mathewhe/aqua_rat huggingface dataset:
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 27 years
(B) 87 years
(C) 18 years
(D) 19 years
(E) 16 years
Rationale: 9 * 2 = 18 years
Answer: C
Answer: (C) 18 years
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 27kmph. For how many minutes does the bus stop per hr
(A) 12 min
(B) 11 min
(C) 13 min
(D) 20 min
(E) 30 min
Rationale: Due to stoppages,it covers 27km less.
time taken to cover 27 km is [27/54 *60] min = 30min
Answer is E.
Answer: (E) 30 min
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 5
(D) 2
(E) 3
Rationale: 2x * x = 128 => x= 8
Answer: A
Answer: (A) 8
Question: Calculate the amount that an investor needs to be invest to earn $1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11% compounded semi-annually?
(A) 8000
(B) 8100
(C) 8900
(D) 8600
(E) 8400
Rationale: the approach is substitution,
our interest requirement is $1005 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields 460 in 12 months
8900 yielded $1005
using the formula
A = P(1 + r/n)nt
hence answer is C
Answer: (C) 8900
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 10 nor by 35?
(A) 884
(B) 890
(C) 892
(D) 910
(E) 945
Rationale: Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)
In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2
Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 910
Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
D
Answer: (D) 910
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number of employees who take the subway to work?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let part time emp=x
Let full time emp=y
then,
48=x+y.........(1)
(1/3)x+(1/4)y=No. of ppl taking the subway
4x+3y/12=No. of ppl taking the subway
using 1
x/12+3*48/12=No. of ppl taking the subway
so, the minimum value of x has to be 12.
Hence to maximize the no. put 36 for x
36/12+12/4=15
ANSWER:D
Answer: (D) 15
Question: Mismatched Joe is in a pitch dark room selecting socks from his drawer. He has only six socks in his drawer, a mixture of black and white. If he chooses two socks, the chances that he draws out a white pair is 2/3. What are the chances that he draws out a black pair?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Since there is a 2/3 chance of drawing a white pair,
Then there must be 5 white socks and only 1 black sock.
The chances of drawing two whites would thus be: 5/6 x 4/5 = 2/3 .
With only 1 black sock, there is no chance of drawing a black pair.
So, Zero chance of drawing a black pair.
ANSWER:E
Answer: (E) 0
Question: The radius of a cylindrical vessel is 7cm and height is 2cm. Find the whole surface of the cylinder?
(A) 308 sq cm
(B) 220 sq cm
(C) 396 sq cm
(D) 132 sq cm
(E) 138 sq cm
Rationale: r = 7 h = 2
2πr(h + r) = 2 * 22/7 * 7(9) = 396
ANSWER:C
Answer: (C) 396 sq cm
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 1000 years is:
(A) 587 x 10^13 miles
(B) 999× 1238 miles
(C) 346 × 1012 miles
(D) 247 × 1012 miles
(E) 587 × 1012 miles
Rationale: The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 1000 years is:
= 587 * 10^10 x 10 ^3 = 587 x 10^13 miles
Answer :A
Answer: (A) 587 x 10^13 miles
Question: The number 149 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A)  19
(B)  16
(C)  15
(D)  14
(E)  13
Rationale: 2^2 + 8^2 + 9^2 = 149 --> 2 + 9 + 8 = 19.
A
Answer: (A)  19
Question: A milkman mixed 10 liters of water to 50 litres of milk of Rs.16 per liter, then cost price of mixture per liter is
(A) Rs.15.16
(B) Rs.13.33
(C) Rs.15
(D) Rs.14.23
(E) Rs.15.23
Rationale: Total mixture = 10w + 50m = 60
Total S.P= 16*60= Rs.960 @ Rs.16/lit
Now one can easily see in the statement that the milkman will get profit of 10 litres.
So, Gain = 10*60= Rs.160
Also, Gain = SP - CP
160=960-CP
CP = 800 for 60litres
so CP for 1 litre = 800/60 = 13.33
ANSWER:B
Answer: (B) Rs.13.33
Question: The average (arithmetic mean) of the even integers from 0 to 100 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 50 inclusive?
(A) 24
(B) 25
(C) 26
(D) 48
(E) 50
Rationale: So, according to A mean of a set of even numbers from 0 to 100 =(0+100)/2=50 and mean of a set of even numbers from 0 to 50 =(0+50)/2=25
Difference=50-25=25
Answer: B.
Answer: (B) 25
Question: B and C start a business with Rs.4000 and Rs.12000 respectively. How should they share their profits at the end of one year?
(A) 3:1
(B) 1:5
(C) 1:4
(D) 1:3
(E) 1:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by B and C =
4000 : 12000 => 1:3 .
Answer:D
Answer: (D) 1:3
Question: Find the number which when added to itself 13 times, gives 112.
(A) 7
(B) 8
(C) 9
(D) 11
(E) 12
Rationale: Explanation:
Let the number be x. Then, x + 13x = 112 14x = 112 x = 8.
Answer: B
Answer: (B) 8
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:5
(B) 5:3
(C) 8:6
(D) 7:6
(E) 9:8
Rationale: 4:5
3:2
------
12:15:10
12:10
6:5
ANSWER A
Answer: (A) 6:5
Question: In a sports contest there were m medals awarded on n successive days (n > 1). On the first day 1 medal and 1/7 of the remaining m " 1 medals were awarded. On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on. On the nth and last day, the remaining n medals were awarded. how many medals were awarded altogether?
(A) 36 medals
(B) 37 medals
(C) 38 medals
(D) 35 medals
(E) 34 medals
Rationale: 1st day=1+35/7=6 remaining 30 medals
2nd day=2+28/7=6 remaining 24 medals
3rd day=3+21/7=6 remaining 18 medals
...
6th day 6 medals
6*6=36 medals
6 days
ANSWER:A
Answer: (A) 36 medals
Question: What will be the remainder when 17^200 is divided by 18
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 17^200 % 18
(17-18)^200 % 18
(-1)^200 % 18
1 % 18 = 1
ANSWER:A
Answer: (A) 1
Question: The price of a certain painting increased by 30% during the first year and decreased by 20% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
(A) 102%
(B) 105%
(C) 120%
(D) 135%
(E) 104%
Rationale: Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 30 = 130
Price at the end of year 2 = 130 - 130*0.20 = 130*0.80 = 104
Hence required answer = (104/100)*100% = 104%
Answer is E.
Answer: (E) 104%
Question: 39 persons can repair a road in 12 days,working 5 hours a day.In how many days will 30 persons,working 6 hours a day,complete the work ?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Solution
Let the required number of hours per day be x.
Less persons, More days (Indirect Proportion)
More working hrs per days, Less days (Indirect Proportion)
∴ 30 × 6 × x = 39 × 5 × 12 ⇔ x = 39x5x12/30x6 =x =13. Answer B
Answer: (B) 13
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. Find his average after 17th inning?
(A) 19
(B) 29
(C) 39
(D) 49
(E) 59
Rationale: Solution
Let the average after 17th inning = x. Then, average after 16th inning = (x - 3)
Average
=16 (x-3)+87
= 17x or x=(87-48)
= 39.
Answer C
Answer: (C) 39
Question: A man can row with a speed of 5 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) A)15
(B) B)18
(C) C)10
(D) D)11
(E) E)15
Rationale: M = 5
S = 5
DS = 5 + 5 = 10
Answer:C
Answer: (C) C)10
Question: A four digit number divisible by 7 becomes divisible by 3 when 19 is added to it. The largest such number is :
(A) 4461
(B) 4473
(C) 4479
(D) 4487
(E) 4491
Rationale: Out of all the 5 options, only 4487 is NOT divisible by 3. All others are divisible
So Answer = D (No further calculation required)
Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3
19 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3
Applying the above rule,It means that the number which we are going to add should be non-divisible by 3
So comes the answer = 4487
Answer : D
Answer: (D) 4487
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 41st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
(A) 19
(B) 25
(C) 30
(D) 32
(E) 44
Rationale: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 41st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
30 floors/120 floors per minute=1/4 minutes
11+57/4=25
41-63/4=25
Answer : B
Answer: (B) 25
Question: Find the area of circle whose radius is 35m?
(A) 2883
(B) 1543
(C) 7673
(D) 3850
(E) 1788
Rationale: 22/7 * 35 * 35
= 3850
Answer: D
Answer: (D) 3850
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 7 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
(A) 396
(B) 1260
(C) 550
(D) 7920
(E) 15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 7 and 11..ie., 5 possible numbers
Possible combinations for X1,X2 would be 5C2 = 10
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 10 * 55 = 550
Ans. C
Answer: (C) 550
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 17, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/80
Rationale: Choose x as a multiple of 17, I chose 64:
So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is D.
Answer: (D)  3x/40
Question: Bottle R contains 250 capsules and costs $6.25. Bottle T contains 100 capsules and costs $3.0. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
(A)  $0.25
(B)  $0.12
(C)  $0.05
(D)  $0.003
(E)  $0.005
Rationale: Cost per capsule in R is 6.25/250=0.625/25=0.025
Cost per capsule in T is 3.00/100=0.03
The difference is 0.005
The answer is E
Answer: (E)  $0.005
Question: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
(A) 33 1/3 %
(B) 40%
(C) 50%
(D) 60%
(E) 66 2/3%
Rationale: Let the total # of passengers be 100.
Now, 20 passengers held round-trip tickets AND cars.
As 60% of the passengers with round-trip tickets did not take their cars then 40% of the passengers with round-trip tickets did take their cars, so # of passengers with round-trip tickets AND cars is 40% of the passengers with round-trip tickets.
If we take # of the passengers with round trip tickets to be xx then we'll have 0.4x=200.4x=20 --> x=50x=50.
Answer: C.
Answer: (C) 50%
Question: If k is a non-negative integer and 18^k is a divisor of 624,938 then 6^k - k^6 =
(A) 0
(B) 1
(C) 36
(D) 118
(E) 420
Rationale: 6+2+4+9+3+8 = 32, so this number is not divisible by 3 and thus not divisible by 18.
Therefore, k=0
6^k - k^6 =1-0=1
The answer is B.
Answer: (B) 1
Question: 20 men do a work in 20days. How many men are needed to finish the work in 4days?
(A) 50
(B) 20
(C) 30
(D) 100
(E) 15
Rationale: men required to finish the work in 4days = 20*20/4 = 100
Answer is D
Answer: (D) 100
Question: What is the value of: 5^10 - 5^9 + 5^8 ?
(A)  5^9
(B)  15^9
(C)  21(5^8)
(D)  29(5^8)
(E)  29(5^10)
Rationale: 5^10 - 5^9 +5^8 = 5^8 (5^2 - 5 + 1) = 5^8 (25 - 5 + 1) = 21 (5^8), Answer C.
Answer: (C)  21(5^8)
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is
(A) 8/17
(B) 7/15
(C) 3/15
(D) 8/15
(E) 1/4
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 4 days they work 35 * 4 = 140
Remaining work is 300 - 140 = 160
Remaining fraction of work is = 160/300 = 8/15
Answer D
Answer: (D) 8/15
Question: Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together?
(A) 1.5
(B) 2
(C) 2.4
(D) 3
(E) 3.6
Rationale: Answer is 3.6 hours.
Tom does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: (E) 3.6
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 4m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 54
(B) 32
(C) 75
(D) 28
(E) 16
Rationale: A/8 = 4 * 4 => A = 4 * 4 * 8
x * 2x = 4 * 4 * 8
x = 8 => 2x = 16
Answer:E
Answer: (E) 16
Question: When a=4+(2/4) and b=4-(2/4), (2^a^2)/(2^b^2)=?
(A) 260
(B) 256
(C) 240
(D) 210
(E) 225
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/4 and a+b=8, 2^(a-b)(a+b)=2^(4/4)(8)=2^8=256
Therefore, the answer is B
Answer: (B) 256
Question: Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page?
(A) 6:26
(B) 6:56
(C) 7:26
(D) 7:56
(E) 8:26
Rationale: Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom.
The answer is C.
Answer: (C) 7:26
Question: Jason can row his boat with the stream at 50 km/h and against the stream in 2 km/h. Jason's rate is?
(A) 18 kmph
(B) 24 kmph
(C) 35 kmph
(D) 15 kmph
(E) 12 kmph
Rationale: DS = 50
US = 2
S = ?
S = (50 - 2)/2 = 24 kmph
Answer:B
Answer: (B) 24 kmph
Question: A rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 244ft
(B) 88ft
(C) 122ft
(D) 178ft
(E) 66ft
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
8 x Breadth = 680
Breadth = 85 feet
Area to be fenced = 2B + L = 2 (85) + 8 = 178 feet
Answer: D) 178ft
Answer: (D) 178ft
Question: 20 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 380
(B) 470
(C) 560
(D) 650
(E) 740
Rationale: 2*20C2 = 2*190 = 380
The answer is A.
Answer: (A) 380
Question: Find the number which when added to itself 13 times, gives 112.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let the number be x. Then, x + 13x = 112 14x = 112 x = 8.
ANSWER:B
Answer: (B) 8
Question: Kuber borrowed rs 169 due in 2 years at 4%per annum compound interest.Find the Present worth?
(A) 160.15
(B) 225
(C) 156.25
(D) 180.25
(E) 150.5
Rationale: Compound interest=[169*(1+(4/100))^2]
=[169*((104/100)^2)]
=(169*((26/25)^2))
=(169*25*25)/(26*26)
=Rs.156.25
Option C
Answer: (C) 156.25
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 40% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 100
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: total marks:1500 for three exams
40% of 1500=600
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =600
X=100
ANSWER:A
Answer: (A) 100
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 59 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
(A) 62 degrees
(B) 32 degrees
(C) 65 degrees
(D) 66 degrees
(E) 67 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (59 * 4) = 236 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 4 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 4 or x = 4. Answer: B
Temperature on the 5th day = 8x = 32 degrees.
Answer: (B) 32 degrees
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
(A) 33
(B) 88
(C) 27
(D) 80
(E) 12
Rationale: We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Answer:D
Answer: (D) 80
Question: Divide Rs. 800 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) s.800
(B) s.200
(C) s.600
(D) s.500
(E) s.900
Rationale: A+B+C = 800
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 800 => 200
ANSWER:B
Answer: (B) s.200
Question: In N is a positive integer less than 200, and 10N/60 is an integer, then N has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: (A).
10n/60 must be an integer. => 1n/6 must be an integer. Hence n must be a multiple of 2*3.
=> n has 2 different prime integers.
Answer: (A) 2
Question: On a certain number line, conditions are a<b<c<d<e and ab>0. Which of the following must be true?
I ab>0 II cd>0 III de>0
(A) I&II only
(B) II only
(C) III only
(D) I only
(E) II and III only
Rationale: Givena<b<c<d<e and abcde>0.
Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.
We are given : I ab>0 II cd>0 III de>0
case 1: a and b can be negative/positive and if they are... we get greater than 0.
case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0.
case 2: we have de , then c and d both can be negative/positive and if they are... we get greater than 0.
if cd both negative , then de both have to negative in order to get greater than 0. In order to abcde>0 , cde can't be negative else we get -ve value, then we need to have either a or b as negative then ab can't be greater than 0.
so cde have to be positive.
D
Answer: (D) I only
Question: If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark?
(A) 60%
(B) 80%
(C) 65%
(D) 75%
(E) None of these
Rationale: A's marks = 80 ; B's marks = 60.
Let x% of A = B => x/100 * 80 = 60
=> x = (60 * 100)/80 = 75
B's marks is 75% of A's marks.
ANSWER:D
Answer: (D) 75%
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 7 businessmen, how many possible team submissions are possible?
(A) 76
(B) 130
(C) 162
(D) 198
(E) 202
Rationale: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 7C2 = 84
2) 2 tech1 businessman: 4C2 x 7C1 =42
3) 3 tech0 businessmen: 4C3 = 4
Total: 84+42+4 = 130
Answer: B
Answer: (B) 130
Question: 2.09 can be expressed in terms of percentage as
(A) 2.09%
(B) 20.9%
(C) 209%
(D) 0.209%
(E) None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
2.09 * 100 = 209
Answer: Option C
Answer: (C) 209%
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 256
(B) 375
(C) 287
(D) 255
(E) 123
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Answer: (B) 375
Question: If the time is currently 1:30 pm, what time will it be in exactly 642 hours?
(A) 3:30 am
(B) 4:30 am
(C) 5:30 am
(D) 6:30 am
(E) 7:30 am
Rationale: 642 = 26(24) + 18/24
The time will be 18 hours later than 1:30 pm which is 7:30 am.
The answer is E.
Answer: (E) 7:30 am
Question: Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/4 of capacity in 9 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
(A) 3.25
(B) 3.6
(C) 4.2
(D) 4.4
(E) 7.2
Rationale: Time taken by First tank Fill 1/4 the tank = 9 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 36 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/36)+(1/9) = 5/36 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 36/5 hours =7.2 hours
Answer: option E
Answer: (E) 7.2
Question: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 4x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?
(A) –3
(B) –5
(C) –6
(D) –7
(E) –9
Rationale: Since f(x) defines maximum of 2x + 4 and 12 + 4x,
to find those x when 2x+4 has greater value,
2x + 4 > 12 + 4x
or x < -4
Only value that satisfy this is -5.
Answer is (B),
Answer: (B) –5
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 22 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
(A) 25.0
(B) 30.6
(C) 37.8
(D) 40.2
(E) 45.1
Rationale: Day 1
2t+3=22
t=9.5
Day 2
t+3
9.5+3=12.5
9.5r+12.5(r+15)=1020
r=37.8
Answer:C
Answer: (C) 37.8