price of the article be x.
Then,2(84 –x) = 96 – x
l68 – 2x= 96 – x \ x = 72
Answer A
Answer: (A) 72.0
Question: What is the area of square field whose side of length 13 m?
(A) 169
(B) 196
(C) 266
(D) 288
(E) 261
Rationale: 13 * 13 = 169 sq m
Answer: A
Answer: (A) 169
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
(A) 70%
(B) 90%
(C) 60%
(D) 50%
(E) 65%
Rationale: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
Answer:C
Answer: (C) 60%
Question: A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 32 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
(A) 3x/4
(B) 4x/5
(C) 7x/5
(D) 5x/7
(E) 4x/3
Rationale: t = S1/V1 = S2/V2
or, 24/x = 32/y
or, y = 24x/32 = 3x/4 (Answer A)
Answer: (A) 3x/4
Question: An employer has 7 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
(A) a) 1,490
(B) b) 132
(C) c) 210
(D) d) 60
(E) e) 23
Rationale: 7C3 * 4C2 = 210. Answer C.
Answer: (C) c) 210
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 5?
(A) 1/45
(B) 2/45
(C) 2/15
(D) 4/15
(E) 1/5
Rationale: The number of ways to choose two cards is 10C2=45.
There are 2 ways, {1,2} and {1,3}, to get a sum less than 5.
P(sum less than 5)=2/45
The answer is B.
Answer: (B) 2/45
Question: If each edge of cube increased by 25%, the percentage increase in
(A) 55
(B) 52.25
(C) 59.75
(D) 51.75
(E) 56.25
Rationale: 100 × (125)/100 × (125)/100 = 156.25 => 56.25%
Answer is E.
Answer: (E) 56.25
Question: A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 48x
(D) 80x
(E) x/75
Rationale: Revolutions - circumference of the rim.
=> 20pi*X*60 = 15pi*Revolutions
=> 4/3 *X *60 = Revolutions => 80X - Option D
Answer: (D) 80x
Question: 36 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 12
(B) 16
(C) 13
(D) 18
(E) 19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 36 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 36 x 5 x 12
x = (36 x 5 x 12)/(30 x 6)
x = 12
ANSWER A
Answer: (A) 12
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 6 days
(B) 8 days
(C) 5 days
(D) 9 days
(E) 4 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer:D
Answer: (D) 9 days
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 0.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
(A) {3, 4, 5, 10, 11}
(B) {3, 9, 10, 10, 11}
(C) {3, 5, 9, 10, 16}
(D) {1, 5, 7, 10, 11}
(E) {5, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 9 to 10 + 2*{SD} = 11.
A. {3, 4,5, 10, 11} --> only 2 numbers are in this range. Discard.
B. {3,9, 10, 10, 11} --> 4 numbers are in this range. OK.
C. {3,5, 9, 10, 16} --> only 2 numbers are in this range. Discard.
D. {1,5, 7, 10, 11} --> only 2 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> only 1 number is in this range. Discard.
Answer: B.
Answer: (B) {3, 9, 10, 10, 11}
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 50
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40
Question: Express a speed of 36 kmph in meters per second?
(A) 10 mps
(B) 76 mps
(C) 26 mps
(D) 97 mps
(E) 16 mps
Rationale: 36 * 5/18
= 10 mps
Answer:A
Answer: (A) 10 mps
Question: The sum of two number is 120 and their difference is 30. Find the numbers.
(A) 95,25
(B) 55,65
(C) 75,45
(D) 65,55
(E) 85,35
Rationale: Let the two number be x and y. x+y =120.......(1) x- Y =30.........(2)
=>2X=150 =>X=75. x-y =30 =>y =45. The two numbers are 75,45 Ans : C
Answer: (C) 75,45
Question: Eight years ago Anita was P times as old as Ben was. If Anita is now 27 years old, how old is Ben now in terms of P ?
(A) 19/P + 8
(B) P/19 +8
(C) 17 - P/8
(D) 17/P
(E) 11.5P
Rationale: let's call Ben age eight years ago is x
so eight years ago Anita was: 27-8 = 19 years old
and eight years ago Anita was P times as old as Ben was
=> 19/x = P
=> x = 19/P
=> Now Ben age will be : x+8 = 19/P+8
=> the answer is A
Answer: (A) 19/P + 8
Question: There are three prizes to be distributed among seven students. If no students gets more than one prize, then this can be done in?
(A) 10
(B) 45
(C) 35
(D) 20
(E) None of these
Rationale: Explanation :
3 prize among 7 students can be distributed in 7C3 ways = 35 ways.
Answer : C
Answer: (C) 35
Question: A CHOCOLATE manufacturer produces 400 units of a certain model each month at a cost to the manufacturer of £40 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £40,000?
(A) 123
(B) 213
(C) 440
(D) 550
(E) 540
Rationale: 400(x-40)≥40,000
x-40≥400
x≥440
Answer: Option C
Answer: (C) 440
Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
(A) 1
(B) 5
(C) 2
(D) 3
(E) 8
Rationale: 4456 (742
42
--
25
24
--
16
12
--
4
=> (6-4) =2
ANSWER C
Answer: (C) 2
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 177
(B) 190
(C) 178
(D) 124
(E) 121
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: B
Answer: (B) 190
Question: One hour after Matthew started waking from t to y, a distance of 45km, Johnny started walking along the same road from y to t. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 19.5
Rationale: Just an alternative method...
After the first hour the distance t is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.
Hence A.
Answer: (A) 24
Question: In an election, 68% of the voters exercised their franchise. Of these, 48% were women. The number of males exercising their franchise was 53,040. How many eligible voters were there in all?
(A) 102,000
(B) 150,000
(C) 234,000
(D) 252,000
(E) 288,000
Rationale: Let total number of eligible voters= x
Number of people who voted = (68/100)*x
Percentage of women of people who voted = 48 %
Therefore Percentage of men of people who voted = 52 %
(52/100)*(68/100)*x = 53040
=> (13/25)*(17/25)*x = 53040
=> x = 1,50,000
Answer B
Answer: (B) 150,000
Question: The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day Rs. 1,325 were collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
(A) Rs. 750
(B) Rs. 1000
(C) Rs. 850
(D) Rs. 1250
(E) None of these
Rationale: Let x be the number of passengers and y be the fare taken from passengers.
3xy + 50xy = 1325 => xy = 25
Amount collected from II class passengers = 25 × 50 = Rs. 1250.
Answer:	D
Answer: (D) Rs. 1250
Question: If rupee one produces rupees nine over a period of 30 years, find the rate of simple interest?
(A) 30 %
(B) 22 3/2 %
(C) 22 1/8 %
(D) 22 1/2 %
(E) 22 1/2 %
Rationale: 9 = (1*30*R)/100
R = 30 %
Answer:A
Answer: (A) 30 %
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 135 girls, the total number of students in the college is?
(A) 562
(B) 351
(C) 452
(D) 416
(E) 512
Rationale: Let the number of boys and girls be 8x and 5x
Then , 5x = 135
x= 27
Total number of students = 13x = 13*27 = 351
Answer is B
Answer: (B) 351
Question: The average height of 15 girls out of a class of 60 is 138 cm. and that of the remaining girls is 142 cm. The average height of the whole class is :
(A) 132 cms
(B) 141 cms
(C) 142 cms
(D) 152 cms
(E) 161 cms
Rationale: Explanation:
Average height of the whole class =(15×138+45×142/60)=141 cms
Answer B
Answer: (B) 141 cms
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 18
Rationale: Speed of the first train =	(120/10) m/sec = 12 m/sec.
Speed of the second train =(120/15)	m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =	[(120 + 120)/20]	sec = 12 sec.
Answer :B
Answer: (B) 12
Question: The probability that a man will be alive for 10more yrs is 1/3 & the probability that his wife will alive for 10 more yrs is 5/8. The probability that none of them will be alive for 10 more yrs, is
(A) 1/8
(B) 1/4
(C) 2/3
(D) 3/4
(E) 2
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/4
Ans.(B)
Answer: (B) 1/4
Question: The distance from City A to City B is 100 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
(A) 45
(B) 48
(C) 50
(D) 52
(E) 54
Rationale: The time it takes Bob to drive to City B is 100 / 40 = 2.5 hours.
Alice needs to take less than 2 hours for the trip.
Alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour.
The answer is C.
Answer: (C) 50
Question: The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 38 cm2
(B) 27 cm2
(C) 45 cm2
(D) 25 cm2
(E) 35 cm2
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 * 36/2
= 45 cm2
Answer: C
Answer: (C) 45 cm2
Question: If a class of 10 students has seven men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
(A) 7!6!
(B) 5!5!
(C) 4!4!
(D) 10!
(E) 10!/5!
Rationale: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest six can be fixed in 6! ways...
also rest seven position of women can be fixed in 7!..
total ways 7!6!
A
Answer: (A) 7!6!