mathewhe/aqua_rat huggingface dataset:
Question: At a certain university, 70% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
(A) 25
(B) 37.5
(C) 50
(D) 62.5
(E) 75
Rationale: answer is 75%
total women = 70%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 20%
but question wants to know the percent of men that are tenured
20%/40%=50%
C
Answer: (C) 50
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 22 kmph
(B) 77 kmph
(C) 14 kmph
(D) 88 kmph
(E) 12 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer:C
Answer: (C) 14 kmph
Question: Which of these must the factor M of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
(A) M=1,2 only
(B) M=2,3 only
(C) M=1,2,3 only
(D) M=1,2,3,4 only
(E) All of them
Rationale: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Answer: (D) M=1,2,3,4 only
Question: Of the 800 employees in a certain company, 70% have serviced more than 10 years. A number of y of those who have serviced more than 10 years will retire and no fresh employees join in. What is y if the 10 years employees become 60% of the total employees?
(A) 150
(B) 200
(C) 250
(D) 450
(E) 550
Rationale: TOTAL 10 YRS
Original: 800 560
New: 800-y 560-y
560-y = .6 (800 -y)
560-y = 480 - .6y
80 = .4y
800/4 = y
y= 200
Answer: 200	ANSWER:B
Answer: (B) 200
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
answer :D
Answer: (D) 10
Question: Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next six years and 12% per annum for the period beyond ten years. If he pays a total of 12,160 as interest only at the end of 15 years, how much money did he borrow?
(A) 8000
(B) 10,000
(C) 12,000
(D) 9,000
(E) None of these
Rationale: Let the Principal = P
Then P×8×4/100+P×10×6/100+P×12×5/100
= 12160
⇒ 152P = 12160 × 100
or 12160×100/152=8000
Answer A
Answer: (A) 8000
Question: If Q is an odd number and the median of Q consecutive integers is 130, what is the largest of these integers?
(A) (Q + 130)/2
(B) Q/2 + 129
(C) Q/2 + 130
(D) (Q + 129)/2
(E) (Q - 1)/2 + 130
Rationale: Consider the easiest case, say Q=3, then;
Set = {129, 130, 131};
The largest integer = 131.
Now, plug Q=3 into the answers to see which yields 131.
Answer: E.
Answer: (E) (Q - 1)/2 + 130
Question: An article is bought for Rs.675 and sold for Rs.1215, find the gain percent?
(A) 33 1/9%
(B) 33 8/3%
(C) 33 1/3%
(D) 33 2/3%
(E) 80%
Rationale: 675 ---- 540
100 ---- ? => 80%
Answer: E
Answer: (E) 80%
Question: A car traveled from San Diego to San Francisco at an average speed of 54 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
(A) 24.
(B) 32.
(C) 36.
(D) 42.
(E) 44.
Rationale: Let the time taken be = x
One way distance = 54x
Total distance traveled = 2 * 54x = 108x
Total time taken = x + 2x = 3x
Average speed = 108x/3x = 36
Answer: C
Answer: (C) 36.
Question: If (400)(7,000) = (28,000)(100^x), what is the value of x?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: (400)(7,000) = (2,800)(100^x)
=> (400)(7,000)/2,800 = 100^x
=> 100 = 100^x
=> 100^1 = 100^x
Since, base is same so powers will be same too.
So, x=1
Answer will be E
Answer: (E) 1
Question: In g is a positive integer smaller than 200 and (14g)/60 is an integer, then g has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 7g/30 tells us that g is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Answer: (B) 3
Question: Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 10, 14 and 18 seconds. ?
(A) 636
(B) 631
(C) 633
(D) 610
(E) 630
Rationale: LCM of 9, 10, 14 and 18 is
630
LCM=630
ANSWER:E
Answer: (E) 630
Question: A monkey start climbing up a tree 21 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
(A) 15 hrs
(B) 18 hrs
(C) 19 hrs
(D) 17 hrs
(E) 16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 18hrs it wil be 18ft.
But since the height of the tree is 21 ft, so if the monkey hops up the tree in the next hr i.e 19th hr then it reaches at the top of the tree.
hence it takes 19 hrs for monkey to reach at the top
ANSWER:C
Answer: (C) 19 hrs
Question: A grocery shop has a sale of Rs. 6735, 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) 4691
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6735+6927+6855+7230+6562+x)/6 =6500
=>6735+6927+6855+7230+6562+x =6×6500
=> 34309+x=39000
=> x=39000−34309
=4691
ANSWER:D
Answer: (D) 4691
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long S will the conference last if there are a total of 6 seminars that day?
(A) 5 hours and 15 minutes
(B) 5 hours and 20 minutes
(C) 5 hours and 25 minutes
(D) 5 hours and 30 minutes
(E) 5 hours and 35 minutes
Rationale: Shouldnt the answer be 5 hours 20 mins?
Break = b
Seminar= 10b
9am to 11:40am= 160mins
3s+b=160
30b+b=160
b=160/31
6 seminar will take
6s+2b
=60b+2b
=62b
=62*160/31
=320
S=5 hours 20 mins.B
Answer: (B) 5 hours and 20 minutes
Question: If abc represents a positive three-digit number, where a, b and c are one-digit integers, which of the following CAN be true?
(A) a + b + c = 9
(B) a – b - c = 9
(C) b – c - a = 9
(D) Both A and C
(E) Both A and B
Rationale: The (hundreds place digit, a) cannot be zero, but (tens and ones place digits; b and c) can be zero.
A is NOT possible
B is possible
C is possible
D is possible
E is possible
Answer: E
Answer: (E) Both A and B
Question: Mayank Bothra purchased 20 dozens of toys at the rate of 375 Rs per dozen .He sold each one of them at the rate of Rs 33.What was his percentage profit?
(A) 5.6 %
(B) 6.5 %
(C) 7.5 %
(D) 7.6 %
(E) None
Rationale: Sol.
Cost = 375 * 20 = 7500
sale price 33 * 20 * 12
= 7920 profit = 420 profit in % = 420/7500 * 100 =5.6 %
Ans: A.
Answer: (A) 5.6 %
Question: Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them.
(A) Rs. 115
(B) Rs. 116
(C) Rs. 117
(D) Rs. 118
(E) None
Rationale: Solution:
Let the average expenditure of all the nine be x.
Then, 12 × 8 + (x + 8) = 9x.
Therefore, x = 13.
Total money spent,
= 9x = Rs.(9 × 13) = Rs.117
Answer: Option C
Answer: (C) Rs. 117
Question: N and M are each 3-digit integers. Each of the numbers 3,4, 5, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
(A) 59
(B) 49
(C) 58
(D) 113
(E) 131
Rationale: You have 6 digits: 3, 4, 5, 6, 7, 8
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 3 and 8 in the hundreds places and reserve them for the tens places . Now what are the options?
Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible.
487 and 536 (difference is 49) or
Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 685 and 734 (difference is 49)
B
Answer: (B) 49
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:9. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 9
(B) 17
(C) 13
(D) 10
(E) 12
Rationale: 7*5: 5*x = 7:9
x = 9
Answer: A
Answer: (A) 9
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/9
(C) 1/6
(D) 1/2
(E) 1/5
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: A sum of money deposited at C.I. amounts to Rs.1820 in 4 years and to Rs.2402 in 5 years. Find the rate percent?
(A) 30%
(B) 31%
(C) 34%
(D) 19%
(E) 50%
Rationale: 1820 --- 582
100 --- ? => 31%
Answer: B
Answer: (B) 31%
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) 6:3
(B) 6:9
(C) 6:5
(D) 6:1
(E) 6:4
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Answer: (C) 6:5
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 80 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 8.6 years and the standard deviation is 3.4 years, what percent of the distribution has more than 12.0 years as a shelf’s average life?
(A) 23%
(B) 22%
(C) 21%
(D) 20%
(E) 19%
Rationale: Average = 8.6
SD = 3.4
8.6 - 3.4 < 80% of distribution < 8.6 + 3.4
5.2 < 80% of distribution < 12.0
40% is outside this range.
Given: Distribution is symmetric. So 20% of distribution is less than 5.2 and the other 20% of distribution is greater than 12.0.
Answer: D
Answer: (D) 20%
Question: The simple interest on a sum of money will be Rs. 600 after 10 years.If the principal is trebled after 5 years,what will be the total interest at the end of the tenth year ?
(A) Rs. 600
(B) Rs. 900
(C) Rs. 1200
(D) Rs. 1500
(E) None
Rationale: Solution
22.22
Let the sum be Rs. x. Now, S.I. = Rs. 600,T = 10 years.
Rate = % = (100x600/X x 10)% =(6000/X)%
S.I. for first 5 years = Rs.(X x 5 x 6000/X x 100) = Rs. 300.
S.I. for first 5 years = Rs. (3X x 5 x 6000/X x 100)= Rs. 900.
∴ Total interest = Rs. 1200.
Answer C
Answer: (C) Rs. 1200
Question: A hall 20m long and 15m broad is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at the rate of Rs.3.50 per sq. meter is
(A) 500
(B) 600
(C) 650
(D) 700
(E) 750
Rationale: Area of verandah = [(25Ãƒâ€”20)?(20Ãƒâ€”15)]mÂ²=200 mÂ²
Cost of flooring = Rs.(200Ãƒâ€”3.50) = Rs.700
Answer :D
Answer: (D) 700
Question: If the LCM of A and B is 72 and their HCF is 6, what is the product of A & B?
(A) 432
(B) 433
(C) 434
(D) 435
(E) 436
Rationale: The most important property of LCM (the least common multiple) and GCD (the greatest common divisors) is: for any positive integers x and y, x∗y=GCD(x,y)∗LCM(x,y) so AB=72*6=432.
ANSWER:A
Answer: (A) 432
Question: If a,b,c,d,e is an arithmetic sequence which of the following is also an arithmetic sequence?
I. 5a, 5b, 5c, 5d, 5e
II. a-6, b-6, c-6, d-6, e-6
III. a^8, b^8, c^8, d^8, e^8
(A) I and II
(B) II only
(C) II and III
(D) III only
(E) I only
Rationale: lets look at the three choices...
I. 5a, 5b, 5c, 5d, 5e
since the difference is constant, it is an arithmetic sequence...
II. a-6, b-6, c-6, d-6, e-6
since the difference is constant, it is an arithmetic sequence
III. a^8, b^8, c^8, d^8, e^8
since the difference is not constant it is not be an arithmetic sequence...
only l and ll.. ans A....
Answer: (A) I and II
Question: Sonika bought a V.C.R. at the list price of 18,500. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
(A) 19,980
(B) 19,780
(C) 19,680
(D) 19,380
(E) None of these
Rationale: Sol. List price of V.C.R. =18,500
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,500
= 8⁄100 × 18500 = 1480
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,500 + 1480
= 19,980. Answer A
Answer: (A) 19,980
Question: The two lines y=x and x=-6 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The point of intersection is (-6,-6).
The triangle has a base of length 6 and a height of 6.
area = (1/2)*base*height = (1/2)*6*6 = 18
The answer is D.
Answer: (D) 18
Question: Find the simple interest on $10000 at 4% per annum for 12 months?
(A) $400
(B) $500
(C) $650
(D) $710
(E) $1000
Rationale: P = $10000
R = 4%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*4*1/100 = $400
Answer is A
Answer: (A) $400
Question: In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 30%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 45 are employed males, hence 19% are employed females.
(employed females)/(total employed people)=19/64=30%
Answer: C.
Answer: (C) 30%
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 29 sec
(C) 26 sec
(D) 27 sec
(E) 34 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25
= 40 sec
Answer: A
Answer: (A) 40 sec
Question: If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10)
II. P(P(10))
III. P(P(P(10)))
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: 2 is the only even prime number. Now, the sum of first 10 prime numbers = 9*odd + 2 = odd. Thus P(10) = odd.
Again, the sum of the first n -odd primes = (n-1)*odd+2 = even.Thus, p(P(10)) = even.
Similarly, the sum of the first m - even primes = (m-1)*odd+2 = odd.
I and III.
ANSWER:C
Answer: (C) I and III only
Question: A beekeeper has 900,000 bees living in ten beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
(A) 18000
(B) 109756
(C) 46700
(D) 657587
(E) 4645747
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+9*(0.8)*x = 900,000 => 8.2x = 900,000 => x = 109756.
B is the answer.
Answer: (B) 109756
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -9 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
(A) -9,-9,-9
(B) -9,9,9
(C) 1,1,1
(D) -9,81,9
(E) 9,9,81
Rationale: Mean: If all values are multiplied by -9 then their sum will also be multiplied by -9 so Mean will also get -9
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -9 then the difference between the mean and the individual values also gets multiplied by -9 and the square of that difference becomes 81. So, the variance gets multiplied by a factor of 81
SD:
Standard Deviation is the square root of variance so sqrt(81)=9. So SD gets multiplied by a factor of 9.
So, answer will be D.
Answer: (D) -9,81,9
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) A)0.8321
(B) B)0.7
(C) C)0.895
(D) D)0.7531
(E) E)0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.35*20 = 7.
So, out of 100 matches 60 + 7 = 67 are won.
It is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67 = 0.895...
Answer: C.
Answer: (C) C)0.895
Question: Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is
(A) Rs 200
(B) Rs 300
(C) Rs 400
(D) Rs 500
(E) Rs 600
Rationale: Explanation:
Let C = x.
Then B = x/2
and A = x/4
A:B:C = 1:2:4.
C's share Rs.[(4/7)*700) = 400
Option C
Answer: (C) Rs 400
Question: A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average of 4375 items per month over the whole?
(A) 4500
(B) 4600
(C) 4680
(D) 4710
(E) None
Rationale: Sol.
Required average = (4375 x 12) - (4000 x 3 ) / 9
⇔ 52500 - 12000 / 9
⇔ 40500 / 9
= 4500.
Answer A
Answer: (A) 4500
Question: A number is increased by 30 % and then decreased by 30 %. Find the net increase or decrease per cent.
(A) 9%
(B) 8%
(C) 7%
(D) 3%
(E) 6%
Rationale: Let the number be 100.
Increase in the number = 30 % = 30 % of 100
= (30/100 Ã— 100)
= 30
Therefore, increased number = 100 + 30 = 130
This number is decreased by 30 %
Therefore, decrease in number = 30 % of 130
= (30/100 Ã— 130)
= 3900/100
= 39
Therefore, new number = 130 - 39 = 91
Thus, net decreases = 100 -91 = 9
Hence, net percentage decrease = (9/100 Ã— 100) %
= (900/100) %
= 9 %
Answer:A
Answer: (A) 9%
Question: Set M contains numbers that satisfy the condition that, if integer x is in the set then x+1 will also be in the set M. If 0 is one of the value in the set, which of the following numbers must also be present in the set M.
I. 1
II. 3
III. 2
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.
Now, if 0 is in the set, then 0+1=1mustbe in the set. Since 1 is in the set then 1+1=2mustbe in the set, also 3.
Answer: E.
Answer: (E) I, II and III
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 10 minutes
(B) 20 minutes
(C) 15 minutes
(D) 12 minutes
(E) 18 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
ANSWER:A
Answer: (A) 10 minutes
Question: The value of land increases by m% during June and decreases by n% during July. If the value of the land is the same at the end of July as at the beginning of June, what is n in terms of m?
(A) 200m/(100+2m)
(B) 100m/(100+m)
(C) m(2+m)/(1+m)2
(D) m(200+m)/10000
(E) 2m/m+2m
Rationale: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
B
Answer: (B) 100m/(100+m)
Question: If a rectangular room measures 8 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
(A) 24,000
(B) 16,000,000
(C) 2,400,000
(D) 24,000,000
(E) 240,000,000
Rationale: B. 160,000,000
8*100*5*100*4*100 = 160,000,000
Answer: (B) 16,000,000
Question: In 26 minutes, the minute hand gains over the hour hand by
(A) 116°
(B) 125°
(C) 143°
(D) 158°
(E) 172°
Rationale: In one hour, the hour hand moves 30°, which is 0.5° each minute.
In one hour, the minute hand moves 360°, which is 6° each minutes.
The minute hand gains 5.5° each minute.
In 26 minutes, the minute hand gains 26 * 5.5° = 143°.
The answer is C.
Answer: (C) 143°
Question: The total of 342 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is
(A) 238
(B) 290
(C) 278
(D) 200
(E) 288
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (342 - x).
0.20 * (x) + 0.25 (342 - x) = 71 => x = 290..
Answer: B) 290
Answer: (B) 290
Question: Ben earns $12,800 a year. About 15% is taken out for taxes.
How much is taken out for taxes?
(A) $19200
(B) $11920
(C) $1920
(D) $19820
(E) $10920
Rationale: 15/100=x/12.800
Divide by the remaining number:
1920/192000
100
$1920
correct answer C
Answer: (C) $1920
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/8%
(B) 11 1/5%
(C) 11 1/9%
(D) 11 12%
(E) 11 5/9%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Answer: (C) 11 1/9%
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 50%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 50%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer C.
Answer: (C) 40% decrease
Question: By selling an Shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
(A) 9%
(B) 2%
(C) 8%
(D) 5%
(E) 6%
Rationale: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Answer: (C) 8%