mathewhe/aqua_rat huggingface dataset:
Question: A line has a slope of 3/4 and intersects the point W (-12, -39). At which point does this line intersect the x-axis?
(A) (40,0)
(B) (30,0)
(C) (0,40)
(D) (40,30)
(E) (0,30)
Rationale: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point W of intersection is (40,0).
A is the correct answer.
Answer: (A) (40,0)
Question: 5 persons working eight hours daily can complete a wall in 10 days. When they have Worked for 4 days, 5 more persons are brought to work. The wall can now be completed in?
(A) one more day
(B) two more days
(C) three more days
(D) four more days
(E) five more days
Rationale: Let D be the number of required days
Using the chain rule,
M1 x T1 = M2 x T2 + M3 x T3
5 x 8 x 10 = (4 x 5 x 8) + (10 x 8 x D)
D = 3.
Hence, the wall will be completed in 3 more days.
ANSWER:C
Answer: (C) three more days
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 11 pencils and 16 charts have been brought to the meeting, how many people are present?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 11
Total charts are 11 so A + 2B = 16
Add both: 3A + 3B = 27 so A + B = 9
Total number of people = 9
D
Answer: (D) 9
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 12 kmph, then the speed in downstream is?
(A) 27
(B) 23
(C) 20
(D) 32
(E) 12
Rationale: M = 20
S = 12
DS = 20 + 12 = 32
Answer: D
Answer: (D) 32
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 328
(B) 279
(C) 215
(D) 288
(E) 211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.Answer: C
Answer: (C) 215
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
(A) 7/18
(B) 2/7
(C) 7/9
(D) 4/7
(E) 4/5
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Option A
Answer: (A) 7/18
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) A)3/7
(B) B)5/8
(C) C)5/6
(D) D)6/7
(E) E)7
Rationale: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y = 5/6
C)
Answer: (C) C)5/6
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4554, how much was it in the beginning?
(A) 7349
(B) 6300
(C) 6325
(D) 6939
(E) 2989
Rationale: X * (90/100) * (80/100) = 4554
X = 6325
Answer: C
Answer: (C) 6325
Question: An Olympic diver received the following scores: 4, 3, 7, 6, and 5. The standard deviation of her scores is in which of the following ranges?
(A) 2.4 to 2.8
(B) 1.4 to 1.8
(C) 3.4 to 3.8
(D) 4.4 to 4.8
(E) 5.4 to 5.8
Rationale: 4+3+7+6+5/5 = 5
|4-5| = 1 1^2 = 0
|3-5| = 2 2^2 = 4
|7-5| = 2 2^2 = 4
|6-5| = 1 1^2 = 1
|5-5| = 0 0^2 = 0
SD = sqrt 10/5 =1.41
Answer : B
Answer: (B) 1.4 to 1.8
Question: In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is-
(A) 42
(B) 32
(C) 48
(D) 28
(E) 38
Rationale: X/63 = 24.
X = 24 *63.
So correct answer would be,
(24 *63) /36 = 42.
ANSWER : A
Answer: (A) 42
Question: A shopkeeper purchased 150 identical pieces of calculators at the rate of 250 each. He spent an amount of 2500 on transport and packing. He fixed the labelled price of each calculator at 320. However, he decided to give a discount of 5% on the labelled price. What is the percentage profit earned by him ?
(A) 14 %
(B) 15 %
(C) 16 %
(D) 20 %
(E) None of these
Rationale: C.P. of 150 calculators
= 150 × 250 + 2500 = 37500 + 2500 = 40000
Labelled price of 150 calculators
= 150 × 320 = 48000
Discount allowed = 5%
∴ S.P. of 150 calculators
= 48000 – 5% = 45600
∴ Profit % = 5600⁄40000 × 100 = 14
Answer A
Answer: (A) 14 %
Question: The largest six digit number which is a perfect cube, is:
(A) 970299
(B) 907289
(C) 992289
(D) 900279
(E) 999999
Rationale: Explanation:
99*99*99 = 970299
Answer: A
Answer: (A) 970299
Question: if x = 4 + 4 - 4 + 4 - ......¥ find the value of x
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x=4+4-x.
2x=8.
x=4
ANSWER:D
Answer: (D) 4
Question: A women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
(A) 2 1/5 Km
(B) 3 1/5 Km
(C) 4 1/3 Km
(D) 8 Km
(E) 8 1/3 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 5*6/1 * 16/60
= 30/1 * 16/60
= 30 * 4/15
= 8 Km
D
Answer: (D) 8 Km
Question: In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of
male staff to female staff
(A) 3 : 2
(B) 5 : 2
(C) 2 : 1
(D) 4 : 3
(E) 3: 5
Rationale: Expl : 10% of MS = 1/4th of FS -> 10MS/100 = 1/4FS -> MS = 5/2 FS
:. MS/FS = 5/2 = MS : FS = 5 : 2
Answer: B
Answer: (B) 5 : 2
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2877
(C) 267
(D) 2787
(E) 281
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer:A
Answer: (A) 3944
Question: In how many ways letters of the word RSCUPERATE be arranged?
(A) 154546
(B) 154632
(C) 164333
(D) 243456
(E) 302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: (E) 302400
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 1
(B) 1/256
(C) 81/256
(D) 175/256
(E) 144/256
Rationale: "A man can hit a target once in 4 shots" means that the probability of hitting the target is 1/4, thus the probability of missing the target is 1-1/4=3/4.
The probability that he will hit a target while shooting 4 times is basically the probability that he will hit at least once, so 1-(the probability that he will miss all 4 times): P=1−(34)^4=175/256.
Answer: D.
Answer: (D) 175/256
Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
(A) 0
(B) 20
(C) 10
(D) 8
(E) 4
Rationale: Solution:
Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.
Total number of candidates = 200.
Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.
We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.
Answer C
Answer: (C) 10
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 46 years. What will be the age of the B ten years hence?
(A) 22
(B) 92
(C) 26
(D) 96
(E) 51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 46 => b + c = 92 --- (2)
From (1) and (2), we cannot find b.
Answer: B
Answer: (B) 92
Question: By selling 22 pencils for a rupee a man loses 40%. How many for a rupee should he sell in order to gain 40%?
(A) 8.56
(B) 9.35
(C) 9.43
(D) 6.56
(E) 5.5
Rationale: 60% --- 22
140% --- ?
60/140 * 22 = 9.43
Answer: C
Answer: (C) 9.43
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
(A) 31
(B) 42
(C) 102
(D) 52
(E) 62
Rationale: Answer: Option B
5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: (B) 42
Question: A certain club has 20 members, including Harry. One of the 20 members is to be chosen at random to be the president, one of the remaining 19 members is to be chosen at random to be the secretary, and one of the remaining 18 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
(A)  1/720
(B)  1/80
(C)  1/10
(D)  1/9
(E) 2/20
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/20 and the probability that Harry will be selected to be the treasurer is also 1/20. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/20+1/20=2/20
Answer: E.
Answer: (E) 2/20
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 187 kmph
(C) 164 kmph
(D) 175 kmph
(E) 106 kmph
Rationale: 624/6
= 104 kmph
Answer: A
Answer: (A) 104 kmph
Question: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
(A) 40
(B) 80
(C) 120
(D) 160
(E) 180
Rationale: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to Q then from Q to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Answer: (D) 160
Question: If a - b = 3 and a^2 + b^2 = 33, find the value of ab.
(A) 12
(B) 15
(C) 10
(D) 18
(E) 13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 33 - 9 = 24
ab = 12.
Answer is A.
Answer: (A) 12
Question: A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?
(A) 55 km/h
(B) 65 km/h
(C) 85 km/h
(D) 75 km/h
(E) 90 km/h
Rationale: Let d be the distance bewteen A and B
T1 = d / 50 : travel time from A to B
Let S be the speed from B to A
T2 = d/S : travel time from B to A
60 = 2d/(T1 + T2) : average speed for the whole trip
60 = 2d/(d/50 + d/S) : substitute T1 and T2
S = 75 km/hour : solve the above equation for S.
correct answer is D)75 km/h
Answer: (D) 75 km/h
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.9 sec
(C) 8.9 sec
(D) 6.9 sec
(E) 2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Answer: (A) 2.5 sec
Question: The current birth rate per thousand is 32, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
(A) 2.1%
(B) 3.2%
(C) 3.9%
(D) 4%
(E) 5.1%
Rationale: Net growth on 1000 = 32-11 = 21
Net growth on 100 = 21*100/1000 = 2.1%
Answer is A
Answer: (A) 2.1%
Question: An amount of Rs.80,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
(A) 2378
(B) 20000
(C) 2697
(D) 5000
(E) 6971
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 80,000
Thus we get, 2Q + Q + Q + 4Q = 80,000
8Q = 80,000 or Q = Rs. 10000
Thus, R = Rs. 10000, P = 20000 & S = Rs. 40000
Hence, the required difference = (S – P) = (40000 – 20000) = Rs. 20000
ANSWER:B
Answer: (B) 20000
Question: A man bought a horse and a carriage for 3000. He sold the horse at a gain of 20% and the carriage at a loss 10%, there by gaining 2% on the whole. Find the cost of the horse.
(A) 1000
(B) 1200
(C) 1500
(D) 1700
(E) None of these
Rationale: Let the C.P. of horse = x
Then the C.P. of carriage = (3000 – x)
20% of x – 10% of (3000 – x) = 2% of 3000
⇒ x⁄5 - (3000−x)/10=60
⇒ 2x - 3000 + x = 600
⇒ 3x = 3600 ⇒ x = 1200
Answer B
Answer: (B) 1200
Question: Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 5 kilometers per hour?
(A) 15
(B) 12.5
(C) 10
(D) 8
(E) 7.75
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
5= 2*3*x/3+x
x= 15
A is the answer
Answer: (A) 15
Question: A 6% stock yields 8%. The market value of the stock is:
(A) 48
(B) 75
(C) 55
(D) 46
(E) 57
Rationale: For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.100
---- x 6	= Rs. 75.
8
Market value of Rs. 100 stock = Rs. 75.
Answer: Option B
Answer: (B) 75
Question: The price of 3 chudi and 6 tops is Rs. 1500. With the same money one can buy 1 chudi and 12 tops. If one wants to buy 5 tops, how much shall she have to pay ?
(A) 500
(B) 1000
(C) 1200
(D) 1300
(E) 1500
Rationale: Let the price of a chudi and a top be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
cost of 5 tops = 5*100 = 500
Answer : A
Answer: (A) 500
Question: 20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability.
(A) 1/19
(B) 2/29
(C) 3/29
(D) 4/29
(E) 5/29
Rationale: 20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person
(s1 p s2) be 1 set
then 20-3 persons => 17 persons + 1 set= 18
18 can be arranged in 17! ways bcz it is circular permutuation
the 2 sis can be arranged in 2! ways
and the p place can be filled in 18 ways
and the total permutations are 19!
probability is = (2!*18*17!)/(19!)
= 2/19
ANSWER:B
Answer: (B) 2/29
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
(A) 10.35 a.m
(B) 10.15 a.m
(C) 10.55 a.m
(D) 10.22 a.m
(E) 10.25 a.m
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer: E
Answer: (E) 10.25 a.m
Question: A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 10 sec
(B) 8 sec
(C) 6 sec
(D) 4 sec
(E) 2 sec
Rationale: Explanation:
Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110/(110/6) = 6 s
Answer: Option C
Answer: (C) 6 sec
Question: Henry solved a certain number of algebra problems in an hour, his older brother Frank solved
four times as many. Together they solved 80. How many were solved by each?
(A) H-12 F-49
(B) H-30 F-83
(C) H-20 F-90
(D) H-16 F-64
(E) H-40 F-100
Rationale: I am looking for the number of problems solved by Henry (H) and Frank (F).
Who solved the least number of problems? Hopefully, you said Henry.
So let H = x
Frank solved four times as many, therefore
F = 4x
Read the problem again to find a relationship. Together they solved 80. That means that
H + F = 80 Substituting
x + 4x = 80 Solving for x
5x = 80
x = 16
Therefore Henry solved 16 and Frank solved 4 times 16 of 64 problems.
correct answer D
Answer: (D) H-16 F-64
Question: A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
(A) 981
(B) 1000
(C) 1011
(D) 1101
(E) 1110
Rationale: The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.=1000
Answer: B.
Answer: (B) 1000
Question: Jonathan’s grandparents lend $30,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
(A) 30,000∗0.1^5
(B) 30,000∗0.5
(C) 30,000∗1.5
(D) 30,000∗1.1^5
(E) (30,000∗0.1)^5
Rationale: if you are like me and have used S.I = P x R x T formula in school, while the question is asking for Amount in 5 years. so (c) 30,000∗ 1.5
Ans : C
Answer: (C) 30,000∗1.5
Question: The sum e of prime numbers that are greater than 60 but less than 70 is
(A)  67
(B)  128
(C)  191
(D)  197
(E)  260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum e of 61 and 67 is 128.
Answer B.
Answer: (B)  128
Question: If a = 1 and b = -2, then (2a^2 + b)(w + y) + (a + b)(w - y) =
(A) 0
(B) 2x
(C) y - w
(D) x - y
(E) x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(w+y)=y-w => Smash C
Answer: (C) y - w
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
(A) 11
(B) 72
(C) 36
(D) 99
(E) 27
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: B
Answer: (B) 72
Question: What is the largest possible value of cc if 5c+(d−12)^2=235?
(A) 17
(B) 25
(C) 35
(D) 42
(E) 47
Rationale: To maximize c, we should minimize (d-12)^2. (d-12)^2 is a square of a number, thus its smallest possible value is 0 (for d = 12).
In this case we'd have 5c + 0 = 235 --> c = 47.
Answer: E.
Answer: (E) 47
Question: The value of (34.31*0.5*1.567)/(0.0673*23.25*7.57) is close to
(A) 2
(B) 1.15
(C) 2.05
(D) 2.27
(E) 2.35
Rationale: (34.31*0.5*1.567)/(0.0673*23.25*7.57) = 26.882/11.845
= 2.27
ANSWER:D
Answer: (D) 2.27
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 8 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 25
(B) 35
(C) 75
(D) 80
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 8 = 76
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 76 + 4 = 80
D
Answer: (D) 80
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey?
(A) 3.00kmph
(B) 2.50kmph
(C) 3.50kmph
(D) 3.11kmph
(E) 3.90kmph
Rationale: M = 4.5
S = 2.5
DS = 7
US = 2
AS = (2 * 7 * 2) /9 = 3.11
Answer:D
Answer: (D) 3.11kmph
Question: If a^2bc^2 = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. a^2c^2 = 1
(A) I
(B) II
(C) III
(D) none
(E) I&II
Rationale: D
Answer: (D) none
Question: In a ratio which is equal to 4:6, if the antecedent is 30, then the consequent is?
(A) 72
(B) 85
(C) 64
(D) 51
(E) 45
Rationale: We have 4/6 = 30/x
4x = 30*6
x = 45
consequent = 45
Answer is E
Answer: (E) 45
Question: How many days will there be from 25th January,1996 to 15th May,1996(both days included)?
(A) 112
(B) 103
(C) 111
(D) 120
(E) 121
Rationale: Explanation:
Number of days from 25-Jan-1996 to 15-May-1996 (both days included)
= 7(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 112
Answer: Option A
Answer: (A) 112
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 4 years?
(A) x (1+n/100)^5 - x
(B) x (1+n/100)^4 - x
(C) 3x (1+n/100)^4 - x
(D) x (1+n/100)^6 - x
(E) 2x (1+n/100)^4 - x
Rationale: Amount after 4 years compounded yearly = x (1+n/100)^4
Thus profit = Final amount - original principle = x (1+n/100)^4 - x . Answer : B
Answer: (B) x (1+n/100)^4 - x
Question: The ratio of 2 numbers is 2:5 and their H.C.F. is 6. Their L.C.M. is ?
(A) 20
(B) 24
(C) 52
(D) 36
(E) 60
Rationale: Let the numbers be 2x and 5x
Their H.C.F. = 6
so the numbers are 2*6 , 5*6 = 12,30
L.C.M. = 60
Answer is E
Answer: (E) 60
Question: If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ?
(A) 33
(B) 76
(C) 29
(D) 10
(E) 17
Rationale: Explanation:
Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
GREEN = 7 + 18 + 5 + 5 + 14 = 49
Thus we get,
VIOLET = 22 +9 +15+12 + 5 + 20 = 83
PINK = 16 + 9 + 14 + 11 = 50
Thus, difference is 83 – 50 = 33.
ANSWER: A
Answer: (A) 33