mathewhe/aqua_rat huggingface dataset:
Question: A train running at the speed of 40 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 100 m
(B) 150 m
(C) 187 m
(D) 167 m
(E) 197 m
Rationale: Speed = 40 * 5/18 = 100/9 m/sec
Length of the train = speed * time = 100/9 * 9
= 100 m
Answer: A
Answer: (A) 100 m
Question: If a sequence of 8 consecutive odd integers with increasing values has 11 as its 7th term, what is the sum of the terms of the sequence?
(A) 12
(B) 24
(C) 36
(D) 48
(E) 60
Rationale: Let x be the first term.
Then x + 12 = 11 and x = -1
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-1) + 56 = 48
The answer is D.
Answer: (D) 48
Question: Mrs. Evans gave a test to her freshmen economics class, which has 30 students enrolled and 25 of them answered question 1 correctly. If 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly?
(A) 30
(B) 28
(C) 26
(D) 22
(E) 19
Rationale: Total number of enrolled students = 30
Number of students who did not take test = 5
Hence, number of students who took test = 30 - 5 = 25
Number of students who answered Q2 correctly =22, therefore, all students who took test answered Q2 correctly.
So, number of students who answered Q1 correctly, also answered Q2 correctly = 22.
Number of students who answered both Q1 & Q2 correctly = 22.
ANSWER:D
Answer: (D) 22
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a for 2 years. Find his gain in the transaction per year.
(A) 100
(B) 150
(C) 225
(D) 112.5
(E) 212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 6 % p.a for 2 years
Simple interest that he gets = PRT/100=5000×6×2/100=600
His overall gain in 2 years = Rs.600 - Rs.400 = Rs.200
His overall gain in 1 year = 200/2 = Rs.100
Answer : Option A
Answer: (A) 100
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1733.33
(D) 1800
(E) 2025
Rationale: 300 gallons of water increases capacity by 30% that means
30% is 300 gallons, so 100% would be = 300*100/30= 1000 gallons
Now 1000 +300 gallons is 75% capacity of tank.
so 100% capacity would be= 1300 *100/75= 1733.33
C is the answer
Answer: (C) 1733.33
Question: There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 10,400 milk chocolates per month, what was it one month ago?
(A) 10,000 chocolates
(B) 9000 chocolates
(C) 8000 chocolates
(D) 7000 chocolates
(E) None of these
Rationale: Let one month ago, production be x chocolates.
Then, 130 % of x = 10400
⇒ x = 10400×100/130=8000 chocolates
Answer C
Answer: (C) 8000 chocolates
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 2 sec. What is the length of the fast train?
(A) 11 1/9 m
(B) 11 7/4 m
(C) 11 7/2 m
(D) 11 7/9 m
(E) 11 7/7 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 2 = 100/9 = 11 1/9 m.Answer:A
Answer: (A) 11 1/9 m
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?
(A) 400 meters
(B) 1111 meters
(C) 1777 meters
(D) 1822 meters
(E) None of these
Rationale: Relative speed of the train with respect to the motorbike should be the speed with which the length of the train is covered in 40 secs.
Calculate the relative speed => 100 - 64 = 36 kmph and time is 40 sec = 40/3600 hrs
Distance (in this case the length of the train ) = S*T = 36*40/3600
.4 km or 400meters.
So Answer (A)
Answer: (A) 400 meters
Question: In measuring the sides of a rectangle, one side is taken 12% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
(A) 3.5%
(B) 6.4%
(C) 3%
(D) 5%
(E) 2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 112*95=10,640, which is 6.4% greater than the actual area.
Answer: B.
Answer: (B) 6.4%
Question: What Is The Next Number
12 13 15 17 111 113 117 119 123 129 131?
(A) 137
(B) 220
(C) 129
(D) 428
(E) 224
Rationale: 137
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer A
Answer: (A) 137
Question: Operation#is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%
Rationale: Any multiple of 4 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
Answer: (A) 0%
Question: A and B go around a circular track of length 1800 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 165 sec
(C) 186 sec
(D) 167 sec
(E) 360 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM {1800/ (36 * 5/18) , 1800/ (54 * 5 /18) }
= LCM (180, 120)
=360 sec.
Answer:E
Answer: (E) 360 sec
Question: A theater box office sold an average (arithmetic mean) of 64 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 80, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
(A) 1:2
(B) 1:4
(C) 3:7
(D) 7:12
(E) 4:5
Rationale: Deviation from the mean for the daytime staff = 80 - 64 = 16.
Deviation from the mean for the evening staff = 64 - 60 = 4.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 4:16 = 1:4.
The answer is B.
Answer: (B) 1:4
Question: The area of a parallelogram is 288sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 12
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 2x * x = 288 => x= 12
Answer: A
Answer: (A) 12
Question: The difference between the compound interest and simple interest on a certain sum at 20% per annum for 2years is $500. Find the sum?
(A) $10000
(B) $50000
(C) $15200
(D) $12500
(E) $15000
Rationale: Let the sum be $x
C.I. = x(1+20/100)^2 - x = 35x/100
S.I. = (X*20*2)/100 = 2x/5
C.I.- S.I. = (35x/100)-(2x/5) = 5x/100
5x/100 = 500
x = 10000
Answer is A
Answer: (A) $10000
Question: 5 is added to a certain number, the sum is multiplied by 5, the product is divided by 5 and 5 is subtracted from the quotient. The remainder left is half of 60. What is the number?
(A) 21
(B) 20
(C) 2
(D) 30
(E) 45
Rationale: Let number is X.
When 5 added to it,
= (X+5)
5 multiplied to sum,
= 5 *(X +5)
Now,
= [{5 *(X +5)} /5]
And,
= [{5 *(X +5)} /5] - 5
According to question,
[{5 *(X +5)} /5] - 5 = half of 60
[(5X + 25) /5) = 30 +5
5X + 25 = 35 *5
X + 5 = 7 *1
X + 5 = 7
X = 7 - 5
X = 2
So, required number is: 2.
ANSWER : C
Answer: (C) 2
Question: There are 6 people at a party sitting at a round table with 6 seats: A, B, C, D, E and F. A CANNOT sit next to either D or F. How many ways can the 6 people be seated?
(A) 720
(B) 120
(C) 108
(D) 84
(E) 48
Rationale: A,B,C,D,E and F can sit in (6-1)! ways -- 120
Now consider this, when we take AD as one person all of them can sit in AD, B, C, D ,E --> (5-1)! --> 24
now, this calculation considers clockwise and anti clockwise as different, i.e AD is different from DA. Therefore we have to divide this figure by 2, because We do not want to distinguish between AD and DA.
Hence there are 12 cases when AD sit to each other ( irrespective of AD or DA )
Similarly, there are 12 cases when AF sit to each other.
Similarly, we can say ADF can also be clockwise and anticlockwise, but we have to realize that, when counting AD and AF we have counted DAF or FAD TWICE ( once for each ) therefore we need to deduct the arrangement for DAF only once.
If DAF were 1 person, possible number of arrangements -- ADF,B,C,E --> 3!
We will not count it twice because we need to deduct this only once from AD and AF combination !
Therefore total count
5! - (4!/2 + 4!/2 -3!) = 120 - (12 + 12 -12 ) = 108
ANS:C
Answer: (C) 108
Question: On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?
(A) 1 : 3
(B) 2 : 3
(C) 2 : 1
(D) 3 : 1
(E) 4 : 5
Rationale: Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10
Required ratio = 20 : 10 = 2 : 1
C
Answer: (C) 2 : 1
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 4. If the sum of their ages is 132, what is the difference between the ages of Patrick and Monica?
(A) 27
(B) 48
(C) 45
(D) 72
(E) 33
Rationale: Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:4x
Rationalizing their ages. ratio of their ages will be 9x:15x:20x
Sum=44x=132
x=3
Difference if ages of Pa and Mo=20x-9x=11x=11*3=33
Answer E
Answer: (E) 33
Question: The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 700 per sq. metre.
(A) s. 15,550
(B) s. 15,400
(C) s. 16,500
(D) s. 17,600
(E) s. 17,900
Rationale: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.
Cost of paving = Rs. (800 Ã— 22) = Rs. 15400
Answer: Option B
Answer: (B) s. 15,400
Question: What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 12% p.a.?
(A) s:10123.19
(B) s:10123.29
(C) s:10123.20
(D) s:10123.28
(E) s:16197.12
Rationale: Amount
= [40000 * (1 + 12/100)3]
= 40000 * 28/25 * 28/25 * 28/25
= Rs. 56197.12
C.I. = (56197.12 - 40000)
= Rs:16197.12
Answer: E
Answer: (E) s:16197.12
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
(A) 10 min
(B) 15 min
(C) 20 min
(D) 25 min
(E) 30 min
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Answer: (A) 10 min
Question: The probability that Alex will solve a problem is 1/5. What is the probability that he solves at least one problem out of 4 problems?
(A) 64/125
(B) 256/625
(C) 64/625
(D) 369/625
(E) 359/625
Rationale: The probability that Alex will not solve a problem = 4/5. The probability that Alex will not solve 10 problems = (4/5)4 = 256/625.
Hence, the probability that Alex will solve at least one problem
= 1 - 256/625 = 369/625.
ANSWER:D
Answer: (D) 369/625
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 750km?
(A) 10hrs
(B) 15hrs
(C) 20hrs
(D) 25hrs
(E) 18hrs
Rationale: 1 hour he ride 50km
he ride 750km in = 750/50 * 1 = 15hours
Answer is B
Answer: (B) 15hrs
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 507 sq m, then what is the breadth of the rectangular plot?
(A) 16
(B) 17
(C) 13
(D) 19
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 507
3b2 = 507
b2 = 169
b = 13 m.
Answer: Option C
Answer: (C) 13
Question: Pujara has a certain average of runs for his 8 matches in Border Gavaskar Trophy. In the ninth match he scores 100 runs and thereby increases his average by 9 runs. His new average of runs is:
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: let his average run in 8 matches be x
total runs for 8 matches = 8x
total runs for 9 matches = 8x+100
average runs for 9 matches = (8x+100)/9
(8x+100)/9 = x + 9
8x+100 = 9x + 81
x= 19
new average = 19+9 = 28
ANSWER:A
Answer: (A) 28
Question: A father said to his son, “I was as old as you are at present at the time of your birth”.If the father’s age is 38 years now,the son’s age five years back was :
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 39 years
Rationale: Solution
Let the son's present age be x years.Then,(38-x)=x ⇔ 2x = 38 ⇔ x = 19.
∴ Son's age 5 years back = (19 - 5) years =14 years. Answer B
Answer: (B) 19 years
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 27
(B) 30
(C) 31
(D) 33
(E) 34
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
A
Answer: (A) 27
Question: 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. Find the amount required to purchase the shares.
(A) 312000
(B) 313000
(C) 314000
(D) 315000
(E) 312500
Rationale: Face value of each share = Rs.20
Market value of each share = Rs.25
Number of shares = 12500
Amount required to purchase the shares = 12500 × 25 = 312500
Answer is E.
Answer: (E) 312500
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years X in which the population would be doubled assuming there is no emigration or immigration is
(A) 20
(B) X=25
(C) X=30
(D) X=35
(E) 40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000= 1000(1+(2/100))^n
n=35 Answer is D.
Answer: (D) X=35
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 15 a.m
(B) 8 a.m
(C) 12 a.m
(D) 02 a.m
(E) 05 a.m
Rationale: Suppose they meet x hours after 5 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 8 a.m.
Answer:B
Answer: (B) 8 a.m
Question: If in a company the female employees is 80% of male employees. What is the percentage of male employees in terms of female employees?
(A) 125%
(B) 112%
(C) 60%
(D) 12%
(E) 8%
Rationale: The female employees is 80% of male employees
If male employees=10
female employees=8
We are asked to find the percentage of male employees in terms of female employees
M/F=10/8=10 1/8=1.25=125%
Answer is A
Answer: (A) 125%
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability R that each number is different ?
(A) A.18/25
(B) B.4/5
(C) C.81/100
(D) D.9/10
(E) E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability R= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: (A) A.18/25
Question: The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 210, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 240
Rationale: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 2/5 x = 210
Hence, x = 150. So, number of timeshare condos available at Playa del Mar = 150
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 2/5x = 2/5x = 3/5(150) = 90
The correct answer is B
Answer: (B) 90
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 3 men and 2 women will do that task.
(A) 4/7
(B) 3/10
(C) 3/18
(D) 13/16
(E) 4/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
3 m + 2 w =8 w
Answer is 8/14 = 4/7
Answer: A
Answer: (A) 4/7
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel H if the median is 10 gallons?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel H= 2
Answer: (B) 2
Question: Two employees M and N are paid a total of Rs. 550 per week by their employer. If M is paid 120 percent of the sum paid to N, how much is N paid per week?
(A) Rs.200
(B) Rs.230
(C) Rs.250
(D) Rs.300
(E) Rs.320
Rationale: Let the amount paid to M per week = x
and the amount paid to N per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C)
Answer: (C) Rs.250
Question: . A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104
(B) 55
(C) 66
(D) 288
(E) 2761
Rationale: 624/6 = 104 kmph
Answer: A
Answer: (A) 104
Question: Alfred buys an old scooter for $4700 and spends $800 on its repairs. If he sells the scooter for $5800, his gain percent is?
(A) 5.45%
(B) 6.23%
(C) 7%
(D) 8.12%
(E) 10%
Rationale: C.P. = 4700+800 = $5500
S.P. = $5800
Gain = 5800-5500 = $300
Gain% = 300/5500 * 100 = 5.45%
Answer is A
Answer: (A) 5.45%
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is?
(A) 36
(B) 50
(C) 88
(D) 66
(E) 23
Rationale: Speed of the train relative to man
= (200/20) m/sec = 5 m/sec. [5 * (18/5)] km/hr
= 18 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5
= 18 ==> x
= 23 km/hr.
Answer:E
Answer: (E) 23
Question: Find the perimeter and area of the rectangle of length 15 cm and breadth 11 cm.
(A) 71 cm2
(B) 121 cm2
(C) 165 cm2
(D) 171 cm2
(E) 221 cm2
Rationale: length = 15 cm, breadth = 11 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (15 + 11) cm
= 2 × 26 cm
= 52 cm
We know that the area of rectangle = length × breadth
= (15 × 11) cm22
= 165 cm2
ANSWER : C
Answer: (C) 165 cm2
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 288
(C) 376
(D) 397
(E) 592
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: A
Answer: (A) 432
Question: If 5 is 10 percent of 25 percent of a certain number, what is the number?
(A) 190
(B) 21
(C) 150
(D) 200
(E) 250
Rationale: Using elimination method to pick the correct option it will be discovered that option D i.e 200 is the correct option because 25% of 200 is 50 and 10% of 50 is 5.
ANSWER:D
Answer: (D) 200
Question: If the area of a square with sides of length 6 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 12
(D) 9
(E) 18
Rationale: Let length of rectangle = L
6^2 = L*4
=> L = 36/4 = 9
Answer D
Answer: (D) 9
Question: What is the remainder when 1250*1040*1057*1145 is divided by 32?
(A) 3
(B) 5
(C) 0
(D) 2
(E) 9
Rationale: OA is 'C'.
OE:
take the remainder from each of 1250/32, 1040/32 and so on..
1250/32 gives remainder = 2
1040/32 gives remainder = 16
1057/32 gives remainder = 1
1145/32 gives remainder = 25
the net remainder is the product of above individual remainders. i.e = 2*16*1*25
break them into pairs 2*16/32 gives remainder 0
and 1*25/32 gives remainder 25
so 0*25/32 gives remainder 0.
Answer: C
Answer: (C) 0
Question: 9 years ago I was five times as old as my eldest son. Today I am 3 times his age. How old am I now?
(A) 45
(B) 54
(C) 34
(D) 58
(E) 56
Rationale: x-9=5(y-9)
& x=3y
x-9=5x/3-45
x=54
ANSWER:B
Answer: (B) 54
Question: How many three-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?
(A) 8
(B) 0
(C) 6
(D) 10
(E) 12
Rationale: A number ending with 2 can never be a perfect square.
Answer: B
Answer: (B) 0
Question: A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be?
(A) 13min 20sec
(B) 10min
(C) 11min 30sec
(D) 12min 15sec
(E) 15min 15sec
Rationale: Speed = 10*60/12 = 50 km/hr
new speed = 50-5 = 45 km/hr
time taken = 10/45 = 60*2/9 = 13 min 20 sec
Answer is A
Answer: (A) 13min 20sec
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 121 m
(B) 128 m
(C) 125 m
(D) 120 m
(E) 198 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer:D
Answer: (D) 120 m
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: Speed in still water =	1	(11 + 5)/2 kmph = 8 kmph.
Answer:C
Answer: (C) 8
Question: The smallest value of n, for which 2n + 1 is not a prime number is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Sol.
= (2 × 1 + 1) = 3,
= (2 × 3 + 1) = 7,
= (2 × 4 + 1) = 9, which is not prime.
Therefore n = 4.
Answer B
Answer: (B) 4
Question: Calculate how many men are needed to finish a specific task in 10 days if it will take 30 men to complete the same task in 60 days?
(A) 180
(B) 185
(C) 170
(D) 280
(E) 182
Rationale: men required to finish the work in 10 days = 30*60/10 = 180
Answer is A
Answer: (A) 180
Question: A train 320 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
(A) 77 kmph
(B) 95 kmph
(C) 94 kmph
(D) 98 kmph
(E) 96 kmph
Rationale: S = 320/12 * 18/5
= 96 kmph
Answer: E
Answer: (E) 96 kmph
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
(A) 2%
(B) 5%
(C) 3%
(D) 4%
(E) 8%
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer: B
Answer: (B) 5%
Question: If g(x) = ax^5 + bx^3 + 6, and g(5) = 10, then g(–5) =?
(A)  – 10
(B)  – 8
(C)  – 6
(D)  0
(E)  2
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 6 = 10
or, 5^5 a + 5^3 b = 4
g(-5) = -5^5 a - 5^3 b + 6 = - (5^5 a + 5^3 b) + 6 = - 4 + 6 = 2 = (E)
Answer: (E)  2
Question: If 5 men and 2 boys working together, can do three times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 9:2
(B) 5:2
(C) 1:2
(D) 1:4
(E) 1:8
Rationale: M + 2B = 3(1M + 1B)
5M + 2B = 3M + 3B
2M = 1B
The required ratio of work done by a man and a boy = 1:2
ANSWER:C
Answer: (C) 1:2
Question: P and Q invested in a shop. The profits were divided in the ratio of 5: 2 respectively. If P invested Rs. 5600, the amount invested by Q is:
(A) 3500
(B) 5600
(C) 2200
(D) 2400
(E) None
Rationale: Suppose Q invested Rs. y. Then, 5600/y = 5/2 or y = [5600 x 2 / 5] = 2240
Answer E
Answer: (E) None
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 47.55 kg
(B) 48 kg
(C) 48.55 kg
(D) 49.25 kg
(E) 59.25 kg
Rationale: 16*50.25+8*45.15/24=48.55
ANSWER:C
Answer: (C) 48.55 kg
Question: What is the least integer that is a sum of four different prime numbers each greater than 30?
(A) 148
(B) 150
(C) 152
(D) 154
(E) 156
Rationale: The sum of the four smallest primes greater than 30 is 31+37+41+43=152.
The answer is C.
Answer: (C) 152