mathewhe/aqua_rat huggingface dataset:
Question: he average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.2
(B) 59.5
(C) 52.8
(D) 52.5
(E) 52.1
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80
= 52.5
Answer:D
Answer: (D) 52.5
Question: A certain bakery baked a batch of 400 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
(A) 13
(B) 27
(C) 41
(D) 43
(E) 51
Rationale: Cookies which have both nuts and chocolate chips = 235
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(235+x)/(400+x) = 6/10
=>2350 + 10x = 2400 + 6x
=> 4x = 50
=> x = 12.5
Therefore x = 13
Answer A
Answer: (A) 13
Question: A certain car uses one gallon of gasoline every 38 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
(A) 15%
(B) 20%
(C) 22.5%
(D) 45%
(E) 50%
Rationale: 4 miles on the highway = 4/38 gallons;
4 miles in the city = 4/20 gallons;
Total = 4/38 + 4/20 = 29/95 gallons.
8 miles on the highway = 8/38 gallons .
The % change = (29/95 - 8/38)/(8/38) = 0.45.
Answer: D.
Answer: (D) 45%
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long Q would it take Victor to complete 10 jobs without any supervision?
(A) 34
(B) 52
(C) 60
(D) 70
(E) 92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need Q 10(t + 3) = 60 days.
Answer: C.
Answer: (C) 60
Question: Each child has 6 crayons and 12 apples. If there are 12 children, how many crayons are there in total?
(A) 22
(B) 65
(C) 72
(D) 78
(E) 90
Rationale: 6*12=72.Answer is C
Answer: (C) 72
Question: If a town of 25,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
(A) 26000
(B) 27000
(C) 28000
(D) 29000
(E) 30000
Rationale: Let population in the beginning = 100
at the end of 1st year population = 100+1% of 100 = 100+1 = 101
at the end of 2nd year population = 101+1% of 101 = 101+1 approx = 102 approx (on the lower side because 1% of 101 is greater than 1)
at the end of 3rd year population = 102+1% of 102 = 102+1 approx = 103 approx (on the lower side because 1% of 102 is greater than 1)
at the end of 4th year population = 103+1% of 103 = 103+1 approx = 104 approx (on the lower side because 1% of 103 is greater than 1)
at the end of 5th year population = 104+1% of 104 = 104+1 approx = 105 approx (on the lower side because 1% of 104 is greater than 1)
i.e. 5% greater than 25000 = 25000+5% of 25000 = 25000+1250 = 26250 (on the lower side)
i.e. Population must be greater than 26250 but since the closest option is 26000 so
Answer: option A
Answer: (A) 26000
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
(A) 11
(B) 18
(C) 19
(D) 287
(E) 27
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years.
Answer: C) 19
Answer: (C) 19
Question: If x and y are prime numbers such that x > y > 5, then x^2 − y^2 must be divisible by which one of the following numbers?
(A)  3
(B)  7
(C)  5
(D)  9
(E)  12
Rationale: If x=7 and y=5, then x^2-y^2=24 and 24 is divisible only by 12 from the options, thus it must be correct.
Answer: E.
Answer: (E)  12
Question: X can run a kilometer race in 4 1/2 min while Y can run same race in 5 min. How many meters start can X give Y in a kilometer race, so that the race mat end in a dead heat?
(A) 50 m
(B) 200 m
(C) 150 m
(D) 100 m
(E) 250 m
Rationale: D
100 m
X can give Y (5 min - 4 1/2 min) = 30 sec start.
The distance covered by Y in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
X can give Y 100m start.
Answer: (D) 100 m
Question: A boy has Seven trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
(A) 38 ways
(B) 87 ways
(C) 66 ways
(D) 98 ways
(E) 121 ways
Rationale: Explanation:
The boy can select one trouser in seven ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 14 = 98 ways.
Answer: D
Answer: (D) 98 ways
Question: A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability Q that you can still row the canoe?
(A) 9/25
(B) 10/25
(C) 6/10
(D) 2/3
(E) 21/25
Rationale: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.
Using the idea that the probability Q of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer: 1 – 4/25 = 21/25.Answer choice E.
Answer: (E) 21/25
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $120,000?
(A) 15
(B) 21
(C) 18
(D) 20
(E) 24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 10,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 40,000.00 takes the same (72/x) no of years to double 120,000.00.
72/x = 6 years.
So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
80,000 - 120,000 = 3 years
total 21 years.
Answer B
Answer: (B) 21
Question: The compound ratio of 3:4, 3:2 and 4:5?
(A) 1:9
(B) 1:7
(C) 1:2
(D) 9:10
(E) 1:4
Rationale: 3/4 * 3/2 * 4/5
= 9/10
=9:10
Answer: D
Answer: (D) 9:10
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio R of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
(A) 8:3
(B) 3:2
(C) 4:3
(D) 2:3
(E) 3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio R of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: (B) 3:2
Question: A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 51%.
Rationale: 25% of 2 litres = 0.5 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.9 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 29%
ANSWER:D
Answer: (D) 29%.
Question: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 36 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17
(B) 36
(C) 70
(D) 13
(E) 12
Rationale: 1/18 - 1/36 = 1/36
36 minutes
Answer: B
Answer: (B) 36
Question: The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
(A) 0
(B) 2
(C) 2.5
(D) 7/3
(E) 10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+4)^2A2= (2x-3)^2
L1= x+5L2= 2x-3
P1 = 4( x+4)P2=4(2x-3)
P1+P2=32
4( x+4) +4(2x-3)=32..............> X=7/3
Answer: D
Answer: (D) 7/3
Question: In a two-digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to 10. What is the number?
(A) 14
(B) 41
(C) 41
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the ten's digits be x. Then, unit's digit = 4x.
∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2.
So, ten's digit = 2, unit's digit = 8.
Hence, the required number is 28.
Answer D
Answer: (D) None of these
Question: If p and q are integers, such that p < 4 < q, and s is a nonnegative integer, which of the following must be true?
(A) p^2 < q^2
(B) p + q = 0
(C) sp < sq
(D) sp ≠ sq
(E) p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 5
S = 0
Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 NOT TRUE
Answer D: SP ≠ SQ... This is TRUE
Answer E: P/Q < S... not TRUE
D
Answer: (D) sp ≠ sq
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers W are there between #6 +2 and #6 +6 , inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: (A) None
Question: If (18^a) * 9^(3a – 1)= (2^7)(3^b) and a and b are positive integers, what is the value of a?
(A) 22
(B) 11
(C) 9
(D) 6
(E) 7
Rationale: (18^a) * 9^(3a – 1)= (2^7)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^7)(3^b)
Just compare powers of 2 from both sides
Answer = 7 = E
Answer: (E) 7
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III.a/b > 1
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: (D) I and II only
Question: If a radio is purchased for Rs 490 and sold for Rs 465.50
Find the loss%?
(A) 5%
(B) 4%
(C) 6%
(D) 8%
(E) 7%
Rationale: C.P=Rs 490 S.P=Rs 465.50
Loss=C.P-S.P=490-465.50=Rs 24.50
Loss%=(loss*100)/C.P%
=(24.50*100)/490%=5%
ANSWER A 5%
Answer: (A) 5%
Question: An isosceles triangle those sides are 13cm,13cm,10cm long inscribed in a circle.find the radius of the circle
(A) 8 cm
(B) 9 cm
(C) 10 cm
(D) 11 cm
(E) 7 cm
Rationale: a,b,c are sides of triangle ,ad is the median, ad^2=ab^2-bd^2 then ad=12,the centriod median divides into 2:1 ratio so 12 will be divide into 2:1 ratio so 8 is radius.
so ans is 8 cm
ANSWER:A
Answer: (A) 8 cm
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm. What is the area of the region where the two circles intersect?
(A) 16 - 4pi
(B) 4 - pi
(C) 2pi - 4
(D) 8pi - 16
(E) pi^2 - 4
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = 8pi - 16
The answer is D.
Answer: (D) 8pi - 16
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?
(A) 3366
(B) 2777
(C) 3001
(D) 3000
(E) 2811
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer:D
Answer: (D) 3000
Question: Out of 17 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 12â„13
(B) 11â„13
(C) 10â„15
(D) 1â„15
(E) 19/24
Rationale: Total possible ways of selecting 4 students out of 17students = 17C4 = =2380
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 12C4=495
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 17C4 â€“ 12C4 = 1885
âˆ´ Probability = 1885â„2380 = 19/24
Answer E
Answer: (E) 19/24
Question: If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 7 time the part of C .Find the ratio among their parts.
(A) 1:2:4
(B) 1:4:1
(C) 14:7:1
(D) 2:4:1
(E) 4:3:2
Rationale: By the assumptions as mentioned we have A=2B and B=7C. So A=2(7C) and we get A=14C. We have, therefore, A:B:C = 14C:7C:C. By cancelling the ratio with C we have 14:7:1. The answer is, therefore, C.
Answer: (C) 14:7:1
Question: a circular wheel radius is 1.75m.for covering 11k.m how much time it revolve?
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) 50
Rationale: distance traveled in 1 round=perimeter={2*22/7*175/100}m
=11 m
total no. of revolution in covering 11 km=11000/11=1000
answer C
Answer: (C) 1000
Question: A 200 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train?
(A) 228
(B) 108
(C) 1266
(D) 188
(E) 80
Rationale: S = 200/9 * 18/5 = 80 kmph
Answer: E
Answer: (E) 80
Question: A rectangular plot measuring 90 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) 34
(B) 77
(C) 36
(D) 56
(E) 91
Rationale: Explanation:
perimeter of the plot = 2(90+50) = 280m
no of poles =280/5 =56m
Answer: D
Answer: (D) 56
Question: What will come in place of the x in the following Number series? X, 22, 30, 46 ,78, 142
(A) 35
(B) 56
(C) 18
(D) 87
(E) 98
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 18
Answer: (C) 18
Question: A sum of Rs. 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs. 106, find the money lent at each rate.
(A) 700
(B) 500
(C) 300
(D) 900
(E) None of them
Rationale: Let the sum lent at 8% be Rs. x and that at 6% be Rs. (1550 - x).
=((x*8*1)/100) + ((1550-x)*6*1)/100=106
= 8x + 9300 –6x=10600  2x = 1300  x = 650.
Therefore, Money lent at 8% = Rs. 650. Money lent at 6% = Rs. (1550 - 650) = Rs. 900.
Answer is D.
Answer: (D) 900
Question: Find large number from below question The difference of two numbers is 1370. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1641
(B) 1376
(C) 1456
(D) 1555
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1370).
x + 1370 = 6x + 15
5x = 1355
x = 271
Large number = 271+1370 = 1641
A
Answer: (A) 1641
Question: What is 2 2/3 - 1 1/4 divided by 1/2 - 1/5 ?
(A) 17/36
(B) 36/17
(C) 17/6
(D) 17/4
(E) 85/18
Rationale: 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/2 - 1/5 = (5-2)/10 = 3/10
So 17/12/3/10 = 17/12 *10/ 3 = 85/18
Answer - E
Answer: (E) 85/18
Question: You have 6 sticks of lengths 20, 30, 40, 50, 60 and 70 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
(A) 3
(B) 6
(C) 7
(D) 13
(E) 12
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Based on this there can be only 13 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60), (50, 60, 70), (40,60, 70), (30,60, 70), (20,60, 70). (30, 50, 70), (40, 50,70)
Answer; D.
Answer: (D) 13
Question: In a class there are 30 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 400
(B) 500
(C) 600
(D) 530
(E) 750
Rationale: Explanation:
We can select one boy from 30 boys in 30 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 30 * 25 ways i.e., = 750 ways.
Answer: Option E
Answer: (E) 750
Question: Cindy paddles her kayak upstream at x kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
(A) mnp
(B) mn/p
(C) (x + n)/p
(D) xnp/(x + n)
(E) px/n- pn/x
Rationale: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/x
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/x)+(d/n)
=d(x+n)/xn
d=pxn/(x+n)=D
Answer: (D) xnp/(x + n)
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 30 minutes?
(A) 150km
(B) 151.2km
(C) 152.5km
(D) 153km
(E) 155km
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 1/2 hours = 7/2 hours
Distance = speed * time = 12 * 18/5 * 7/2 km = 151.2 km.
Answer:B
Answer: (B) 151.2km
Question: If x is the median the set {9/2, x,11/3, 28/9, 21/5}, x could be
(A) 16/5
(B) 17/5
(C) 21/7
(D) 4
(E) 31/7
Rationale: The median is the middle number once all the numbers are arranged in increasing/decreasing order.
We see that
11/3 = 3.something,
28/9 = 3.something
21/5 = 4.something
9/2 = 4.something
So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)
Answer (D)
Answer: (D) 4
Question: In Kaya's teacher's desk there are 3 pink highlighters, 7 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?
(A) 11
(B) 15
(C) 77
(D) 33
(E) 88
Rationale: Add the numbers of highlighters.
3 + 7 + 5 =15.
Answer is B.
Answer: (B) 15
Question: A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
(A) A)37/256
(B) B)56/256
(C) C)65/256
(D) D)70/256
(E) E)81/256
Rationale: More than 5 times tails = 6times + 7times+8times = 8C6 + 8C7 + 8C8 = 37
- - - - - - - -
2 2 2 2 2 2 2 2
2^8 times total events and 37 events where tails side up .
So probability = 37/2^8 = 37/256 (Answer A)
Answer: (A) A)37/256
Question: How many numbers from 2 to 15 are exactly divisible by 2?
(A) A)2
(B) B)3
(C) C)5
(D) D)7
(E) E)8
Rationale: 2/2 = 1 and 15/2 = 7
7 - 1 = 6
6 + 1 = 7 Numbers.
Answer : D
Answer: (D) D)7
Question: The contents of a certain box consist of 80 apples and 30 oranges. How many oranges must be added to the box so that exactly 50% of the pieces of fruit in the box will be apples?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65
Rationale: apple = (apple + orange + x)*0.5
80 = (30 + 80 + x)*0.5
x = 50
Answer: B
Answer: (B) 50
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 18%
(B) 72%
(C) 32%
(D) 12%
(E) 52%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer:D
Answer: (D) 12%
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 1/9
(B) 2 1/6
(C) 2 1/2
(D) 2 1/1
(E) 6 1/2
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7 = 2 1/2 hours.Answer:E
Answer: (E) 6 1/2
Question: A trained covered x km at 50 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 22
(B) 99
(C) 25
(D) 66
(E) 887
Rationale: Total time taken = x/50 + 2x/20 hours
= 6x/50 = 3x/25 hours
Average speed = 3x/(3x/25) = 25kmph
Answer: C
Answer: (C) 25
Question: Ramu bought an old car for Rs. 41000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) A)14%
(B) B)16%
(C) C)19.8%
(D) D)22%
(E) of these
Rationale: Total CP = Rs. 41000 + Rs. 13000 = Rs. 54000 and SP = Rs. 64900
Profit(%) = (64900 - 54000)/55000 * 100 = 19.8%
ANSWER:C
Answer: (C) C)19.8%
Question: If 7^k = 2, then 7^(4k+2) =
(A) 729
(B) 754
(C) 784
(D) 783
(E) 108
Rationale: 7^k=2
7^4k=2^4
7^4k=16
7^(4k+2)
=7^4k*7^2
=16*49
=784
Answer: C
Answer: (C) 784
Question: In your classes you counted 128 hands. How many students were at the class?
(A) 64
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 128
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 128 by 2
128 ÷ 2 = 64
Therefore, there were 64 students at the class.
ANSWER IS A
Answer: (A) 64
Question: If 30 toys cost Rs, 234, what do 35 toys cost?
(A) 273
(B) 564
(C) 546
(D) 654
(E) None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
x=(35 X 234)/30 =273
Answer is A
Answer: (A) 273
Question: A sum of Rs.6800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) A)282
(B) B)4420
(C) C)8383
(D) D)8383
(E) E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 6800[1 + 10/100][1 + 20/100][1 + 25/100]
A = 6800 * 1.65
A = Rs.11220
So the interest = 11220-6800 = Rs.4420
Answer: B
Answer: (B) B)4420
Question: A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 5%, he is only able to save Rs. 400 per month. What is his monthly salary?
(A) Rs.6500
(B) Rs.7500
(C) Rs.7200
(D) Rs.7273
(E) Rs.6300
Rationale: Income = Rs. 100
Expenditure = Rs. 90
Savings = Rs. 10
Present Expenditure 90+90*(5/100) = Rs.94.5
Present Savings = 100 – 94.5 =Rs. 5.50
If savings is Rs. 5.50, salary = Rs. 100
If savings is Rs.400, salary = 100/5.5*400 = 7273
Answer : D
Answer: (D) Rs.7273
Question: The average (arithmetic man) of three integers a, b, and c is exactly one third the median. If a < b < c and a = 0, what is the value of c/b?
(A) 1
(B) 3
(C) 4
(D) 5
(E) Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=1b/3 --> since a=0, then (0+b+c)/3=b/3 --> c=3b/3 --> c/b=1.
Answer: A.
Answer: (A) 1