mathewhe/aqua_rat huggingface dataset:
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 200 m, in what time will they cross other travelling in opposite direction?
(A) 17 sec
(B) 12 sec
(C) 16 sec
(D) 15 sec
(E) 20 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (200 + 200)/20 = 20 sec.
Answer:E
Answer: (E) 20 sec
Question: What is the least number to be subtracted from 800 to make it a perfect square?
(A) 1
(B) 16
(C) 20
(D) 71
(E) 60
Rationale: The numbers less than 800 and are squares of certain number is 784.
The least number that should be subtracted from 800 to make it perfect square = 800 - 784 = 16.
ANSWER:B
Answer: (B) 16
Question: Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?
(A) (3ac)/(a+c)
(B) (4a-12c)/(3ac)
(C) (3ac)/(4a-12c)
(D) (ac)/(a+2c)
(E) (ac)/(a+c)
Rationale: work time
A 1 a
B 1/4 b
A+B 1/3 c
A's rate = 1/a
B's rate = 1/4b
when they are working together , their combined rate is 1/a + 1/(4b) = (1/3)/c
1/(4b) = 1/(3c) - 1/a
=> b = 3ac /(4a-12c)
Answer is C.
Answer: (C) (3ac)/(4a-12c)
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 9 hours and 25 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 5:3
(C) 4:4
(D) 4:9
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √9 = 5:3
Answer:B
Answer: (B) 5:3
Question: What is the smallest positive integer that can be multiplied by 605 to make it a perfect square?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 605 is multiplied by 5 gives 3025
Its a square root of 55
Answer is 5 -Option C
Answer: (C) 5
Question: If 45-[28-{37-(15-*)}]= 54, then * is equal to:
(A) -29
(B) -19
(C) 15
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 54 => 45-[28-{37-15+*}]=54
45-[28-37+15-*]=54 => 45[43-37-*]=54
45-[6-*]=54 => 45-6+*=54
39+*=54 => *=54-39
= 19
ANSWER:C
Answer: (C) 15
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 5/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
(A) 1/4
(B) 3/40
(C) 13/40
(D) 7/20
(E) 13/22
Rationale: P(1 and not 2)=5/8*(1-3/5)=1/4
Answer: A.
Answer: (A) 1/4
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 8n + 4
(C) 9n + 2
(D) 9n + 3
(E) 9n + 4
Rationale: n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [3+ (n-1)]
= $ n+2
total cost
8n+n+2 = 9n+2	;
ANSWER:C
Answer: (C) 9n + 2
Question: |8 - 3| - |4 - 6| = ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
Rationale: |8 - 3| - |4 - 6| = | 5 | - | -2 | = 5 - 2 = 3
correct answer A
Answer: (A) 3
Question: When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 5. If 1 < m < 200, what is the greatest possible value of m?
(A) 47
(B) 65
(C) 103
(D) 117
(E) 161
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
161 = 153 + 8 (153 divisible by 9)
161 = 156 + 5 (156 divisible by 13)
it fits the result
Answer = E
Answer: (E) 161
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 9% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
(A) 7 : 8
(B) 5 : 4
(C) 2 : 3
(D) Data inadequate
(E) None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 9% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.09x = 600
or 720 – 600 = 0.09x – 0.04x
or, 120 = 0.05x
x = 4200
Reqd ratio of population of males and females
4200/9000−4200=4200/4800=7:8
Answer A
Answer: (A) 7 : 8
Question: A library has an average of 540 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 300
(B) 276
(C) 290
(D) 285
(E) None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (540x5 + 240x25) /30) = 290
Answer: Option C
Answer: (C) 290
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 60 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
(A) 50 miles
(B) 60 miles
(C) 70 miles
(D) 80 miles
(E) 90 miles
Rationale: Every hour, Nil gets ahead of Ethan 60 - 20 =
40 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 60 × 1 = 60 miles.
correct answer B
Answer: (B) 60 miles
Question: A volume of 10940 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
(A) 2812
(B) 8231
(C) 2734
(D) 2735
(E) 4254
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 10940l can be kept in (10940/4) hemispheres
ans.2735
ANSWER:D
Answer: (D) 2735
Question: If 20% of a certain number is 60, then what is 80% of that number?
(A) 220
(B) 210
(C) 240
(D) 250
(E) 260
Rationale: Explanation:
20% = 20*3 = 60
80% = 80*3= 240
Answer: Option C
Answer: (C) 240
Question: The Racing magic takes 150 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Time taken by Racing magic to make one circle = 150 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 150 seconds = 450 seconds
Time taken for them to meet at the starting point for the second time = 2*450=900 seconds = 15 mins
Answer E
Answer: (E) 15
Question: At a simple interest 800 becomes 956 in three years. If the interest rate, is increased by 3%, how much would 800 become in three years?
(A) 1020.80
(B) 1004
(C) 1028
(D) Data inadequate
(E) None of these
Rationale: Rate of interest = 956−800/3×800×100=6.50%
\Amount = 800 + 800×9.5×3/100
= 800 + 228 = 1028
Answer C
Answer: (C) 1028
Question: On a certain plane, 2/5 of the passengers speak English and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
(A) 12
(B) 15
(C) 100
(D) 124
(E) 130
Rationale: Assume the total members = x
English = .4x
Hebrew = .75x
English + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only English = .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only English = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 100 Only English = .25*100 = 25, Only Hebrew = .6*100 = 60, both = .15*100 = 15. We have the people as whole numbers. CORRECT
D. 124
E. 130
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Answer: (C) 100
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 14
(B) 56
(C) 25
(D) 28
(E) 62
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100
= (100 * 30)/40
= 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer:C
Answer: (C) 25
Question: On what dates of April, 2001 did Wednesday fall?
(A) 4th,11th,18th,29th
(B) 4th,11th,18th,25th
(C) 4th,11th,18th,85th
(D) 4th,11th,18th,79th
(E) 4th,11th,18th,24th
Rationale: Explanation:
We shall find the day on 1st April, 2001.
1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th
Answer: B) 4th,11th,18th,25th
Answer: (B) 4th,11th,18th,25th
Question: A race course is 400 m long. AA and BB run a race and AA wins by 5m. BB and CC run over the same course and BB win by 4m. CC and DD run over it and DD wins by 16m. If AA and DD run over it, then who would win and by how much?
(A) 7.1 m
(B) 7.2 m
(C) 8 m
(D) 9 m
(E) 11 m
Rationale: If AA covers 400m, BB covers 395 m
If BB covers 400m, CC covers 396 m
If DD covers 400m, CC covers 384 m
Now if BB covers 395 m, then CC will cover 396400×395=391.05396400×395=391.05m
If CC covers 391.05 m, then DD will cover 400384×391.05=407.24400384×391.05=407.24
If AA and DD run over 400 m, then DD win by 7.2 m
Option B
Answer: (B) 7.2 m
Question: A runs 1 2/3 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
(A) 200 m
(B) 300m
(C) 270m
(D) 160m
(E) 150m
Rationale: Explanation:
Ratio of the speeds of A and B =5 : 1 = 5 :3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of 5/2X80 m=200m
Winning post is 200 m away from the starting point.
ANSWER IS A
Answer: (A) 200 m
Question: Sum of the numbers from 1 to 20 is
(A) 210
(B) 110
(C) 220
(D) 105
(E) None of these
Rationale: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 20.
So S20=20×21/2=210
Correct Option: A
Answer: (A) 210
Question: In how many different ways can the letters of the word 'CAREER' be arranged?
(A) 10 ways
(B) 20 ways
(C) 180 ways
(D) 60 ways
(E) 40 ways
Rationale: Totally there are 6 letters on the word CAREER. it contains 1C,1A,2R,2E.
The no of ways is 6!/2!2!=180 ways.
ANSWER:C
Answer: (C) 180 ways
Question: 5KM is how many miles?
(A) 2miles
(B) 3.5miles
(C) 1.5miles
(D) 3.0miles
(E) 3.125miles
Rationale: 3.125 Miles
5/1.6=3.125
Answer:E
Answer: (E) 3.125miles
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
(A) 7/12
(B) 6/7
(C) 5/12
(D) 8/7
(E) 8/15
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12.
Option: C
Answer: (C) 5/12
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
(A) 5 days
(B) 6 days
(C) 9 days
(D) 2 days
(E) 12 days
Rationale: 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer:A
Answer: (A) 5 days
Question: Look at this series: 42, 42, 30, 30, 18, 18, .. What number should come next?
(A) 06
(B) 12
(C) 14
(D) 32
(E) 42
Rationale: In this series, each number is repeated, then 12 is subtracted to arrive at the next number.
The answer is option A (06)
Answer: (A) 06
Question: A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 18,000
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =45000
no of items required = 45000/2.5 = 18000
Answer: C
Answer: (C) 18,000
Question: On dividing 83 by a number, the quotient is 9 and the remainder is 2. Find the divisor?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: d = (D-R)/Q
= (83 - 2)/9
= 81/9 = 9
C)
Answer: (C) 9
Question: 2 + 2^2 + 2^3 + ... + 2^9 = ?
(A) 1000
(B) 1011
(C) 1019
(D) 1021
(E) 1022
Rationale: This is a G.P. in which a = 2, r = 22 = 2 and n = 9.
2
Sn = a(rn - 1) / (r - 1)= 2 x (29 - 1) / (2 - 1)= 2 x (512 - 1) = 2 x 511 = 1022.
E)
Answer: (E) 1022
Question: Yesterday it took Robert 4 hours to drive from City A to City B. Today it took Robert 3.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?
(A)  90
(B)  120
(C)  150
(D)  210
(E)  300
Rationale: 2d/60 = 7 ( because time = 4 + 3.5 - 0.5 hrs)
=> d = 210
Answer - D
Answer: (D)  210
Question: The length of the bridge, which a train 110 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 265
(B) 244
(C) 245
(D) 238
(E) 236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (110 + X)/30 = 25/2 ==> 2(110 + X) = 750 ==> X = 265 m.
Answer: Option A
Answer: (A) 265
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in
(A) 5 hours
(B) 7 hours
(C) 8 hours
(D) 14 hours
(E) None
Rationale: Solution
Work done by the leak in 1 hour	=(1/2 - 3/7)
‹=›1/14.
Leak will empty the tank in 14 hours.
Answer D
Answer: (D) 14 hours
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 5 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
(A) 1/5
(B) 1/2
(C) 2/3
(D) 4/5
(E) 6/5
Rationale: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 1/5 A)
Answer: (A) 1/5
Question: Which of the following points falls outside of the region defined by 2y≤6x−16?
(A) (5, 1)
(B) (3, -8)
(C) (2, 0)
(D) (0, -14)
(E) (1, -2)
Rationale: Equation given is 2y<=6x-12
Simplifying this; y<=3x-6
Plug in the values provided in the options,
A. 1<=11
B. -8<=3
C. 0<=0
D.-14<=-12
E. -2<=-13
Option E is the answer.
Answer: (E) (1, -2)
Question: Look at this series: 6.2, 6.8, 7.4, 8, ... What number should come next?
(A) 9
(B) 8.9
(C) 8.7
(D) 8.6
(E) 8.5
Rationale: D
8.6
In this simple addition series, each number increases by 0.6.
Answer: (D) 8.6
Question: A Man travelled a distance of 70 km in 9 hours. He travelled partly on foot at 6 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
(A) 16 km
(B) 14 km
(C) 12 km
(D) 42 km
(E) None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 70 km
So,
6x + 9(9-x) = 70
=> 3x = 21
=> x = 7
So distance traveled on foot = 6(7) = 42 km
Answer: Option D
Answer: (D) 42 km
Question: A bookseller sells his books at a 20% markup in price. If he sells a book for $36.00, how much did he pay for it?
(A) $34.40
(B) $34.00
(C) $32.00
(D) $30.00
(E) $35.00
Rationale: Let the cost price of book = x
Selling price of book = 36$
Markup % = 20
(120/100)x = 36
=> x = 30
Answer D
Answer: (D) $30.00
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 2-cent and 20-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought?
(A) 5
(B) 10
(C) 55
(D) 80
(E) 95
Rationale: Let:
# of 2 and 20 cents stamps = n
# of 10 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
2n + 20n + 10(2n) + m = 265 cents
42n + m = 265
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
42*5 + m = 265
m = 55 i.e. 55 stamps 1 cents each
Answer: C
Answer: (C) 55
Question: Series C(n) is such that i*C(i) = j*C(j) for any pair of positive integers (i, j). If C(1) is a positive integer, which of the following is possible?
I. 2*C(100) = C(99) + C(98)
II. C(1) is the only integer in the series
III. The series does not contain negative numbers
(A) I only
(B) II only
(C) IIII only
(D) IIIII only
(E) I, IIIII
Rationale: First thing I want to understand is this relation: i*C(i) = j*C(j) for any pair of positive integers. I will take examples to understand it.
When i = 1 and j = 2, C(1) = 2*C(2)
So C(2) = C(1)/2
When i = 1 and j = 3, C(1) = 3*C(3)
So C(3) = C(1)/3
I see it now. The series is: C(1), C(1)/2, C(1)/3, C(1)/4 and so on...
II and III are easily possible. We can see that without any calculations.
II. C(1) is the only integer in the series
If C(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except C(1)
III. The series does not contain negative numbers
Again, same series as above applies. In fact, since C(1) is a positive integer, this must be true.
I. 2*C(100) = C(99) + C(98)
2*C(1)/100 = C(1)/99 + C(1)/98 (cancel C(1) from both sides)
2/100 = 1/99 + 1/98
Not true hence this is not possible
Answer (D)
Answer: (D) IIIII only
Question: At a meeting of 8 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
(A) 2400
(B) 2800
(C) 3200
(D) 3600
(E) 4000
Rationale: 8 people can be arranged around a table in 7! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 7 units around a table is 6!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 7! - 2*6! = 5*6! = 3600
The answer is D.
Answer: (D) 3600
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
(A) 1:4
(B) 1:5
(C) 2:3
(D) 3:2
(E) 2:5
Rationale: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/4 dollars --> the profit from one mango = 1/4 - 1/5 = 1/20 dollars.
The selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/5 - 1/6 = 1/30 dollars.
The profit from one mango from the first stack is 4 times the loss from one mango from the second stack. the ratio is
1/20*30/1= 3:2
D
Answer: (D) 3:2
Question: A certain country had a total annual expenditure of $9.6 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
(A)  $ 500
(B)  $1,000
(C)  $2,000
(D)  $3,000
(E)  $4,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (9,6 x 10^11) / 240 000 000 = (9,6 x 10^11) / (2,4 x 10^8) = 4 x 10^(11-8) =
4 x 10^3 = 4000.
Answer is E.
Answer: (E)  $4,000
Question: What will be the reminder when (31^31+31) is divided by 32?
(A) 72
(B) 43
(C) 91
(D) 40
(E) 30
Rationale: (x^n+1) will be divisible by (x+1) only when n is odd;
(31^31+1) will be divisible by (31+1);
(31^31+1)+30 when divided by will give 30 as remainder.
Correct Option : E
Answer: (E) 30
Question: Shiva decided to drive through the city and on the first day he drove for only 7 miles. On the last day he drove for 51 miles, increasing his journey 4 miles each day. Calculate the number of days he traveled and how far did he travel?
(A) 335 miles in 10 days
(B) 348 miles in 12 days
(C) 338 miles in 15 days
(D) 358 miles in 12 days
(E) 368 miles in 12 days
Rationale: According to the question
miles travelled in 2nd day = 7+4
miles travelled by 3rd, 4th....= 7 + 2*4,7 + 3*4......
A.P. = 7,7+4,7+2*4,......7 + ( n-1)4
IT's given
7 + (n-1)4 = 51
(n-1)4 = 44
n -1 = 11
n = 12
Total number of days = 12
total miles travelled Shiva
= n/2(a + l) [ a = 1st term , l = last term]
= 12/2(7 + 51)
= 6(58)
= 348
so total miles 348 travelled in 12 days
ANSWER:B
Answer: (B) 348 miles in 12 days
Question: If 10 machines can produce 20 units in 10 hours, how long would it take 40 machines to produce 100 units?
(A) 9.5
(B) 6.4
(C) 2.3
(D) 8.9
(E) 12.5
Rationale: 10 machines would produce 100 units in 50 hours. Increasing the amount of machines by 4 would mean dividing 50 hours by 4.
50/4 = 12.5
Answer : E
Answer: (E) 12.5
Question: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
(A) 10
(B) 12
(C) 13
(D) 15
(E) 8
Rationale: A:B= 60: 45
A:C = 60: 40
B/C = (B/A*A/C) = (45/60 * 60/40) = 45/40 = 90/80
=90:80
=>10 points of 90
ANSWER A
Answer: (A) 10
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.5 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 63,000
(B) 2,000,000
(C) 2,030,000
(D) 2,040,000
(E) 2,300,000
Rationale: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
2,300,000
E
Answer: (E) 2,300,000
Question: If the cost price is 89% of selling price then what is the profit percentage.
(A) 8.35
(B) 9.35
(C) 10.35
(D) 11.35
(E) 12.35
Rationale: selling price=Rs100 : then cost price=Rs 89:profit =Rs 11.
Profit={(11/89)*100}%=12.35%
Answer is E.
Answer: (E) 12.35
Question: If positive integer n is divisible by both 5 and 18, then n must be divisible by which of the following?
(A) 8
(B) 12
(C) 17
(D) 30
(E) 48
Rationale: A number divisible by both 5,18 is 90 which s divisible by 30.
IMO : Answer D 30
Answer: (D) 30
Question: There are 100 students in 3 sections A, B and C of a class. The average marks of all the three sections was 84. The average of B and C was 87.5 and the average marks of students in A section was?
(A) 20
(B) 99
(C) 28
(D) 27
(E) 12
Rationale: Numbers of students in section A = x
Numbers of students in section B and C = (100 – x)
x 70 + (100 – x) 87.5 = 84 100
70x + 87.5 100 – 87.5x = 8400
8750 – 17.5x = 8400
17.5x = 8750 – 8400 => x = 20.
Answer: A
Answer: (A) 20