mathewhe/aqua_rat huggingface dataset:
Question: The side of a square has the length of 10. What is the area of the region shaded?
(A) 48-8π
(B) 48-6 π
(C) 24+6π
(D) 16+8π
(E) 64-10π
Rationale: The area of a square whose side is 10 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is E.
Answer: (E) 64-10π
Question: Aman started a business investing Rs. 30,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 36:105:118
(B) 36:105:112
(C) 12:105:110
(D) 12:105:112
(E) 36:105:111
Rationale: Explanation:
Aman : Rakhi : Sagar = (30000 * 36) : (105000 * 30) : (140000 * 24)
= 36:105:112
Answer: B
Answer: (B) 36:105:112
Question: Which of the following is greatest?
(A) 2/10
(B) 2/10^2
(C) 2/10^3
(D) 2/10^4
(E) 2/10^6
Rationale: 2/10 > 2/100 > 2/1000 > 2/10000 > 2/1000000
Answer : A
Answer: (A) 2/10
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 65
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
Answer A.
Answer: (A) 60
Question: If each of the two lines L1 and L2 is parallel to line L3, which of the following must be true?
(A) Lines L1 , L2, and L3 lie in the same plane
(B) Lines L1 , ,L2 and L3 lie in different planes
(C) Line L1 is parallel to line L2
(D) Line L1 is the same line as line L2
(E) Line L1 is the same line as line L3
Rationale: If each of the two lines L1 and L2 is parallel to line L3,
it means L1 || L2 || L3.
And thats exactly in answer choice C.
Answer: (C) Line L1 is parallel to line L2
Question: 8 , 16 , 24 , 32, 64 ....
In the sequence find the wrong term
(A) 8
(B) 16
(C) 24
(D) 32
(E) 64
Rationale: In the sequence except 24 all others are the cube root of 2
so the answer is option C) 24
Answer: (C) 24
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.176 in 4 Years?
(A) 5%
(B) 8%
(C) 3%
(D) 9%
(E) 5.5%
Rationale: 176 = (180*4*R)/100
R = 5.5%
Answer: E
Answer: (E) 5.5%
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2m
(B) 3m
(C) 5m
(D) 6m
(E) 7m
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3
Answer:B
Answer: (B) 3m
Question: A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 30 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
(A)  $180,000
(B)  $185,000
(C)  $190,000
(D)  $200,000
(E)  $205,000
Rationale: 30% of 1000 = 300 worked for 30 hours
Payment @ 5/hr
Total Payment = 300*30*5 = 45000
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 45000+100000 + 40000 +15000 = 200000
Hence , answer is D
Answer: (D)  $200,000
Question: if 6 women take an hour to dig a ditch, then how long should 18 women take a dig to ditch of the same type?
(A) 25 min
(B) 20 min
(C) 28 min
(D) 15 min
(E) 10 min
Rationale: if 6 women take an hour to dig a ditch, then
18 men will take 6*60/18 = 20 mins to dig a ditch of the same type.
ANSWER:B
Answer: (B) 20 min
Question: What is the range of values of b for which 1 - b^8 < 0 ?
(A) b < -1 or b > 1
(B) -1 <= b <= 1
(C) b > 1
(D) b < -1
(E) 0 <= b <= 1
Rationale: Stem can be rephrased as -
b^8 - 1 > 0
Hence b > 1 or b < -1
ANSWER:A
Answer: (A) b < -1 or b > 1
Question: Alex climbs a mountain peak and back from base. He takes the exact same route both ways. On the trip out he climbs up at an average speed of 5 miles per hour. On the trip back he climbs down at an average speed of 25 miles per hour. What is his approximate average speed for the round trip in miles per hour?
(A) 8.33
(B) 18.3
(C) 20
(D) 22
(E) 25
Rationale: Average speed = total distance/total time
Here distance to peak and back is same as he takes the same route.
D = 5T1 and D=25T2
Therefore, T1 = D/5 and T2 = D/25
T1+T2 = 6d/25
Therefore, average speed = 2d/6d/25 =2d * 25/6d
Answer is 8.3 Since, the options are far away we need not solve till the decimal points
So correct answer is option A
Answer: (A) 8.33
Question: It was at a cocktail party in New York that I met Stephanie. We exchanged our phone numbers and decided to meet each other soon.
When she rang up and invited me to her house this is how she gave the number of her house.
I live in a long street. Numbered on the side of my house are the houses one, two, three and so on. All the numbers on one side of my house add up exactly the same as all the numbers on the other side of my house. I know there are more than fifty houses on that side of the street, but not so many as five hundred'
can you find Stephanie's house number?
(A) 200
(B) 204
(C) 199
(D) 206
(E) 210
Rationale: B
204
The numbers of the houses on each side will add up alike if the number of the house be 1 and there are no other houses, and if the number be 6 with 8 houses in all, if 35 with 49 houses, if 204 with 288 houses, if 1189 with 1681 houses and so on. But we know that there are more than 50 and less than 500 houses, and so we are limited to a single case.
The number of the house must be 204.
Answer: (B) 204
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 40, how many horses are there ?
(A) 8
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: legs 8*4 = 32
now half on their horses so remaining on the walk so 4 men
4 men has 8 legs
so, 8+ 32 = 40 legs walking
ANSWER:A
Answer: (A) 8
Question: On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 46 centimeters assuming that 1-inch is 2.54 centimeters?
(A) 174.2
(B) 212
(C) 288.1
(D) 290
(E) 282.4
Rationale: 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 46 cm.:
46/(2.54*1.5) = x / 24 ---> x = 24*46/(3.81) = 290
Answer will be D.
Answer: (D) 290
Question: If 65 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 45%
(B) 40%
(C) 35%
(D) 30%
(E) 25%
Rationale: 65% answered the first question correctly and 20% answered neither correctly.
Then 15% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 55% - 15% = 40%.
The answer is B.
Answer: (B) 40%
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is......
(A) 99
(B) 100
(C) 87
(D) 95
(E) 90
Rationale: DETAILED SOLUTION
10 students have scored 600 marks amongst them, and no one is allowed to score lesser than 40 or higher than 100. The idea now is to maximize what the highest scorer gets.
The 5 least scores have an average of 55, which means that they have scored 55 x 5 = 275 marks amongst them. This leaves 325 marks to be shared amongst the top 5 students. Lets call them a, b, c, d and e. Now, in order to maximize what the top scorer “e” gets, all the others have to get the least possible scores (and at the same time, they should also get distinct integers.)
The least possible score of the top 5 should be at least equal to the highest of the bottom 5. Now we want to make sure that the highest of the bottom 5 is the least possible. This can be done by making all scores equal to 55. If some scores are less than 55, some other scores have to be higher than 55 to compensate and make the average 55. Thus the highest score is the least only when the range is 0.
So now, we have the lowest value that the top 5 can score, which is 55. The others have to get distinct integer scores, and as few marks as possible, so that “e” gets the maximum.
So, 55 + 56 + 57 + 58 + e = 325
e = 99 marks.
Answer choice (A)
Answer: (A) 99
Question: Two vessels contains equal number of mixtures milk and water in the ratio 4:2 and 5:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
(A) 3:1
(B) 9:13
(C) 5:11
(D) 11:3
(E) 15:4
Rationale: The ratio of milk and water in the new vessel is = (4/6 + 5/6) : (2/6 + 1/6)
= 9/6 : 3/6 = 3:1
Answer is A
Answer: (A) 3:1
Question: Three men A,B, C and two women X, Y are to be seated in one row. Of all the seating arrangements possible, in how many of them X sits to the immediate left of one of the men?
(A) 12
(B) 48
(C) 60
(D) 72
(E) 96
Rationale: take Men, X as one combination..
so total seats now are 4...
so ways 4 can be arranged is 4!..
but the men can be A, B or C, so 3 ways..
answer = 4!*3 = 24*3 = 72
ANSWER:D
Answer: (D) 72
Question: The smallest 5 digit number exactly divisible by 41 is?
(A) 10003
(B) 10004
(C) 10007
(D) 10009
(E) 10010
Rationale: The smallest 5-digit number = 10000.
41) 10000 (243
82
---
180
164
----
160
123
---
37
---
Required number = 10000 + (41 - 37)
= 10004.
Option B
Answer: (B) 10004
Question: Mom mixed 2 1/2 pounds of apples, 1 1/8 pounds of grapes and 1 1/4 pounds of pears for a
salad. After setting aside 1 1/2 pounds of salad for today, she divided the rest of the salad equally
into 3 containers. What is the weight of the salad in one container?
(A) 1 1/8 lb
(B) 2 1/8 lb
(C) 3 1/8 lb
(D) 4 1/8 lb
(E) 5 1/8 lb
Rationale: 2 1/2 + 1 1/8 + 1 1/4 = 4 7/8 pounds of salad
4 7/8 - 1 1/2 = 3 3/8 pounds left
3 3/8 ÷ 3 = 27/8 ÷ 3/1 = 27/8 x 1/3 =
9/8 = 1 1/8 lb. in a container
correct answer A
Answer: (A) 1 1/8 lb
Question: A single letter is selected at random from the word 'MISSING'. The probability that it is a vowel is..??
(A) 2/11
(B) 2/7
(C) 4/11
(D) 3/7
(E) 1
Rationale: total vowels = 2, total number of letters = 7
so probability = 2/7
ANSWER:B
Answer: (B) 2/7
Question: A crew is made up of 8 men; the rest are women. 66+2/3% of
the crew are men. How many people are in the crew?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 62+2/3/100=8/x
Multiply the opposites:
100 x 8 = 800
Divide by the remaining number:
800'/'66+2/3=800/1'/'200/3
-(800)/1*3/-(200)
erasing 800=4
erasing 200=1
we have
12/1
=12
correct answer B
Answer: (B) 12
Question: 41% of 801 – 150.17 = ? – 57% of 910
(A) 797
(B) 697
(C) 687
(D) 699
(E) 799
Rationale: Explanation:
328 – 150 = 178
X – 519 = 178
X = 697
Answer: Option B
Answer: (B) 697
Question: A certain fruit stand sold apples for $0.80 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $7.20, what total number of apples and bananas did the customer purchase?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Let's start with 1 apple for $0.80.
Let's subtract $0.80 from $7.20 until we get a multiple of $0.50.
$7.20, $6.40, $5.60, $4.80, $4.00 = 8*$0.50
The customer purchased 8 bananas and 4 apples.
The answer is C.
Answer: (C) 12
Question: For what value of x, is |x – 3| + |x + 1| + |x| = 11?
(A)  0
(B)  3
(C)  -3
(D)  4
(E)  -2
Rationale: For what value of x, is |x – 3| + |x + 1| + |x| = 11?
It's easiest just to plug in answer choices:
(C): -3
|x – 3| + |x + 1| + |x| = 11?
|-3 - 3| + |-3 + 1| + |-3| = 11?
|6| + |2| + |3| = 11
(C)
Answer: (C)  -3
Question: A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
(A) 1/3 of the butt
(B) 2/3 of the butt
(C) 1/4 of the butt
(D) 1/8 of the butt
(E) 1/9 of the butt
Rationale: Wine containing 40%spirit Wine containing 16% spirit
Wine containing 24% spirit
8 16
They must be mixed in the ratio of =1:2.
Thus 1/3 of the butt of sherry was left
hence the butler drew out 2/3 of the butt.
ANSWER : B 2/3 of the butt
Answer: (B) 2/3 of the butt
Question: John is traveling to a meeting that is 26 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
(A) 25 mph
(B) 37 mph
(C) 41 mph
(D) 52 mph
(E) 56 mph
Rationale: Well 52mph. D. Time*rate=distance --> 0.5*rate=26 --> rate=52
Answer: (D) 52 mph
Question: Find the number which is nearest to 457 and is exactly divisible by 11.
(A) 450
(B) 451
(C) 460
(D) 462
(E) None
Rationale: Solution
On dividing 457 by 11, remainder is 6.
Required number is either 451 or 462
Nearest to 456 is	= 462.
Answer D
Answer: (D) 462
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.931. Find the cost of each ice-cream cup?
(A) 25
(B) 76
(C) 29
(D) 12
(E) 20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 931
96 + 225 + 490 + 6x = 931
6x = 120 => x = 20.
Answer:E
Answer: (E) 20
Question: Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
(A) 2088
(B) 2000
(C) 3087
(D) None of these
(E) Cannot be determined
Rationale: Solution:
Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11
Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400
Therefore Shyam's share = (441/841) * 5887 = 3087.
Answer C
Answer: (C) 3087
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 5
(B) 4
(C) 3
(D) 6
(E) 8
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: A
Answer: (A) 5
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, B receives:
(A) s. 11,000
(B) s. 11,300
(C) s. 11,500
(D) s. 11,700
(E) s. 11,900
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (35000 x 17/50) = Rs. 11,900.
E
Answer: (E) s. 11,900
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 152000 m^2
(B) 1532500 m^2
(C) 153000 m^2
(D) 153300 m^2
(E) 153600 m^2
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
E)
Answer: (E) 153600 m^2
Question: The average number of shirts with Salman, Ambani and Dalmiya is 69, if all of them reached a shopping mall in Delhi and purchased 12 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 81
(C) 62
(D) can't be determined
(E) None of these
Rationale: Answer
Required average
= Old average + New average
= 69 + 12 = 81
Correct Option: B
Answer: (B) 81
Question: The three competitors in a race have to be randomly chosen from a group of three men and four women. How many different such trios contain at least one woman?
(A) 31
(B) 34
(C) 37
(D) 40
(E) 43
Rationale: The total number of ways to choose three runners 7C3 = 35
The number of trios with only males is 3C3 = 1
The number of trios which include at least one woman is 34.
The answer is B.
Answer: (B) 34
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 100
(B) 150
(C) 200
(D) 250
(E) 300
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1]
= 200.
ANSWER C 200
Answer: (C) 200
Question: Lindsay can paint 1/x of a certain room in 15 minutes. What fraction of the same room can Joseph paint in 15 minutes if the two of them can paint the room in an hour, working together at their respective rates?
(A) A)1/4x
(B) 4x/(x – 4)
(C) (x – 4) / 4x
(D) 1/ (x – 4)
(E) (x – 4) / x
Rationale: Lindsey and Joseph together can paint the room in 1 hour
in 15 mins they can paint 1/4 part of the room.
Lindsay alone paints 1/x part of the room in 15 mins
Take Joseph paints 1/y parts in 15 mins
1/x + 1/y = 1/4
1/y = 1/4 - 1/x = (x-4)/4x ANs C
Answer: (C) (x – 4) / 4x
Question: If n is a positive integer, then n*(n+1)*(n+2) is
(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even
Rationale: n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8)
E
Answer: (E) divisible by 4 whenever n is even
Question: If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?
(A) 18
(B) 2
(C) -1
(D) -3
(E) -4
Rationale: consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) + (X+4)
doing this leaves us with 3X + 6
what even number can we substitute in X to yield an answer choice
A works 18 (plug in 4 for X)
Answer: (A) 18
Question: A retailer buys 40 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1% ,what is the profit % ?
(A) 5
(B) 10
(C) 15
(D) 20
(E) None of them
Rationale: let the market price of each pen be Rs 1
then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60
profit %=((3.60*100)/36) %=10%
Answer is B.
Answer: (B) 10
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/6
(C) 8 1/0
(D) 8 1/2
(E) 8 1/5
Rationale: (4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: (A) 8 1/3
Question: The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is?
(A) 25
(B) 20
(C) 15
(D) 30
(E) 18
Rationale: Let the total number of workers be x
1000x = 5000*5 + 500(x-5)
x = 25
Answer is A
Answer: (A) 25
Question: If 18 is 15 percent of 30 percent of a certain number, what is the number?
(A) 9
(B) 36
(C) 40
(D) 81
(E) 400
Rationale: Let the certain number be x.
=> (15/100)*(30/100)*x = 18;
450x=18*10000;
45x = 18000;
x=18000/45
=> x=400;
Ans is (E).
Answer: (E) 400
Question: If 9^y = 3^12, what is y?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: (E) 6
Question: An old priest fell on a bottom of the well of a church.
The well is 18 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
(A) 16-days
(B) 14-days
(C) 11-days
(D) 19-days
(E) 10-days
Rationale: B
14-days
In 13-days, he will climb 13-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: (B) 14-days
Question: Find the surface area of a cuboid 8 m long, 6 m broad and 10 m high
(A) 376 sq.cm
(B) 420 sq.cm
(C) 516 sq.cm
(D) 400 sq.cm
(E) None of these
Rationale: Explanation:
Surface area = [2 (8 x 6 + 6 x 10 + 8 x 10)] cm2 = (2 x 188)cm2 = 376 cm2.
Answer: A
Answer: (A) 376 sq.cm
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 4 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The rate of the pump + leak = 1/4
1/2 - leak's rate = 1/4
leak's rate = 1/2 - 1/4 = 1/4
The leak will empty the tank in 4 hours.
The answer is C.
Answer: (C) 4
Question: A train leaves Mumabai at 9 am at a speed of 45 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 90 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 287
(B) 279
(C) 90
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 45 * 1 = 45 km
So, the distance between first train and second train is 45 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 45 / (90 -45) = 1 hours
So, the two trains meet at 2 p.m. The two trains meet 1 * 90 = 90 km away from Mumbai.
Answer:C
Answer: (C) 90
Question: On the number line, the number p is twice as many units from -2 as -2 is from 3. If p is less than –2, what is the value of p ?
(A) –12
(B) –10
(C) –6
(D) 10
(E) 14
Rationale: Distance between -2 and 3 = 5
Since number p is twice as many units from -2 as -2 is from 3
, therefore p can be -12 Since , p is less than -2 ,
the value of p = -12
Answer A
Answer: (A) –12
Question: What is the smallest integer x for which 27^x > 3^24?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: 27^x> 3^24
Converting into the same bases:
27^x> 27^8
Therefore for the equation to hold true, x> 8 or x= 9
Option C
Answer: (C) 9
Question: Walking at 50% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
(A) 24
(B) 36
(C) 42
(D) 48
(E) 54
Rationale: speed is inversly proprtional to time
walking at 50% of speed meand 1/2s takes 2t.
It takes 24 minutes extra to cover the distance. then
2t=t+24
t=24.
Option A is correct
Answer: (A) 24
Question: A boy is travelling from his home to school at 6km/hr and reached 7min late. Next day he travelled at 12km/hr and reached 8min early. Distance between home and school?
(A) 2km
(B) 3km
(C) 4km
(D) 5km
(E) 6km
Rationale: Let the distance be x
T1 = x/6 hr
T2 = x/12hr
Difference in time = 7+8 = 15 =1/4hr
x/6-x/12 = 1/4
x/12 = 1/4
x = 3 km
Answer is B
Answer: (B) 3km
Question: In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
(A) 8*9!
(B) 7*5!
(C) 5*5!
(D) 9!
(E) 10*8!
Rationale: 10 examination papers arranged
consider x
and req no of arranged = 8*9!
ANSWER A
Answer: (A) 8*9!
Question: Angelina walked 200 meters from her home to the grocery at a constant speed. She then walked 300 meters to the gym at double the speed. She spent 50 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: let the speed be X...
so time taken from home to grocery= 200/x..
the speed to gym = 2x..
so time taken = 300/2x=150/x..
its given 200/x-150/x=50..
50/x=50..
x=1m/secs..
so grocery to gym=2*1=2m/s...
Answer : A
Answer: (A) 2