mathewhe/aqua_rat huggingface dataset:
Question: Gary’s Gas Station serves an average of 12 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
(A) 1,072
(B) 1,200
(C) 1,240
(D) 1,280
(E) 1,320
Rationale: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 12)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 12 + 10) = 16 * 67 = 1072
Answer: A
Answer: (A) 1,072
Question: Which of the following could not be the lengths of the sides of a right angled triangle?
(A) 3, 4, 5
(B) 5, 12, 13
(C) 8, 15, 17
(D) 12, 15, 18
(E) 9, 12, 15
Rationale: A. 5^2 = 3^2+ 4^2
B. 13^2 = 12^2+ 5^2
C. 17^2 = 15^2 + 8^2
D. 18^2 not = 12^2 + 15^2
E. 15^2 = 12^21 + 9^2
Hence answer will be (D)
Answer: (D) 12, 15, 18
Question: A man can row upstream at 10kmph and downstream at 24 kmph. The speed of the stream is
(A) 2.5 km/hr
(B) 4.2 km/hr
(C) 7 km/hr
(D) 10.5 km/hr
(E) None
Rationale: Sol.
Speed of stream = 1/2(24 -10) kmph = 7 kmph.
Answer C
Answer: (C) 7 km/hr
Question: A side of beef lost 40 percent of its weight in processing. If the side of beef weighed 240 pounds after processing, how many pounds did it weigh before processing?
(A) 191
(B) 400
(C) 737
(D) 840
(E) 1,560
Rationale: Let weight of side of beef before processing = x
(60/100)*x = 240
=> x = (240 * 100)/60 = 400
Answer B
Answer: (B) 400
Question: To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 25%, and reduce the price it charges its consumers by 25% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?
(A) 1. No change
(B) 2. 78%
(C) 3. 100%
(D) 4. 300%
(E) 5. 400%
Rationale: Answer is B
Take smart numbers
Let,
L = 20: B = 10: H= 10 of initial box and Price = 100$
Therefore Price / cubic inch = 100 / (20*10*10) =0.05
Now, when dimensions are reduced by 25% and price also reduced by 25%
L = 15; B=7.5; H=7.5 and Price = 75$
Therefore price / cubic inch = 75 / (15*7.5*7.5) =0.089
Percentage change = (0.089 - 0.05) *100/ 0.025 = 78%
Answer: (B) 2. 78%
Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?
(A) 2 days
(B) 3 days
(C) 4 days
(D) 5 days
(E) 6 days
Rationale: A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days
ANSWER B 3 days
Answer: (B) 3 days
Question: Can anyhow help me with an easy solution for this
2, 5, 25, 4, 8, 36, 6, 14, ?
(A) 121
(B) 100
(C) 144
(D) 169
(E) 225
Rationale: 2, 5, 25, 4, 8, 36, 6, 14, ?
5-2=3 and 3+2=5 and 5^2=25
8-4=4 and 4+2=6 and 6^2=36
14-6=8 and 8+2=10 and 10^2=100
ANSWER:B
Answer: (B) 100
Question: How much 60% of 50 is greater than 40% of 30?
(A) 18
(B) 91
(C) 11
(D) 17
(E) 12
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Answer: (A) 18
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 20 and 15 hours respectively and C can empty it in 30 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 7 AM
(B) 5 AM
(C) 6 AM
(D) 4 AM
(E) 11 AM
Rationale: 1 to 2 = 1/20
2 to 3 = 1/20 + 1/15 = 7/60
After 3 AM = 1/20 + 1/15 - 1/30= 5/60
1/20 + 7/60 = 1/6
1 h ---- 5/60
? ----- 1/6
2hours ==> 5 AM
Answer:B
Answer: (B) 5 AM
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/6
(B) 80/7
(C) 80/9
(D) 80/2
(E) 80/1
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer:B
Answer: (B) 80/7
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.25000?
(A) 8275
(B) 1879
(C) 2779
(D) 2672
(E) 2782
Rationale: A = 25000(11/10)^3
= 33275
= 25000
----------
8275
Answer: A
Answer: (A) 8275
Question: If 9 men and 2 boys working together, can do eight 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) 2:5
(B) 1:3
(C) 5:8
(D) 6:1
(E) 7:2
Rationale: 9M + 2B =8(1M + 1B)
9M + 2B = 8M + 8B
1M = 6B
The required ratio of work done by a man and a boy =6:1
Answer:D
Answer: (D) 6:1
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine,Brian,Stephanie
III.Regine
(A) I only
(B) II only
(C) III only
(D) I or II only
(E) I or III only
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: (E) I or III only
Question: The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. Then banker’s discount is :
(A) 500
(B) 750
(C) 890
(D) 1020
(E) None
Rationale: Sol.
T.D. = [B.G. * 100 / R * T] = Rs.[270 * 100 / 12 * 3] = Rs.750.
∴ B.D. = Rs. (750 + 270) = Rs.102
Answer D
Answer: (D) 1020
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing?
(A) 50%
(B) 40%
(C) 30%
(D) 20%
(E) 10%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.12
0.2x = 0.02
x = 0.1 = 10%
The answer is E.
Answer: (E) 10%
Question: In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/4 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
(A) 50
(B) 90
(C) 100
(D) 105
(E) 140
Rationale: Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).
Rented one-bedroom units are 1/4 of all one-bedroom: 1/4*{All one bedroom} = 40 --> {All one-bedroom} = 160
{All two-bedroom} = 490 - 160 = 330
Two-bedroom not rented = 330 - 240 = 90
B
Answer: (B) 90
Question: After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6840. Find the actual price of the good.
(A) Rs. 6000
(B) Rs. 9000
(C) Rs. 10800
(D) Rs. 10000
(E) Rs. 9980
Rationale: Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6840
1 = 6840/68.4
100 = (6840 *100)/68.4 = Rs. 10,000.
Answer: Option D
Answer: (D) Rs. 10000
Question: 7212 + 15.231 - ? = 6879
(A) 359.022
(B) 362.02
(C) 328.221
(D) 348.231
(E) None of these
Rationale: Explanation :
Required Value = 7212 + 15.231 - 6879 = 348.231. Answer : Option D
Answer: (D) 348.231
Question: ?% of 360 = 151.2
(A) 42
(B) 36
(C) 64
(D) 72
(E) None of these
Rationale: ?% of 360 = 151.2
or, ? = 151.2×100/360=42
Answer A
Answer: (A) 42
Question: Ravi and Kavi start a business by investing â‚¹ 3000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 24
(B) 5 : 24
(C) 7 : 24
(D) 1 : 24
(E) 3 : 24
Rationale: Ratio of profit = Ratio of investments
= 3000 : 72000 = 1 : 24
Answer : D
Answer: (D) 1 : 24
Question: The average of first five prime numbers greater than 20 is?
(A) 32.6
(B) 32.9
(C) 32.3
(D) 32.2
(E) 32.7
Rationale: 23 + 29 + 31 + 37 + 41 = 161/5 = 32.2
Answer: D
Answer: (D) 32.2
Question: 80 370 860 1550 ? 3530
(A) 900
(B) 2440
(C) 750
(D) 244
(E) 960
Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
ANSWER:B
Answer: (B) 2440
Question: Which one of the following is divisible by 9?
(A) 23, 50, 821
(B) 28, 70, 052
(C) 42, 13, 533
(D) 64, 000, 80
(E) 65, 000, 90
Rationale: Explanation:
(a) 2350821 = 2+3+5+0+8+2+1 = 21, not divisible by 9
(b) 2870052 = 2+8+7+5+2 = 24, not divisible by 9.
(c) 4213533 = 4+2+1+3+5+3+3 = 19, not divisible by 9.
(d) 6400080 = 6+4+8 = 18, divisible by 9.
Answer: D
Answer: (D) 64, 000, 80
Question: A train is moving at 4/5 of its usual speed. The train is 30 minutes too late. What is the usual time (in hours) for the train to complete the journey?
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: new time = d / (4v/5) = 5/4 * usual time
30 minutes represents 1/4 of the usual time.
The usual time is 2 hours.
The answer is C.
Answer: (C) 2
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.3600. How much third person will get?
(A) 1600
(B) 2878
(C) 2699
(D) 2662
(E) 1821
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 3600 = 1600
Answer: A
Answer: (A) 1600
Question: Evaluate
6202.5 + 620.25 + 62.025 + 6.2025 + .62025
(A) 6791.59775
(B) 6891.59775
(C) 6891.59675
(D) 5891.59775
(E) None of these
Rationale: Explanation:
Just we need to take care to put decimal under decimal, rest add in a simple way
Option B
Answer: (B) 6891.59775
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 33 cm?
(A) 276 sq.cm
(B) 268 sq.cm
(C) 618 sq.cm
(D) 660 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 33
= 660 sq.cm.
Answer:D
Answer: (D) 660 sq.cm
Question: The average weight of three boys P, Q and R is 54 kg, while the average weight of three boys Q, S and T is 60 kg. What is the average weight of P, Q, R, S and T?
(A) 66.4 kg
(B) 63.2 kg
(C) 58.8 kg
(D) Data Inadequate
(E) None of these
Rationale: Explanation:
Total weight of (P + Q + R) = {54*3} kg = 162 kg
Total weight of(Q + S + T) = (60 *3) kg = 180 kg
Adding both, we get : P + 2Q + S + R + T = (162 + 180) kg = 342 kg
So, to find the average weight of P, Q, R, S & T, we ought to know Q's weight, which is not given.
The data is inadequate
ANSWER: D
Answer: (D) Data Inadequate
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 2/7
(D) 5/7
(E) NONE OF THESE
Rationale: P (getting a prize) =	10/(10 + 25)	=	10/35	=	2/7	.
Answer :C
Answer: (C) 2/7
Question: A tree increases annually by 1⁄5 th of its height. If its height today is 50 cm, what will be the height after 2 years?
(A) 64 cm
(B) 84 cm
(C) 72 cm
(D) 64 cm
(E) 74 cm
Rationale: Explanation:
This problem is similar to the problems we saw in compound interest.
We can use the formulas of compound interest here as well.
Rate of increase = 1/5 × 100 = 20%
Height after 2 years = P(1+R/100)T
= 50(1 + 20/100)2 = 50(1 + 1/5)2
= 50(6/5)2 = (50 × 6 × 6)/(5 × 5) = 2 × 6 × 6 = 72 cm
Answer: Option C
Answer: (C) 72 cm
Question: When 0.232323..... is converted into a fraction, then the result is
(A) 23/99
(B) 2/9
(C) 1/5
(D) 23/100
(E) 23/98
Rationale: 0.232323... = 0.23
=	23/99
Answer is A.
Answer: (A) 23/99
Question: If the perimeter of a rectangular garden is 1800 m, its length when its breadth is 400 m is?
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: 2(l + 400) = 1800 => l = 500 m Answer: A
Answer: (A) 500
Question: If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
Rationale: Given: n=20!n=20!. The highest power k for which 2^k is a factor of n can be found with the above formula:
k=20/2+20/4+20/8+20/16=10+5+2+1=18
Answer: D.
Answer: (D) 18
Question: Tina’s cat weighs 2.6 kilograms. Her dog weighs 5 times as much as her cat. How much does her dog weigh in kilograms?
(A) A)10.4kg
(B) B)13kg
(C) C)22kg
(D) D)48kg
(E) E)20kg
Rationale: 2.6*5=13 kg.Answer is B.
Answer: (B) B)13kg
Question: For a certain art exhibit, a museum sold admission tickets to a group of 50 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $6. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
(A) $24960
(B) $25920
(C) $28080
(D) $38500
(E) $48600
Rationale: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*50 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=108*50 --> x=27*50 and 3x=3*(27*50)=27*150.
Therefore, the total revenue from ticket sales that day was 27*50*6+27*150*10=$48,600.
Answer: E.
Answer: (E) $48600
Question: Evaluate combination
100C100
(A) 10000
(B) 1000
(C) 10
(D) 1
(E) 0
Rationale: Explanation:
nCn=1
100C100=1
Option D
Answer: (D) 1
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 85. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
(A) 87
(B) 89
(C) 90
(D) 93
(E) 95
Rationale: Total score on 3 tests = 85*3 = 255
Jerry wants the average to be = 87
Hence total score on 4 tests should be = 87*4 = 348
Score required on the fourth test = 348 - 255 = 93
Option D
Answer: (D) 93
Question: What is the units digit of the solution to 177^28−133^23?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: Let's reduce the clutter and make it easy to solve
So, 7^28 - 3^23 will have the same units digit as the big numbers above
Both 7 and 3 have a cyclicity of 4, i.e. their powers repeat the units digit after every 4th power
So , 7^28 has the same units digit as 7^4 ,which is 1
Similarly, 3^23 has the same units digit as 3^3, which is 7
Now, we get
xx...xx1 - xx....xx7 = xx...xx4
Thus, the units digit of the solution to 177^28 - 133^23 is 4
Correct Option : C
Answer: (C) 4
Question: What is the square root of 324?
(A) A)18
(B) B)9
(C) C)45
(D) D)62
(E) E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
18*18=324
324 divided by x = 18
x=18
(A) 18
Answer: (A) A)18
Question: A company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price of a box did not change and all boxes are full of juice, by approximately what percent did the price of the juice decrease?
(A) 12.00%
(B) 16.67%
(C) 18.33%
(D) 20.00%
(E) 21.50%
Rationale: suppose when v = 5x10x20 = 1000 cm, the price is $1200
per cm price = $1.2
the price is $1200 if v = 6x10x20 = 1000 cm.
per cm price = $1.0
so the price is decreased by $0.2
so the % price decreased by $0.2/1.20 = 16.67%
ANSWER:B
Answer: (B) 16.67%
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 2 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
(A)  1
(B)  6
(C)  7
(D)  11
(E)  10
Rationale: We're told that there are 2 ingredients (we'll call them A, B); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
Total blends = 1
A
Answer: (A)  1
Question: 70,75, 73,76,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70, 73 and 75.
Answer: C.
Answer: (C) 3
Question: How many multiples of 5 are there between 10 and 89, 10 and 89 inclusive?
(A) 17
(B) 16
(C) 18
(D) 19
(E) 20
Rationale: 5 multiples are ...10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,...
,...,
the answer is =16
Answer is B
Answer: (B) 16
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6?
(A) 12.6.
(B) 15.8.
(C) 14.4.
(D) 16.2.
(E) 16.4.
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.3] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer B
Answer: (B) 15.8.
Question: What is the sum of first 10000 numbers in the series -1,+1,-1,+1,-1.......??
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: -1+1=0
and for 10000 numbers it will form 5000 pairs
so 5000*0 = 0
ANSWER:A
Answer: (A) 0
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 10 years?
(A) 30
(B) 35
(C) 40
(D) 50
(E) 60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 10 years = (20 + 10) years =30 years.
Answer : A
Answer: (A) 30
Question: (4!)^n is a factor of 12!, but (4!)^(n+1) is not factor of 12!. What is the value of n?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 24
Question can be rephrased as how many 24's are there in 12!
12 * 2 = 24
4 * 6 = 24
3 * 8 = 24
Value of n = 3
Answer: C
Answer: (C) 3
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $55.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
(A) 25.5
(B) 30.4
(C) 31.8
(D) 32.5
(E) 33.8
Rationale: $69-$55=14$
(14/55)*100=25.5%
ANSWER:A
Answer: (A) 25.5
Question: Bill is golfing with two friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aero flight tees that come by the pair. What is the minimum number of packages of Aero flight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome, if he will buy no more than 1 packages of the generic golf tees?
(A) 16
(B) 10
(C) 9
(D) 4
(E) 2
Rationale: At least 10 golf tees for each member of his threesome = total of at least 3*10 = 30 tees.
1 packages of the generic golf tees, that are packaged by the dozen = 1*12 = 12 tees.
So, Bill must by at least 18 Aero tees. They come by the pair, hence he must by at least 18/2 = 9 packages of Aero flight tees.
Answer: C.
Answer: (C) 9
Question: If the price of 50 toys is 1000, then what will the price of 20 toys ?
(A) 400
(B) 361
(C) 117
(D) 287
(E) 112
Rationale: One toy price = 1000/50 = 20
20 toy price = 20 * 20 = 400
Answer : A
Answer: (A) 400
Question: Arun is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
(A) 22
(B) 38
(C) 12
(D) 99
(E) 28
Rationale: Let the distance be x km
if travels at 10 kmph, Arun will reach point A at 2 pm
if travels at 15 kmph, Arun will reach point 12 noon
=> Time taken when traveling at 10 km = Time taken when traveling at 15 km + 2 hours
⇒x10=x15+2⇒x10−x15=2⇒3x−2x=2×30⇒x=60⇒Distance = 60 km
Examine the any statement say, if travels at 10 kmph, Arun will reach point A at 2 pm
⇒Time taken = DistanceSpeed=6010=6 hours⇒He must have started 6 hours back 2 pm, ie, at 8 am⇒Now he wants to reach at 1 pm. ie; time to be taken = 5 hours⇒Speed needed = DistanceTime=605=12 kmph
Answer : C
Answer: (C) 12
Question: Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 120
(B) 150
(C) 100
(D) 180
(E) 220
Rationale: n(A)=325,n(B)=175,n(AuB)=450-50=400.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-400=100.
Answer is C
Answer: (C) 100
Question: Pipe A can fill a tank in 15 hours, pipe B in 30 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 2.5
(C) 3
(D) 8
(E) None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/15 + 1/30 + 1/40) = 1/8.
âˆ´ All the three pipes together will fill the tank in 8 hours.
Answer D
Answer: (D) 8
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 2277
(C) 2677
(D) 2688
(E) 26711
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: (A) 6620
Question: Let C be defined as the sum of all prime numbers between 0 and 23. What is C/3
(A) 155
(B) 129
(C) 61
(D) 25.3
(E) 43
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19
Sum,C = 77
C/3 = 25.3
Answer D
Answer: (D) 25.3
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 22
(B) 190
(C) 277
(D) 18
(E) 12
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.Answer:B
Answer: (B) 190
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, ?, 47
(A) 31
(B) 34
(C) 36
(D) 31
(E) 33
Rationale: B
34
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Missing Number = 23 + 11 = 34.
Answer: (B) 34
Question: A work crew of 6 Men takes 9 days to complete one-half of a job. If 12 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
(A) 2
(B) 3
(C) 3 1/3
(D) 4
(E) 4 4/5
Rationale: Suppose 1 man can do work in X days..
so 6 men will do in ..
6/X=1/9*1/2 as half job is done
X=108
now 12 more are added then
18/108=1/2*1/d for remaining half job
d=3 Number of days
B
Answer: (B) 3
Question: When 28 is divided by the positive integer r, the remainder is 1. What is the sum of all the possible values of r for which this is true?
(A) 2
(B) 3
(C) 9
(D) 30
(E) 39
Rationale: The only possible values of the form 28=rp+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: (E) 39