mathewhe/aqua_rat huggingface dataset:
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 40,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
(A) 1 million
(B) 1.25 million
(C) 10 million
(D) 12.2 million
(E) 125 million
Rationale: If you type that into the calculator, it results in 12.3 mil
[D], 12.2 mil, is the correct answer... see 2 posts above for quick approx method
Answer: (D) 12.2 million
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs.51.25
(B) Rs.51.27
(C) Rs.51.79
(D) Rs.51.8
(E) Rs.51.93
Rationale: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500)
= Rs.51.25.
Answer: A
Answer: (A) Rs.51.25
Question: If A is to be chosen at random from the set {14, 7, 25, 6} and B is to be chosen at random from the set {2, 5, 8}, what is the probability that AB will be even?
(A) 2/3
(B) 8/3
(C) 5/6
(D) 1/3
(E) 4/3
Rationale: Method-1
AB will be even when
1) A is even and B is odd, Probability of A even is (2/4) and Probability of B odd is (1/3), so Probability of Case(1) = (2/4)*(1/3) = (2/12)
2) A is Odd and B is Even, Probability of A Odd is (2/4) and Probability of B Even is (2/3), so Probability of Case(2) = (2/4)*(2/3) = (4/12)
3) A is even and B is Even, Probability of A even is (2/4) and Probability of B Even is (2/3), so Probability of Case(1) = (2/4)*(2/3) = (4/12)
Total Favorable Probability = (2/12)+(4/12)+(4/12) = (32/12) = 8/3
Answer: option B
Answer: (B) 8/3
Question: A pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king?
(A) 1/113
(B) 2/213
(C) 1/221
(D) 3/341
(E) 3/215
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: (C) 1/221
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If two beavers start to build the same dam at 7:00 AM, and one beaver per hour is added beginning at 4:00 PM, at what time will the dam be complete?
(A) 7:30 PM
(B) 8:00 PM
(C) 9:00 PM
(D) 10:00 PM
(E) 11:00 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 2 beavers in 9 hours is 2/60 *9 = 18/60
In the next hour, 3 beavers do 3/60 for a total of 21/60.
In the next hour, 4 beavers do 4/60 for a total of 25/60.
In the next hour, 5 beavers do 5/60 for a total of 30/60.
In the next hour, 6 beavers do 6/60 for a total of 36/60.
In the next hour, 7 beavers do 7/60 for a total of 43/60.
In the next hour, 8 beavers do 8/60 for a total of 51/60.
In the next hour, 9 beavers do 9/60 for a total of 60/60.
The dam will be completed at 11:00 pm.
The answer is E.
Answer: (E) 11:00 PM
Question: A man sells an article at 15% loss. Had he sold it for Rs. 210/- more he could have gained 20%. What is the cost price of the article?
(A) Rs.420/-
(B) Rs.400/-
(C) Rs.600/-
(D) Rs.680/-
(E) None of these
Rationale: Explanation:
Short cut method:
Loss =====> 15 %
Profit ====> 20 %
~
----------------
35 % ---------> Rs. 210/-
100 % --------> Rs. 600/-
Answer: Option C
Answer: (C) Rs.600/-
Question: The banker's discount on $1600 at 15% per annum is the same as true discount on $1680 for the same time and at the same rate. The time is:
(A) 2 months
(B) 1 months
(C) 4 months
(D) 8 months
(E) 9 months
Rationale: S.I. on $1600 = T.D. on $1680.
THEREFORE $1600 is the P.W. of $1680, i.e., $80 is on $1600 at 15%.
Time =(100 x 80/ 1600 x 15) year	=	1/3	year = 4 months.
ANSWER:C
Answer: (C) 4 months
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 20.9
(B) 28.9
(C) 28.6
(D) 11.5
(E) 12.8
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer: D
Answer: (D) 11.5
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5?
(A) 32
(B) 20
(C) 28
(D) 11
(E) 18
Rationale: Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5
= 20.
Answer: B
Answer: (B) 20
Question: A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?
(A) 180
(B) 225
(C) 285
(D) 300
(E) 330
Rationale: Let the number of 15$ bonds given be x, then the number of 30$ bills given = kx, where k is an integer.
Thus, x+kx = 8 --> x(1+k) = 8. Thus, we could have
x = 1, k=7 --> The value left with him = 510 - (15+210) = 285
x = 8,k =0 --> The value left with him = 510 - (120) = 390
x =4, k =1 --> The value left with him = 510 - (60+120) = 330
x=2,k=3 --> The value left with him = 510 - (30+180) = 300
Thus, the answer is E.
Answer: (E) 330
Question: 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is
(A) 16
(B) 15
(C) 14
(D) 13
(E) 12
Rationale: Percentage of alcohol in new solution
=( 6*.2 + 4 * .1) / 10
=(1.2 + .4 ) / 10
= 1.6/10
=.16
Percentage of alcohol in new solution = 16 %
Answer :A
Answer: (A) 16
Question: If x is divisible by 10, 14, and 70, which of the following must be the least multiple of x?
(A) 70
(B) 140
(C) 210
(D) 350
(E) 700
Rationale: We are looking for the LCM (which is not 0) of 10 = 2*5, 70 = 2*7*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is A.
Answer: (A) 70
Question: Five children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?
(A) 1/30
(B) 1/15
(C) 1/5
(D) 2/5
(E) 7/20
Rationale: Total no of empty space is 5 so total no of ways A B C D and E can sit is 5 !
Solution 1:
Now condition is C&E will sit together
If they sit at 1st and 2nd place . # of ways will be 1*3! but C&E can be either at 1 or at 2 so # of ways will be 1*3!*2!
Similarly they can sit together at position 2 and 3 or 3 and 4 or 4 and 5
So total # ways will be 1*3!*2! + 1*3!*2! + 1*3!*2! + 1*3!*2! = 4 *1*3! *2 !
So probability is (4! * 2! ) / 5! = 2/5
Solution 2:
Consider C*E as 1 person . So we have 4 ppl and 4 places . # of ways they can sit is 4!
C&E can sit as C&E or E&C so total # of ways is 4! * 2!
So probability will be 2/5
Answer:D
Answer: (D) 2/5
Question: A 4 digit number is formed by repeating a 2 digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by
(A) 7
(B) 11
(C) 13
(D) Smallest 3 digit prime number
(E) None
Rationale: Sol.
Smallest 3 digit prime number is 101.
Clearly, 2525 = 25 x 101;
3232 = 32 x 101, etc.
∴ Each such number is divisible by 101.
Answer D
Answer: (D) Smallest 3 digit prime number
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
(A) 2:9
(B) 2:1
(C) 2:7
(D) 2:5
(E) 2:2
Rationale: 12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
Answer:B
Answer: (B) 2:1
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
(A) 5 km/hr
(B) 7 km/hr
(C) 1 km/hr
(D) 9 km/hr
(E) 4 km/hr
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Answer: (A) 5 km/hr
Question: A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is
(A) 23 years
(B) 34 years
(C) 45 years
(D) 54 years
(E) None of these
Rationale: Explanation:
Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
(9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.
Answer: C
Answer: (C) 45 years
Question: 144, 121, 100, 81, 64, ?
(A) 9
(B) 16
(C) 25
(D) 36
(E) 49
Rationale: Explanation :
The pattern is 12^2, 11^2, 10^2, 9^2, 8^2, ...
So next number is 7^2 = 49
Answer : Option E
Answer: (E) 49
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 8
(B) 2
(C) 4
(D) 6
(E) 1
Rationale: 1250 = D(100/4)2
D = 2
Answer: B
Answer: (B) 2
Question: When a boat moves at an average speed of 25 kmph it reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes early. Find the length of journey rounded to two decimal places.
(A) 18.67 km
(B) 24.50 km
(C) 21.88 km
(D) 17.98 km
(E) None
Rationale: Sol.
Difference between timings = 15 min = 1/4 hr.
Let the length of journey be x km.
Then, x/25 - x/35 = 1/4
â‡” 7x - 5x = 43.75
â‡” 2x = 43.75
â‡” x = 21.88 km.
Answer C
Answer: (C) 21.88 km
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 20 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) a) x minutes
(B) b) x/2 minutes
(C) c) 2x/3 minutes
(D) d) 3x/2 minutes
(E) e) 2x minutes
Rationale: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = x/2. hence answer should be
B
Answer: (B) b) x/2 minutes
Question: A library has an average of 510 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) 285
(B) 290
(C) 297
(D) 305
(E) None of these
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285. Answer: A
Answer: (A) 285
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?
(A) A)Rs.180
(B) B)Rs.200
(C) C)Rs.250
(D) D)Rs.280
(E) E)Rs.300
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
Option 'C'
Answer: (C) C)Rs.250
Question: The price of petrol increased by 25% and so a person reduced his consumption by 25%. What percentage is the rise or fall in the expenditure incurred by him on petrol ?
(A) 6.25%
(B) 6.50%
(C) 6.76%
(D) 6.80%
(E) 6.0%
Rationale: Assume he consumes 100 liters of petrol,and petrol costs him Rs.100/-
His total expenditure = Rs.10000/-
Now price got increased by 25%. If a value got increased by 25% then the new value is 125% of the previous value. so 125%(100) = Rs.125
But he reduced his consumption by 25%, so his new consumption is 75%(100) = 75
His total expenditure = 125 x 75 = Rs.9375
Percentage change in the expenditures = 10000−9375/10000×100=6.25%
Answer A
Answer: (A) 6.25%
Question: 9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 8 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
(A)  6
(B)  7
(C)  8
(D)  12
(E)  9
Rationale: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.
Side 1 = 8 m/h --> 4 m in 1/2 hr
Side 2 = 16 m/h --> 8 m in 1/2 hr
to complete this right angle triangle
d^2 = 4^2 + 8^2
d^2 = 80
= ~ 9
Answer option E
Answer: (E)  9
Question: 7 years ago, Paula was 3 times as old as Karl. In 2 years, Paula will be twice as old as Karl. What is the sum of their ages now?
(A) 26
(B) 32
(C) 38
(D) 44
(E) 50
Rationale: P-7 = 3(K-7) and so P = 3K-14
P+2 = 2(K+2)
(3K-14)+2 = 2K+4
K = 16
P = 34
P+K = 50
The answer is E.
Answer: (E) 50
Question: A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:
(A) Rs. 1,368
(B) Rs. 1,468
(C) Rs. 1,568
(D) Rs. 1,668
(E) None
Rationale: Solution: Marked Price = 2000.
SP after first Discount of 20% = 2000 - 20% of 2000 = 1600.
SP after second Discount of 10% = 1600 - 10% of 1600 = 1440.
Now, the final selling price at cash = 1440 - 5% of 1440 = Rs. 1368.
Short-Cut by using Graphic Change
2000(MP)==20%(disc.)==>1600==10%(disc.)==>1440==5%(disc.)==>1368(SP).
Answer: Option A
Answer: (A) Rs. 1,368
Question: An investor receives a total combined return of 6% on his two different investments. On his $10,000 investment he receives a return of 5%. What is the return on his $20,000 investment?
(A) 7.25%
(B) 6.5%
(C) 8%
(D) 8.5%
(E) 9%
Rationale: 0.05 * 10000 + 20000x = 0.06(30000)
solving for x give x = 6.5%
option B
Answer: (B) 6.5%
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) 1278
(B) 2400
(C) 2771
(D) 1271
(E) 1132
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Simplification mcq solution image
Solving (i) and (ii) we get x = 400, y = 200.
∴ Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Answer: B
Answer: (B) 2400
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 150. What is the manager's monthly salary ?
(A) Rs.6003
(B) Rs.6029
(C) Rs.4650
(D) Rs.6108
(E) Rs.6011
Rationale: Explanation:
Manager's monthly salary Rs. (1650 * 21 - 1500 * 20) = Rs.4650.
Answer: C
Answer: (C) Rs.4650
Question: When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?
(A) 20%
(B) 40%
(C) 50%
(D) 80%
(E) 100%
Rationale: et the Marked up price =100..
Selling price= 100-40%of 100=60..
profit= 20%..
therefore the wholesale purchase cost= x.... 1.2x=60
or x=50...
marked price was 100 so 50 over 50...
so answer is 100%..
ANSWER:E
Answer: (E) 100%
Question: If a company allocates 25 percent of its budget to advertising, 5 percent to capital improvements, and 20 percent to salaries, what fraction of its budget remains for other allocations?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/5
Rationale: 100%-(25%+5%+20%)=50% remains for other allocations --> 50% = 50/100 = 1/2.
Answer: D.
Answer: (D) 1/2
Question: If x^2âˆ’2ax+a^2=0 get value of x/a
(A) 2
(B) 5
(C) 6
(D) 8
(E) 1
Rationale: a is obviously non-zero. We divide the equation by
a^2
we get (x/a-1)^2=0
x/a=1
ANSWER E
Answer: (E) 1
Question: A group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over. What is the sum of the two smallest possible values of n?
(A) 33
(B) 46
(C) 49
(D) 53
(E) 86
Rationale: 4x+2 = 5y+2...........ie: 4x-5y = 0
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x is fraction
if y = 4 thus x =5 n =22
if y = 6 thus x = not possible fraction
if y =8 thus x = 10 n =42
summation 22+42 = 64
C
Answer: (C) 49
Question: What will be the day of the week on 1st January, 2010 ?
(A) Friday
(B) Saturday
(C) Sunday
(D) Monday
(E) None of these
Rationale: 2000 years have 2 odd days.
= 11 odd days = 4 odd days.
1st January, 2010 has 1 odd day. Total number of odd days = (2 + 4 + 1) = 7 = 0.
∴ 1st January, 2010 will be Sunday.
Answer C
Answer: (C) Sunday
Question: If y is an integer, then the least possible value of |39 - 6y| is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We know that 6y is a multiple of 6, so let’s first look at the multiples of 6 closest to 39. We have “36” and “42”. Let’s subtract both of these from 39 and see which one produces the smallest result. When 6y = 36, y is 6 and when 6y = 42, y is 7. Let’s start with letting y = 6.
|39-6(6)|
|39-36|
|3| = 3
Next, let’s let y equal 5.
|39-6(7)|
|39-42|
|-3| = 3
We see that the smallest possible value of |39-6y| is 3.
Answer D.
Answer: (D) 4
Question: A miniature gumball machine contains 5 blue, 3 green, and 2 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
(A) 1/10
(B) 1/8
(C) 1/6
(D) 1/5
(E) 1/4
Rationale: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*3*2=30.
P(dispensing one of each color)=30/120=1/4.
The answer is E.
Answer: (E) 1/4
Question: John bought a total of 12 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 50 cents. If the average price of the 12 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let number of mangoes be x, number of oranges be 12-x
0.80x +(12-x)0.50/12 = 0.65
solving for x, we get x = 6 --> Mangoes 6, Oranges 6
Now, number of oranges to be returned be y
[0.80*6 + (6-y)*0.50]/12-y = 0.72
solving for y, y = 4
Ans: A
Answer: (A) 4
Question: A corporation triples its annual bonus to 50 of its employees. What percent W of the employees’ new bonus is the increase?
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Rationale: W of the employees’ new bonus is the increase Hence B.
Answer: (B) 662⁄3%
Question: Three numbers are in the ratio of 2 : 3 : 4. If the sum of the squares of the extremes is 180, then the middle number is:
(A) 6
(B) 12
(C) 15
(D) 9
(E) 7
Rationale: Number be = 2x,3x,4x, (2x)2 + (4x)2 =180
20x =180⇒x =9⇒x=3,
Midline number=3×3=9
Answer: D
Answer: (D) 9
Question: By selling an article at Rs.150, a profit of 25% is made. Find its cost price?
(A) s.486
(B) s.455
(C) s.487
(D) s.120
(E) s.489
Rationale: SP = 150
CP = (SP)*[100/(100+P)]
= 150* [100/(100+25)]
= 150* [100/125]
= Rs.120
Answer: D
Answer: (D) s.120
Question: Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will have to complete?
(A) ab/(a+b)
(B) (a-b)/(a+b)
(C) b/(b-a)
(D) a/(a+b)
(E) b/(a+b)
Rationale: Randy can do the job in a hrs, Alvin can do the job in b hrs.
When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.
Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)
So Randy does b/(a+b) of the work.
Answer (E).
Answer: (E) b/(a+b)
Question: A piece of work can finish by a certain number of men in 100 days. If however, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
(A) 75
(B) 82
(C) 100
(D) 110
(E) 120
Rationale: Originally let there be x men.
Less men, more days (Indirect)
:. (x-10): x : : 100 :110 or x-10/x = 100/110
or 11x-110 = 10x or x =110
So, originally there were 110 men.
ANSWER:D
Answer: (D) 110
Question: 85% of a number is a dded to 24, the result is the same number. Find the number?
(A) 28
(B) 288
(C) 279
(D) number=160
(E) 232
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) number=160
Question: 2,100 has how many positive divisors?
(A) 24
(B) 30
(C) 36
(D) 40
(E) 48
Rationale: By factorization, we can write 2100 as 2100=2^2*3*5^2*7.
The number of factors is (2+1)(1+1)(2+1)(1+1) = 36
The answer is C.
Answer: (C) 36
Question: How many odd, positive divisors does 740 have?
(A) 6
(B) 8
(C) 12
(D) 15
(E) 24
Rationale: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=15 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: D.
Answer: (D) 15
Question: Josh spends a total of $5.5 buying A items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then A may be which of the following?
(A) 99
(B) 100
(C) 101
(D) 112
(E) 113
Rationale: A items in the convenience store$5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: (C) 101
Question: P and Q together can do a work in 6 days. If P alone can do it in 15 days. In how many days can Q alone do it?
(A) 5
(B) 4
(C) 10
(D) 11
(E) 12
Rationale: 1/6-1/15 ==>1/10
==>10
ANSWER C
Answer: (C) 10
Question: Set M contains number that satisfy the condition that, if integer x is in the set then x + 4 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -8 II) 4 III) 8
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Since -4 is in the set, then the set must also include 0, 4, 8, 12, etc...
Depending on whether -4 is the starting element in the set or not, we can have -8...or not.
The answer is D.
Answer: (D) II and III only
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 292 runs?
(A) 6
(B) 6.5
(C) 7.25
(D) 7.5
(E) 8
Rationale: Required run rate = 262 - (3.2 x 10) =	250 = 6.5
40	40
B
Answer: (B) 6.5
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students play only cricket ?
(A) 36
(B) 38
(C) 39
(D) 47
(E) 37
Rationale: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)-N(C∩T)-2(N(B∩T∩C))
=75-30-24-(2*16)
=37
ANSWER:E
Answer: (E) 37
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 2 months
(B) 7 months
(C) 8 months
(D) 10 months
(E) 12 months
Rationale: Explanation:
7 * 8 : 9 * x = 8:9 => x= 7 months
ANSWER:B
Answer: (B) 7 months
Question: If x and y are positive integers and x = 5y + 7, what is the remainder when x is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.
We're told that X and Y are POSITIVE INTEGERS and X = 5Y + 7. We're asked for the REMAINDER when X is divided by 5.
IF....
Y = 1
X = 12
12/5 = 2 remainder 2
Final Answer:
C
Answer: (C) 2