mathewhe/aqua_rat huggingface dataset:
Question: The probability that a computer company will get a computer hardware contract is 4/5 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 9/10, what is the probability that it will get both the contracts?
(A) 1/8
(B) 2/9
(C) 3/10
(D) 4/11
(E) 5/12
Rationale: Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 4/5, P(~B) =5/9
=> P(B) = 1- (3/5) = 2/5.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 9/10 = (4/5) + (2/5) - P(AB).
=> P(AB) = 3/10.
Hence, the required probability is 3/10.
The answer is C.
Answer: (C) 3/10
Question: Out of 5 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?
(A) 21000
(B) 10500
(C) 25200
(D) 10800
(E) None of these
Rationale: Solution
Number of ways of selecting (4 consonants out of 5) and (2 vowels out of 3)
5c4 x 3c2= (5/1)x(3/1) =15
Number of group,each having 4 consonants and 2 vowels = 15
Each group contains 6 letter.
Number of ways of arranging 5 letters among themselves
= 5 ! = (6 x 5 × 4 × 3 × 2 × 1) = 720 .
So, Required number of words = (720 × 15) = 10800 .Answer D
Answer: (D) 10800
Question: A machine puts c caps on bottles in m seconds. How many hours will it take to put caps on b bottles?
(A) 60bm/c
(B) bm/3600c
(C) bc/60m
(D) 60b/cm
(E) b/60cm
Rationale: A machine puts c caps on bottles in m seconds.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/c minutes
In order to calculate the no. of hours taken , divide the product by 3600.
So, our answer is bm/3600c
Answer : B
Answer: (B) bm/3600c
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 4 volts, what was the smallest possible recording in volts?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: if average of 3 is 4 so sum of 3 should be 12
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 5 and 5
so a has to be 2
A
Answer: (A) 2
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?
(A)  18
(B)  12
(C)  20
(D)  32
(E)  36
Rationale: Jan 1 = C
Feb 1 = C - 2
March 1 = C - 4
April 1 = C - 8
May 1 = C - 10
June 1 = C - 12
July 1 = C - 14
Aug 1 = C - 16
Sept 1 = C - 18
Difference between stock on September 1 than were in stock on January 1 will be -
C - ( C - 18 )= 18
Hence answer will be (A)
Answer: (A)  18
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 95%
(B) 25%
(C) 29%
(D) 27%
(E) 21%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: Define q* by the equation q* = π-q. Then ((−π)*)* =
(A)  −2π
(B)  -1
(C)  −π
(D)  2π
(E)  4π
Rationale: for q* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=C
Answer: (C)  −π
Question: Find out the two signs to be interchanged for making following equation correct
5 + 3 x 8 - 12 / 4 =3
(A) 7
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Explanation:
On interchanging - and /, we get the equation as
5 + 3 x 8 / 12 - 4 = 3
or 5 + 3 x (2/3) - 4 = 3
or 3 = 3, which is true.
Answer: B
Answer: (B) 3
Question: Wife man got salary Rs.1000 and Husband got 30% extra compare with A's salary.If boths salary are joined, when will the salary become 10,350?
(A) 120
(B) 130
(C) 135
(D) 142
(E) 150
Rationale: since husband got 30% more,thus the salary is 1300Rs for 30 days(1 month)
in 60 days(2 months) total salary will be :
1000+1300=2300
in 90 days(3 months):
2300+2300=4600
in 120 days(4 months):
4600+4600=9200
now only 800 more amount are required to finish , which will take Half of the month(15 days)
(2300/2=1150-------------->9200+1150=10350)
thus in all 135 days.
Ans:C
Answer: (C) 135
Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
(A) 18
(B) 24
(C) 13
(D) 29
(E) 17
Rationale: Let there were x teams participating in the games, then total number of matches,
nC2 = 153.
On solving we get,
=> n =−17 and n =18.
It cannot be negative so,
n = 18 is the answer
Ans: A
Answer: (A) 18
Question: A train 300 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 48
(C) 29
(D) 27
(E) 21
Rationale: S = (300 + 300)/45 = 600/45 * 18/5 =48
Answer: B
Answer: (B) 48
Question: A grocery shop has a sale of Rs. 6335, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4857
(B) 4184
(C) 4012
(D) 5091
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6335+6927+6855+7230+6562+x)/6 =6500
=>6335+6927+6855+7230+6562+x =6×6500
=> 33909+x=39000
=> x=39000−33909
=5091
ANSWER:D
Answer: (D) 5091
Question: Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {2, 10}
(B) {9, 11}
(C) {10, 18}
(D) {7, 13}
(E) {16, 16}
Rationale: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted
answer is B mean is 10 and S.D decreases minimum.
B
Answer: (B) {9, 11}
Question: Find the odd man out
253, 136, 352, 324, 631, 244
(A) 324
(B) 136
(C) 352
(D) 631
(E) 531
Rationale: The sum all three digits comes to 10 except 324
ANSWER:A
Answer: (A) 324
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 12 days. In how many days Peter complete the work separately.
(A) 26 days
(B) 27 days
(C) 30 days
(D) 25 days
(E) 24 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 12 days which means that the whole job(1) can be completed in X days.
<=> 8/20->12 <=> X=12/(8/20)=30
Thus the answer is C.
Answer: (C) 30 days
Question: The number of new words that can be formed by rearranging the letters of the word 'LETTERRS' is?
(A) 40320
(B) 40318
(C) 40319
(D) 40124
(E) 40154
Rationale: Number of words which can be formed
= 8! - 1 = 40320- 1
= 40319.
Answer:C
Answer: (C) 40319
Question: What is the difference between the largest number and the least number written with the digits 9, 3, 1, 2?
(A) 6084
(B) 3788
(C) 2077
(D) 8082
(E) 1812
Rationale: Explanation:
1239
9321
------------
8082
Answer:D
Answer: (D) 8082
Question: What value will come in place of question mark in the following equation? ? + 0.025 = 80
(A) 1
(B) 5
(C) 6
(D) 3
(E) 2
Rationale: Let x / 0.025 = 80, Then, x = 80 * 0.025 = 2
Answer is E.
Answer: (E) 2
Question: Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 11.88 sec
(B) 13.8 sec
(C) 53.8 sec
(D) 10.8 sec
(E) 10.4 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 190 = 330 m.
Required time = 330 * 9/250 = 11.88 sec.
Answer: A:
Answer: (A) 11.88 sec
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $560 at the end of 3 years and to $660 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $560 - $60 = 500.
The interest rate is $20/$500 = 4%
The answer is B.
Answer: (B) 4%
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
(A) 1/28
(B) 7/30
(C) 1/45
(D) 13/56
(E) 1/72
Rationale: Difference of reciprocals means 1 has to be in the numerator;
So option BD can be ignored
For option A, BE, we require to search two consecutive numbers whose product is the denominator
28 = 4 * 7 ......... Ignore
45 = 5 * 9 ........ Ignore
72 = 8 * 9 ................ Answer
Answer = E
Answer: (E) 1/72
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1504 votes. What is the total number of votes polled?
(A) A)4500
(B) B)5200
(C) C)6900
(D) D)7520
(E) E)6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1504
20x/100 = 1504
x = 1504*100/20 = 7520
Answer is D
Answer: (D) D)7520
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
(A) 2000
(B) 2300
(C) 3000
(D) 3200
(E) 3400
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
C
Answer: (C) 3000
Question: Of 60 applicants for a job, 28 had at least 4 years' experience, 36 had degrees, and 6 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 10
(B) 13
(C) 9
(D) 7
(E) 5
Rationale: 60 - 6 = 54
54 - 28 - 36 = -10
Then 10 are in the intersection between 4 years experience and degree.
Answer : A
Answer: (A) 10
Question: In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 3 sec
(B) 4 sec
(C) 5 sec
(D) 6 sec
(E) 7 sec
Rationale: T = 40/36 * 18/5 = 4 sec
ANSWER:B
Answer: (B) 4 sec
Question: When the integer j is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2j
II. 6j
III. 4j + 6
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I, II, and III
Rationale: is it E.
j= 12*a + 3
2j = 12*2*a + 6
6j = 12*6*a + 18 ( 18 = 12+6)
4j + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: (E)  I, II, and III
Question: If the price of a computer were reduced by 15 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
(A) $844.10
(B) $895.90
(C) $1,055.70
(D) $1,135.60
(E) $1,263.10
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-15/100)------->X(17/20)=A(say)
means X=A*(20/17).....
so initial price to be integer(As per stem) final price must be multiple of 17
if we check options all were divisible by 17 except option (A)..which is Ans.
Ans A
Answer: (A) $844.10
Question: The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 120 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
(A) 42
(B) 44
(C) 60
(D) 48
(E) 50
Rationale: The time it takes Cara to drive to City B is 120 / 30 = 4 hours.
Dan needs to take less than 2 hours for the trip.
Dan needs to exceed a constant speed of 120 / 2 = 60 miles per hour.
The answer is C.
Answer: (C) 60
Question: A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?
(A) 116%
(B) 166.66%
(C) 60%
(D) 100%
(E) 150%
Rationale: Explanation:
Let the cost price of 1 litre pure milk be Re.1, then
{6 litres(milk)->cp=Rs.6, 2 litres(water)->cp=Rs.0}->cp=Rs.6 only
and 8 litre mixture ->SP -> 8 x 2 = Rs.16
Profit %= [16/6 -6]x100=100/6=166.66%
ANSWER IS B
Answer: (B) 166.66%
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 10kmph. What time will they take to be 50km apart?
(A) 1.2hr
(B) 2.5hrs
(C) 3hrs
(D) 5.2hrs
(E) 6hrs
Rationale: To be (10+10) km apart, they take 1 hour
To be 50 km apart, they take 1/20*50 = 2.5 hrs
Answer is B
Answer: (B) 2.5hrs
Question: A train travels 240 km in 3 hours and 450 km in 5 hours.find the average speed of train.
(A) 80 kmph
(B) 60 kmph
(C) 86 kmph
(D) 90 kmph
(E) None of these
Rationale: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 240 + 450 = 690 km
Thus, Total Speed = 8 hrs
or,Average Speed = 690/8
or, 86kmph.
ANSWER:C
Answer: (C) 86 kmph
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 220 meter
(B) 225 meter
(C) 230 meter
(D) 235 meter
(E) None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+270 /9=500 /9
=>x+270=500
=>x=230
So the length of the train is 230 meters
Option C
Answer: (C) 230 meter
Question: If d=1/(2^3*5^8) is expressed as a terminating decimal, how many nonzero digits will d have?
(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^8)
= Multiply and divide by 2^5
=2^5/(2^3*2^5*5^8)
=2^5/10^8
=> non zero digits are 32=> Ans B
Answer: (B) Two
Question: If W is the set of all the integers between 39 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 26
(B) 32
(C) 33
(D) 34
(E) 40
Rationale: Multiples of 2 from 39 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 38=[99/2]-[38/2]=49-19=30
Multiples of 3 from 39 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 38=[99/3]-[38/3]=33-13=20
Multiples of2 and 3 bothi.e.6 from 39 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 38=[99/6]-[38/6]=16-6=10
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 30 + 20 - 10 = 40
Answer Option E
Answer: (E) 40
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many litres of tomato puree will be obtained from 20 litres of tomato juice?
(A) 2 litres
(B) 2.4 litres
(C) 2.5 litres
(D) 6 litres
(E) 4 litres
Rationale: Tomato Juice has 90% water and 10% tomato
Tomato puree has 20% water and 80% tomato
So 20 liter of tomato juice has 20*90/100=18 liters of water and 2 liters of tomato.
As tomato puree has 80% content of tomato, so 2 liters of tomato from 20 liter juice corresponds to 80% so tomato purees that can be obtained=100*2/80=2.5
ANSWER:C
Answer: (C) 2.5 litres
Question: A can do a job in 15days and B in 30days. If they work on it together for 4 days, then the fraction of the work that is left is?
(A) 2/15
(B) 3/5
(C) 3/11
(D) 1/12
(E) 6/13
Rationale: A's 1 day work = 1/15
B's 1day work = 1/30
A+B 1day work = 1/15 + 1/30 = 3/30=1/10
A+B 4days work = 1/10*4 = 2/5
Remaining work = 1 - 2/5 = 3/5
Answer is B
Answer: (B) 3/5
Question: A professional janitor can clean a certain high school in 480 minutes, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
(A) -$56
(B) -$6
(C) $0
(D) $6
(E) $8
Rationale: A professional janitor can clean a certain high school in 480mins or (480/60) or 8 hours
So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR
A student sentenced to detention can clean that same high school in 20 hours
So (applying rule #1), the student can clean 1/20 of the school in ONE HOUR
So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR
1/8 + 1/20 = 5/40 + 2/40 = 7/40
So, in ONE HOUR they can clean 7/40 of the school.
Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.
The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.
Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160
Working ALONE, the janitor takes 8 hours and earns $21/hour
So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168
$168-$160= $8, so the answer is E
Answer: (E) $8
Question: A smartphone manufacturer sold 20 thousand low end smartphone at $100 each within a given period. The company also sold 12 thousand mid range smartphones at $220 each and 5 thousand high end smartphones at $649 each within the same period. What percentage of the company's revenue came from mid range and high end smartphones?
(A) 74.6
(B) 80.5%
(C) 60.%
(D) 70%
(E) 76.2%
Rationale: Correct Answer: A
The company's total revenue from low end smartphones=$100*20000=$2 000 000
The company's total revenue from mid range smartphones=$220*12000=$2 640 000
The company's total revenue from mid range smartphones=$649*5000=$3 245 000
The combined total of all sales=$7 885 000
combined total of mid range and high end sales=5885000
Therefore % of mid range and high end smartphone sales=74.6%
Answer: (A) 74.6
Question: What is the least whole number that should be added to 784839 if it is to be divisible by 10?
(A) 3
(B) 2
(C) 1
(D) 5
(E) 6
Rationale: A number is divisible by 10 if the last digit is 0.
Here, 784839=9, (last digit is not 0.
1 must be added to 784839 to make it divisible by 10
C
Answer: (C) 1
Question: In Orange County, one fourth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 60
(B) 75
(C) 85
(D) 160
(E) 252
Rationale: The number must be a multiple of both 4 and 7 so the answer is 252.
The answer is E.
Answer: (E) 252
Question: An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 15%. Also, if a customer will “buy at least 10” items they will deduct an additional 28% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
(A) $92.00
(B) $88.00
(C) $87.04
(D) $80.96
(E) $60.00
Rationale: Without any discount Sam should pay 10*10=$100. Now, the overall discount would be slightly less than 43%, thus he must pay slightly more than $57. Only answer choice E fits.
Answer: E.
Answer: (E) $60.00
Question: A cistern 12 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
(A) 64
(B) 72
(C) 80
(D) 88
(E) 96
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 12 x 1.25) + 12 x 4]
= 88
The answer is D.
Answer: (D) 88
Question: The charge for a single room at Hotel P is 40 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?
(A) 15%
(B) 20%
(C) 40%
(D) 50%
(E) E.150%
Rationale: P = 0.6R = 0.9G
R = 0.9G/0.6 = 1.5*G
Thus R is 50% greater than G.
The answer is D.
Answer: (D) 50%
Question: In how many ways can 16 different gifts be divided among four children such that each child receives exactly two gifts?
(A) 16^4
(B) (4!)^4
(C) 16!/(2!)^4
(D) 16!/2!
(E) 4^16
Rationale: Total 16 different Gifts, and 4 children.
Thus any one child gets 16C2 gifts,
then the other child gets 14C2 gifts(16 total - 2 already given),
then the third one gets 12C2 gifts,
and the last child gets 10C2 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
16C2 * 14C2 * 12C2 * 10C2 = 16! / (2!)^4
C
Answer: (C) 16!/(2!)^4
Question: 189. The inside dimensions of a rectangular wooden box
are 4 inches by 6 inches by 8inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 8x6 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 6, so the radius will be 3.'
A
Answer: (A)  3
Question: If s and t are positive integers such that s/t = 64.15, which of the following could be the remainder when s is divided by t?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: 0.15 = 3/20
The remainder must be divisible by 3.
The answer is C.
Answer: (C) 18
Question: B and C started a business investing Rs. 72,000 and Rs. 45,000 respectively. In what ratio the profit earned after 7 years be divided between B and C respectively?
(A) 7:5
(B) 5:8
(C) 5:7
(D) 8:5
(E) None of these
Rationale: B:C = 72000 : 45000 = 8:5.
ANSWER:D
Answer: (D) 8:5
Question: Which one the following fractions has the biggest value?
(A) 211/711
(B) 201/711
(C) 191/711
(D) 221/711
(E) 181/711
Rationale: All options have the same denominator 711. If denominator is same, the fraction with the biggest value will be the one with the biggest numerator. Answer (D).
Answer: (D) 221/711
Question: Train E leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
(A) 8:15 am
(B) 8:45 am
(C) 9:00 am
(D) 9:30 am
(E) Cannot be determined from the information given
Rationale: train E will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
Answer: (B) 8:45 am
Question: A alone can finish a work in 20 days. And B alone can finish same work in 25 days.both together work for 5 days.after that B leave that work.in how many days A alone can finish remaining work?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Work of A in 1 day= 1/20, work of B in 1 day = 1/25
(A+B) work in 5 day= 5(1/20+1/25)=5*(5+4)/100=9/20.
Remaining work=[1-9/20]=11/20
11/20 part of work A alone do = [1×20×11/20] days = 11 days
Answer A
Answer: (A) 11
Question: In Town P, 70 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town P are females?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: The percent of the population who are employed females is 70-42 = 28%
The percent of employed people who are female is 28% / 70% = 40%.
The answer is D.
Answer: (D) 40%
Question: The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school?
(A) 48
(B) 64
(C) 70
(D) 80
(E) 84
Rationale: Let day scholars be DS and boarders be B
Given B/DS = 7/16 ---> eq1
Initially B = 560 and x be new boarders joined
Then from eq1 , we get DS = 16/7*560 = 1280
Now , new ration is 560+x / DS = 1/2
560+x / 1280 = 1/2 => 1120+2x = 1280 => 2x = 160 => x = 80
ANS option D
Answer: (D) 80