mathewhe/aqua_rat huggingface dataset:
Question: Martha is 4 times the age of her daughter,Lyndra 4 years ago she was 8 times her daughters age,after how may years will martha be twice lyndra's age
(A) 14y
(B) 28y
(C) 7y
(D) 21y
(E) 22y
Rationale: Let m and l be the present ages of Martha and Lyndra
Then m=4l
4 years ago
(m-4)=8(l-4)
m = 8l-28
Equate "m"
4l = 8l - 28
4l = 28
l = 7
m = 28
After x years , Martha ll be twice of Lyndra
(m+x) = 2(l+x)
28+x = 2*7+2x
28+x = 14+2x
x = 14
So after 14 years martha and lyndra ages ll be 42 and 21
ANSWER:A
Answer: (A) 14y
Question: Find the value of 201834 x 99999 = m?
(A) 20183198166
(B) 20194181766
(C) 20175292556
(D) 20132191166
(E) 20153198166
Rationale: 201834 x 99999 = 201834 x (100000 - 1)
= 201834 x 100000 - 201834 x 1
= 20183400000 - 201834
= 20183198166
A
Answer: (A) 20183198166
Question: A man can row 3.3 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
(A) 1.9
(B) 1.7
(C) 1.2
(D) 1.5
(E) 1.1
Rationale: Speed of boat in still water (b) = 3.3 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.1 km/hr.
Answer: E
Answer: (E) 1.1
Question: The 80-milliliter solution of sugar and water is 20% sugar. How much water (in milliliters) must be added to make a solution that is 5% sugar?
(A) 240
(B) 280
(C) 320
(D) 360
(E) 400
Rationale: In the original solution the amount of sugar is 0.2*80=16 ml.
Let the volume of the new solution be V.
0.05V=16 ml.
V=320 ml.
The amount of water we need to add is 320 - 80 = 240 ml.
The answer is A.
Answer: (A) 240
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 24 hours and 8 hours respectively. The ratio of their speeds is
(A) 4 : 9
(B) 4 : 3
(C) 1 : 3
(D) 4 : 8
(E) 4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 24 = 1 : 3.Answer: C
Answer: (C) 1 : 3
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 22 Kmph
(B) 68 Kmph
(C) 56 Kmph
(D) 11 Kmph
(E) 76 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: (B) 68 Kmph
Question: An aeroplane covers a certain distance of 450 Kmph in 4 hours. to cover the same distance in 3 2/3 hours, it Must travel at a speed of
(A) 440
(B) 490
(C) 640
(D) 740
(E) 250
Rationale: Speed of aeroplane = 450 Kmph
Distance travelled in 4 hours
= 450 * 4 = 1800 Km
Speed of aeroplane to acver 1800 Km in 11/3
= 1800*3/11 = 490 Km
Answer B.
Answer: (B) 490
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
(A) 10.49
(B) 10.4
(C) 10.42
(D) 10.41
(E) 10.46
Rationale: S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D. on Rs. 260 = Rs. 10	x 260 = Rs. 10.40
250
Answer: B
Answer: (B) 10.4
Question: A train 300 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 987
(B) 54
(C) 72
(D) 27
(E) 28
Rationale: Length = Speed * time
Speed = L/T
S = 300/20
S = 15M/Sec
Speed= 15*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 54Kmph
Answer:B
Answer: (B) 54
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 34 Km/hr. His average speed during the whole journey in km/hr. is :
(A) 34
(B) 43
(C) 40
(D) 38
(E) 29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*43*34 / 43+34
= 2924 / 77
= 37.974... = 38
Answer : D
Answer: (D) 38
Question: Preeti covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%.
(A) 60 km/h
(B) 70 km/h
(C) 117.64 km/h
(D) 100 km/h
(E) 125.25 km/h
Rationale: Given Speed = 60 Kmph.
It means Preeti covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km.
50% time reduced = 40 - 50% of 40 = 20 min.
Thus, Preeti needs to cover 40 km in 20 min (0.34 hour).
Speed * Time = Distance.
Speed * 0.34 = 40
Speed = 117.64 kmph.
ANSWER : OPTION C
Answer: (C) 117.64 km/h
Question: If a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours, what is the speed of the boat and the river?
(A) 21 , 21
(B) 9 , 21
(C) 21 , 9
(D) 9 , 9
(E) 20 , 8
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 30 ; Us = 12
x = (30 + 12) / 2 = 42/2 = 21 km/hr
y = (30 - 12)/2 = 18/2 = 9 km/hr
ANSWER: C
Answer: (C) 21 , 9
Question: If a, b and c are forming increasing terms of G.P., r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 = 6.Note that r can be any real no.
(A) 23
(B) 16
(C) 17
(D) 12
(E) 62
Rationale: Explanation:
a,b,c are in G.P. so let the first term of G.P. = arar, and common ratio = r.
Therefore, a = arar, b = aa, c = arar
Given, loga+logb+logclog6=6log⁡a+log⁡b+log⁡clog⁡6=6
⇒logabclog6=6⇒log⁡abclog⁡6=6
⇒log6abc=6⇒abc=66⇒log6abc=6⇒abc=66
put the value of a,b,c in gp format
⇒ar×a×ar=66⇒ar×a×ar=66
⇒a3=66⇒a=36⇒a3=66⇒a=36
Now a = 36r36r, b = 36, c = 36r.
We have to find the minimum value of c - b = 36r - 36.
r can be any number. So for r < 0, we get c - b negative.
When r = 1, c - b = 0
But none of the options are not representing it.
From the given options, r = 4/3, then c = 48. So option d satisfies this.
Answer: D
Answer: (D) 12
Question: One fourth of a solution that was 22% sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 74%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.22+1/4*x=1*0.35 --> x=0.74. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.22+25*x=100*0.35 --> x=0.74.
Answer: A.
Answer: (A) 74%
Question: Working alone, Mary can pave a driveway in 5 hours and Hillary can pave the same driveway in 3 hours. When they work together, Mary thrives on teamwork so her rate increases by 10%, but Hillary becomes distracted and her rate decreases by 10%. If they both work together, how many hours will it take to pave the driveway?
(A) 2 hours
(B) 4 hours
(C) 5 hours
(D) 6 hours
(E) 7 hours
Rationale: Initial working rates:
Mary = 1/5 per hour
Hillary = 1/3 per hour
Rate when working together:
Mary = 1/5 + (1/10*1/5) = 2/9 per hour
Hillary = 1/3 - (1/10*1/3) = 3/10 per hour
Together they work 2/9 + 3/10 = 1/2 per hour
So they will need 2 hours to complete the driveway. The correct answer is A.
Answer: (A) 2 hours
Question: A and B together can do a piece of work in 1 days. If A alone can do the same work in 20days, then B alone can do the same work in?
(A) 0.35 days
(B) 0.45 days
(C) 0.55 days
(D) 0.25 days
(E) 0.95 days
Rationale: B = 1/1 – 1/20 =0.95 days
ANSWER:E
Answer: (E) 0.95 days
Question: Which of the following is a divisible by 9 number ?
(A) 91
(B) 81
(C) 78
(D) 22
(E) 11
Rationale: Explanation :
81 is a divisible by 9
Answer : Option B
Answer: (B) 81
Question: In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ?
(A) 30
(B) 45
(C) 42
(D) 72
(E) 75
Rationale: Let the number of benches in the class be x.
Then, 6(x + 1) = 7x - 5
x = 11.
Hence, number of students in the class	= 6 ( x + 1)
= 6 x 12
= 72.
ANSWER:D
Answer: (D) 72
Question: 75 boys can complete a job in 24 days. How many men need to complete the job twice in 20 days
(A) 160
(B) 170
(C) 180
(D) 190
(E) 200
Rationale: One man can complete the job in 24*75=1800 days
To complete the job twice he would need 3600 days.
Thus, to complete the job in 20 days, 3600/20=180 men are needed.
ANSWER:C
Answer: (C) 180
Question: In a room there are 10 people. Each shake hands with every other person. How many hand shakes?
(A) 50
(B) 62
(C) 75
(D) 45
(E) 61
Rationale: Any pair of person = 10C2 = 10!/8!*2! = 45
Answer is D
Answer: (D) 45
Question: Consider four consecutive integers. What is the sum of the 2nd and fourth numbers if the first number is 13?
(A) 26
(B) 19
(C) 30
(D) 43
(E) None
Rationale: 1st = x = 13
2nd = x+1
3rd = x+2
4th = x+3
------
sum of 2nd and fourth numbers::
x+1+x+3 = 13+1+13+3 = 30
Answer C
Answer: (C) 30
Question: The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both?
(A) Rs.1200,Rs.1800
(B) Rs.1200,Rs.1000
(C) Rs.8200,Rs.1600
(D) Rs.1200,Rs.1960
(E) Rs.1200,Rs.1600
Rationale: The savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively.
3x - 5y = 200 --- (1)
4x - 7y = 200 --- (2)
Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get x = 400.
The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively.
Answer:E
Answer: (E) Rs.1200,Rs.1600
Question: The average of first 12 natural numbers is?
(A) 5.2
(B) 6.5
(C) 5.3
(D) 5.9
(E) 5.1
Rationale: Sum of 12 natural no. = 156/2 = 78
Average = 78/12 = 6.5
Answer:B
Answer: (B) 6.5
Question: A man can do a job in 15 days. His father takes 20 days and his son finishes it in 15 days. How long will they take to complete the job if they all work together?
(A) 6.3
(B) 6.9
(C) 5.5
(D) 6.1
(E) 6.2
Rationale: 1 day work of the three persons = (1/15 + 1/20 + 1/15) = 11/60
So, all three together will complete the work in 300/47 = 5.5 days.
Answer:C
Answer: (C) 5.5
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 28 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=28..
4x+12=28..
x=4..
ans =x+4=4+4=8
Aswer D
Answer: (D) 8
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 1079
(B) 1017
(C) 1023
(D) 1017
(E) 1012
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer: C
Answer: (C) 1023
Question: Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 5 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: One way to do this would be weighted average method..
1) let the average of 5 mocks be x...
so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...
By alligation/weighted average..
the difference in 760 and 726.67 is 5/6 of difference of 760 and x..
760-726.67 = 5/6 * (760-x)
760-x= 33.33*6/5=40...
so x = 720..
the last of mock test will be 720+5+5=730...
so ans = 760-730=30
B
Answer: (B) 30
Question: Set D consists of all the prime numbers between 10 and 25. What is the range of set D?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 23
Rationale: Answer of set D is 12=A
Answer: (A) 12
Question: On a Monday in a certain restaurant, 20 percent of the 170 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
(A) 15%
(B) 16%
(C) 18%
(D) 23%
(E) 30%
Rationale: 20% of 170= 34
10% of 120=12
Total =46
percent for 2 days combined =46/300 ≈0.15. so it should be less than 0.15 so it is 15%
Answer:A
Answer: (A) 15%
Question: How many integers n are there such that 1< 4n +4 < 20?
(A)  Five
(B)  Four
(C)  Three
(D)  Two
(E)  One
Rationale: Solution:
1< 4n + 4 < 20
1< 4n + 4 < 20
We first subtract 4 from all three parts of the inequality, and we obtain:
-3 < 4n < 16
Next, we divide both sides of the inequality by 4 and we get:
-3/4 < n < 4
The answer is B
Answer: (B)  Four
Question: A seller uses 800gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 10% gain on cost price?
(A) 32.5%
(B) 37.5%
(C) 35%
(D) 40%
(E) 50%
Rationale: Selling price of 800gm = 100+10 = $110
Profit = 110-80 = $30
% of profit = 30*100/80 =37.5 %
Answer is B
Answer: (B) 37.5%
Question: A man sitting in a train which is traveling at 60 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
(A) 52 kmph
(B) 58 kmph
(C) 62 kmph
(D) 65 kmph
(E) 75 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 60) kmph = 52 kmph.
Answer : A
Answer: (A) 52 kmph
Question: Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings?
(A) (10!)^3 / 2^10
(B) (10!)^3 / 3^10
(C) 30! / 2^10
(D) 30! / 3^10
(E) 30! / 6^10﻿
Rationale: By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts.
30! / 6^10﻿
ANSWER:E
Answer: (E) 30! / 6^10﻿
Question: The circumferences of two circles are 396 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 29960 sq m
(B) 26950 sq m
(C) 43120 sq m
(D) 27680 sq m
(E) 27786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 396 and 2∏l = 704
s = 396/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{198^2/∏^2 - 352^2/∏^2}
= 198^2/∏ - 352^2/∏
= (198 - 352)(198 + 352)/∏
= (154)(550)/(22/7)
=26950 sq m
Answer:B
Answer: (B) 26950 sq m
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $72000, what is their combined tax rate?
(A) 32%
(B) 34.4%
(C) 35%
(D) 35.6%
(E) 36.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 72000/128000 = 72/128 = 9/16. 9/16 is a little above 8/16 = 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: (D) 35.6%
Question: George owns twelve audio compact discs. If he takes two of them to play on an upcoming car trip, how many different pairs of compact discs could he choose?
(A) 144
(B) 132
(C) 72
(D) 66
(E) 36
Rationale: C212=66
Answer: D.
Answer: (D) 66
Question: The length of the bridge, which a train 250 metres long and travelling at 72 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 350 m
(E) 240 m
Rationale: Speed = [72 X 5/18] m/sec = 20 m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (250 + x)/30 = 20 => 250 + x= 600 => x = 350 m.
ANSWER:D
Answer: (D) 350 m
Question: An inspector rejects 0.0000008% of the meters as defective. How many will be examine to project ?
(A) 2000
(B) 230000000
(C) 2700
(D) 250000000
(E) 250
Rationale: Let the number of meters to be examined be x.
Then, 0.0000008% of x =2
[(8/10000000)*(1/100)*x] = 2
x = [(2*10000000*100)/8] = 250000000
Answer is D.
Answer: (D) 250000000
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 22 sec
(B) 88 sec
(C) 99 sec
(D) 20 sec
(E) 17 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.Answer: D
Answer: (D) 20 sec
Question: A company gives bonus to retailer annually for a set target. This year the retailer has reached 1/4 of his target. If this year his target is increased to 20% from last year, how much target percentage of last year's target he should reach in order to get the bonus.
(A) 5/20
(B) 19/20
(C) 6/5
(D) 10/24
(E) 2/3
Rationale: Given 1/4 and 20% that is 1/5
Let the target of last year be 20
This year's target is 20% more of last year= 24
Target already reached is 1/4 *20=5
Remaining is 24-5=19
Required 19/20
Answer is (B)
Answer: (B) 19/20
Question: Rs. 900 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. 900 become in 3 years ?
(A) Rs. 1020.80
(B) Rs. 1025
(C) Rs. 1064
(D) Data inadequate
(E) None of these
Rationale: Solution
S.I. = Rs.(956-900 )=Rs.56
Rate = (100x56/900x3) = 56/27%
New rate = (56/27 +4)% = 164/27%
New S.I. = Rs.(900 x 164/27 x 3/100) Rs. 164.
∴ New amount = Rs.(900+164)= Rs. 1064.
Answer C
Answer: (C) Rs. 1064
Question: Replace X with the appropriate number in
2 , 4 , 6 , 30 , 32 , 34 , X
(A) 38
(B) 8
(C) 5
(D) 36
(E) 37
Rationale: D
list of consecutive numbers that does not contain a 'e' in the spelling
Answer: (D) 36
Question: A train 190 m long passed a pole in 10 sec. How long will it take to pass a platform 1200 m long?
(A) 80
(B) 73
(C) 78
(D) 67
(E) 56
Rationale: Speed = 190/10 = 19 m/sec.
Required time = (190 + 1200)/19 = 73 sec.
Answer: Option B
Answer: (B) 73
Question: A person walks from one end to the other of a 60-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
(A) 48
(B) 60
(C) 72
(D) 84
(E) 96
Rationale: Let v be the speed of the person and let x be the speed of the walkway.
30(v+x)=60 then 120(v+x)=240
120(v-x)=60
When we add the two equations:
240v=300
v=5/4
time = 60 / (5/4) = 48 seconds
The answer is A.
Answer: (A) 48
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:8
(B) 4:1
(C) 4:3
(D) 4:2
(E) 4:7
Rationale: 12:9
= 4:3
Answer: C
Answer: (C) 4:3
Question: Machine P and Machine Q are each used to manufacture 990 sprockets. It takes Machine P 10 hours longer to produce 990 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
990/x = 990/1.1x + 10
1.1(990) = 990 + 11x
11x = 99
x = 9
The answer is E.
Answer: (E) 9
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(A) Rs. 9423
(B) Rs. 10,250
(C) Rs. 12,500
(D) Rs. 14,000
(E) None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500
ANSWER:E
Answer: (E) None of these
Question: The average marks of 30 students in a class is 100. But a student mark is wrongly noted as 70 instead of 10 then find the correct average marks?
(A) A)78
(B) B)82
(C) C)98
(D) D)91
(E) E)85
Rationale: correct avg marks = 100+(10-70)/30
avg = 100-2 = 98
Answer is C
Answer: (C) C)98
Question: 30 liters of a mixture contains milk and water in the ratio 2:1. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 3:2
(B) 3:1
(C) 4:1
(D) 5:2
(E) 2:1
Rationale: Quantity of milk in 30 liters if mix = 30*2/3 =20 liters
Quantity of milk in 35 liters of new mix = 20+5 = 25 liters
Quantity of water in it = 35-25 = 10 liters
Ratio of milk and water in new mix = 25:10 = 5:2
Answer is D
Answer: (D) 5:2
Question: When 8 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
(A) 1
(B) 3
(C) 8
(D) 31
(E) 64
Rationale: Total outcome is 2^8 = 256
Favourable cases = H_ _ _ _ _ _ H
The second to seventh places can be occupied by either H or T
There are 2^6 =64 ways that can be done.
Hence, the correct option is E
Answer: (E) 64
Question: Find the perimeter and area of a square of side 15 cm.
(A) 144
(B) 169
(C) 196
(D) 121
(E) 225
Rationale: We know that the perimeter of square = 4 Ã— side
Side= 15 cm
Therefore, perimeter = 4 Ã— 15 cm = 60 cm
Now, area of the square = (side Ã— side) sq. units
= 15 Ã— 15 cmÂ²
= 225 cmÂ²
ANSWER : E
Answer: (E) 225
Question: At what rate percent on simple interest will Rs.750 amount to Rs.975 in 5 years?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 225 = (750*5*R)/100
R = 6%.Answer: E
Answer: (E) 6
Question: At the beginning of 1992, Maria's stock portfolio was worth $600,000. During 1992, the portfolio's value increased by 95%. During the next year, the portfolio increased its worth by only 5%. What was Maria's portfolio worth, in dollars, by the end of 1993?
(A) 1,180,000
(B) 1,200,000
(C) 1,200,300
(D) 1,228,500
(E) 1,330,000
Rationale: By the end of 1992, the port folio worth is 1.95 * ($600K)
By 1993, the portfolio is 1.05 * (1.95 * $600K)
=$ 1,228,500
ANSWER:D
Answer: (D) 1,228,500
Question: If A:B = 1/3: 1/4 B:C = 1/3:1/4 then A:B:C?
(A) 1:2:3
(B) 16:12:9
(C) 4:12:16
(D) 9:6:18
(E) 4:6:8
Rationale: A:B = 1/3:1/4= 4:3
B:C = 1/3:1/4 =4:3
--------------------
A:B:C = 16:12:9
Answer: B
Answer: (B) 16:12:9
Question: David biked 16 1/3 miles in 2 hours and 20 minutes. What was his average rate of speed in miles per hour?
(A) 7
(B) 7 2/3
(C) 8 1/3
(D) 9
(E) 9 1/3
Rationale: D = 16(1/3) = 49/3
T = 2(1/3) = 7/3
S = D/T = 7
Answer = A
Answer: (A) 7
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
(A) 238
(B) 600
(C) 299
(D) 277
(E) 1211
Rationale: 72 kmph = 72 * 5/18 = 20 mps
D = Speed * time = 20 * 30 = 600 m.Answer: B
Answer: (B) 600
Question: Which of these numbers is different from the others?
(A) 678
(B) 690
(C) 696
(D) 702
(E) 708
Rationale: All of the numbers are multiples of 6. 702 is the only number that is also a multiple of 9.
Answer: D
Answer: (D) 702
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/39
(C) 31/99
(D) 31/77
(E) 16/99
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: (A) 31/32
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. 850 per sq. metre.
(A) s. 15,550
(B) s. 15,600
(C) s. 16,500
(D) s. 17,600
(E) s. 18,700
Rationale: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.
Cost of paving = Rs. (850 Ã— 22) = Rs. 18700
Answer: Option E
Answer: (E) s. 18,700