mathewhe/aqua_rat huggingface dataset:
Question: Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?
(A) 1 litre paint
(B) 1 litre water
(C) ½ litre water and one litre paint
(D) ½ litre paint and one litre water
(E) ½ litre paint
Rationale: Reqd. ratio = 2 : 1.5 i.e. 4 : 3 between paint and water respectively.
6 litres of paint which is half water(3 litres) and half paint (3 litres)
Right now the ratio is 1:1
Looking at the options,
A. Paint : Water = 4 : 3 which is the reqd. ratio . Correct Answer
B. Paint : Water = 3 : 4
C. Paint : Water = 4 : 3.5
D. Paint : Water = 3.5 : 4
E. Paint : Water = 3.5 : 3
Answer : A
Answer: (A) 1 litre paint
Question: Today Joelle opened an interest-bearing savings account and deposited $6,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
(A) $6,048.00
(B) $6,240.00
(C) $6,450.00
(D) $6,480.00
(E) $6,489.60
Rationale: To calculate the interest earned on the account over two years, we use the following formula:
Interest = Deposit × Interest Rate × Number of Years
Interest = $6,000 × 0.04 = $240.
So, the amount of money in the account after 2 years is:
Total Amount = Initial Deposit + Interest Earned
Total Amount = $6,240(1.04) = 6,489.60.
The correct answer is choice (E).
Answer: (E) $6,489.60
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in?
(A) 08 hours
(B) 12 hours
(C) 03 hours
(D) 04 hours
(E) 21 hours
Rationale: The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer:B
Answer: (B) 12 hours
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
(A) 5:8
(B) 5:6
(C) 5:1
(D) 5:3
(E) 5:2
Rationale: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 1
5:8
Answer:A
Answer: (A) 5:8
Question: If N = 23×34 , M = 22×3×5, then find the number of factors of N that are common with the factors of M.
(A) 3
(B) 9
(C) 8
(D) 6
(E) 2
Rationale: Answer: c
Explanation:
N = 23×34
M = 22×3×5
By taking common powers we get 22×3
So common factors = (2 + 1)(1 + 1) = 6.
(formula for number of factors of a number)
Answer:D
Answer: (D) 6
Question: The average age of 36 students in a group is 13 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 45 years
(C) 51 years
(D) 54 years
(E) 50 years
Rationale: Explanation:
Age of the teacher = (37 * 14 - 36 * 13) years = 50 years. Answer: E
Answer: (E) 50 years
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 31
(C) 16
(D) 18
(E) 10
Rationale: (A + B) - (B + C) = 12
A - C = 12
Answer: A
Answer: (A) 12
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 46 kg, then the weight of B is:
(A) 31 kg
(B) 32 kg
(C) 37 kg
(D) 34 kg
(E) None of these
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (46 x 2) = 92 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 172 …. (iv)
Subtracting (i) from (iv), we get : B = 37.
B’s weight = 37 kg.
Answer: C
Answer: (C) 37 kg
Question: Let a be a positive integer. If r is divisible by 2^a and r is also divisible by 3^(2a), then it is possible that r is NOT divisible by
(A) 6
(B) 3 × 2^a
(C) 2 × 3^(2a)
(D) 6^a
(E) 6^(2a)
Rationale: Since, r is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1
Only for E, 6^(2a) doesn't satisfy, if a = 1 and r=18, it is not divisible by 6^2 (i.e 36)
Hence answer is E
Answer: (E) 6^(2a)
Question: The speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 110 meters?
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: The speed of the boat downstream = 6 + 3 = 9 km/hr
9 km/hr * 5/18 = 2.5 m/s
The time taken to cover 110 meters = 110/2.5 = 44 seconds.
The answer is B.
Answer: (B) 44
Question: A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a green ball is selected?
(A) y/x+5
(B) y/x+4
(C) (y+5)/(x+y+9)
(D) (y+4)/(x+y+9)
(E) (x+4)/(x+y+9)
Rationale: x red balls
y green balls
x+4+y+5 is the total
=x+y+9
y+4 is the number of green balls
so (y + 4)/(x + y + 9)
the answer is D
Answer: (D) (y+4)/(x+y+9)
Question: 10^9 - 10^2 is approximation of which of the following?
(A) 9^7
(B) 9^8
(C) 9^9
(D) 9^11
(E) 10^9
Rationale: => Since 9^2 is a small number compared to 10^9, it can be disregarded. Thus, 10^9-10^2=10^9 is derived and the answer is E.
Answer: (E) 10^9
Question: If x, y, and f are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=f and if x is less than y, which of the following could be the value of f?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: Answer choice C: f= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: f=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Answer: (D) 18
Question: Find the average of first 8 multiples of 5?
(A) 10
(B) 15
(C) 12.5
(D) 22.5
(E) 21
Rationale: average = (5+10+15+20+25+30+35+40)/8 = 22.5
Answer is D
Answer: (D) 22.5
Question: MANO,INC recently conducted a survey and found that 100,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of MANO,INC customers live in urban areas ?
(A) 200,000
(B) 216,000
(C) 360,000
(D) 300,000
(E) 540.0
Rationale: Let's say that we have a starting value of X...
100% of X = X
100% MORE than X = X + X = 2X
200% MORE than X = X + 2X = 3X
300% MORE than X = X + 3X = 4X
Etc.
Here, we're told that 100,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...
3(100,000) = 300,000
Final Answer:D
Answer: (D) 300,000
Question: Which of the following inequalities is equivalent to −5 < x < 1?
(A) |x - 1| < 7
(B) |x + 2| < 3
(C) |x + 3| < 5
(D) |x - 2| < 6
(E) None of the above
Rationale: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -5 < x < 1, let's say by adding y to this inequality we will get into the above format
-5+y < x+y < 1+y
Now, to move this into the mod format, we need to have (-5+y) + (1+y) = 0 => y = 2
Thus, -3< x+2 < 3 => |x+2| < 3.
Hence, answer is B
Answer: (B) |x + 2| < 3
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through H and the letters E and A must be among the letters selected?
(A) 30
(B) 33
(C) 36
(D) 39
(E) 42
Rationale: Besides A and E, there are 6 letters and we can choose one of them.
6C1 = 6
Three letters can be arranged in 3! ways.
The number of arrangements is 6*3! = 36
The answer is C.
Answer: (C) 36
Question: Sachin is younger than Rahul by 4 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 24.58
(B) 24.5
(C) 24.3
(D) 24.9
(E) 14
Rationale: If Rahul age is x, then Sachin age is x-4,
so (x-4)/x = 7/9
=> 9x-36 = 7x
=> 2x = 36
=> x = 18
So Sachin age is 18 - 4 = 14
Answer: E
Answer: (E) 14
Question: In a barrel of juice there is 50 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 6:5.
(C) 3:1.
(D) 4:3.
(E) 3:4
Rationale: Price of 50 L juice= 3x
1L= 3x/50
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/50/4x/80= 6:5
B is the answer
Answer: (B) 6:5.
Question: On a certain day, Peter's farm harvested 1253 oranges. If Peter distributes his oranges evenly across 9 different retail shops, how many oranges would remain with him.
(A) 1 orange
(B) 3 oranges
(C) 5 oranges
(D) 7 oranges
(E) 9 oranges
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 1253.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 1253 = 11 and 9 is divisible by 9.
Hence, we need to add 7 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) 7 oranges
Question: If the radius of a circle is decreased 50%, what happens to the area?
(A) 10% decrease
(B) 20% decrease
(C) 75% decrease
(D) 40% decrease
(E) 50% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 0.5 * old radius
so new area = (0.5)^2 old area => 0.25 of old area => 25% old area
Ans : C
Answer: (C) 75% decrease
Question: In 10 years, P will be as old as Q is now. Ten years ago, Q was twice as old as P was then. How old is P now?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Q = P+10
Q-10 = 2(P-10)
P = 2P-20
P = 20
The answer is B.
Answer: (B) 20
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 80/7 sec
(B) 20/8 sec
(C) 20/7 sec
(D) 20/3 sec
(E) 20/3 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18
= 7*5 = 35 mps.
The time required = d/s
= 100/35
= 20/7 sec.
Answer: C
Answer: (C) 20/7 sec
Question: What is the remainder when 25472 is divided by 2?
(A) 3
(B) 1
(C) 8
(D) 7
(E) 0
Rationale: If the digit in unit place is even, the number will be divisible by 2.
2 is an even number,so the number is divisible by 2
ANSWER:0
Answer: (E) 0
Question: Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
(A) 12 am
(B) 1 pm
(C) 2 pm
(D) 3 pm
(E) 4 pm
Rationale: Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
B
Answer: (B) 1 pm
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 63
(B) 72
(C) 14
(D) 62
(E) 72
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
ANSWER A 63
Answer: (A) 63
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 1323
(B) 9261
(C) 2788
(D) 2999
(E) 1722
Rationale: A = 8000(21/20)3 = 9261
Answer:B
Answer: (B) 9261
Question: If the function f(x) is defined for all real numbers x as the maximum value of 2x + 6 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?
(A) –4
(B) –5
(C) –6
(D) –7
(E) –9
Rationale: Since f(x) defines maximum of 2x + 6 and 12 + 3x,
to find those x when 2x+6 has greater value,
2x + 6 > 12 + 3x
or x < -6
Only value that satisfy this is -7.
Answer is (D),
Answer: (D) –7
Question: The sum of two numbers is 18 and their difference is 12. Find their product.
(A) 104
(B) 108
(C) 45
(D) 325
(E) None
Rationale: Sol.
Let the numbers be x and y.
Then, x + y = 18 and
x - y = 12
2x = 30 +> x = 15. So y = 3
xy = 15*3 = 45
Answer : C
Answer: (C) 45
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 75kmph. When will Raghu overtake Anup?
(A) 8:30am
(B) 9:40am
(C) 10:00am
(D) 12:00pm
(E) 11:00am
Rationale: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 75(x-1)
15x = 75
x = 5 hrs
Required time = 6+5 = 11:00am
Answer is E
Answer: (E) 11:00am
Question: a,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number aabbcc, which of the following must be a factor of aabbcc?
(A) 9
(B) 3
(C) 7
(D) 11
(E) None of these
Rationale: The sum of the digits in place 1,3 and 5 is a+b+c is equal to the sum of the digits in place 2,4 and 6 which is a+b+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.
Answer: D
Answer: (D) 11
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 35 pints of Perfect Pink paint?
(A) 9
(B) 16
(C) 19
(D) 25 1/3
(E) 28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
35 pints will require 9/17 * 35= 19 pints..
C
Answer: (C) 19
Question: One out of every 600 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 60,000
(B) 5,000
(C) 10,000
(D) 50,000
(E) 52,000
Rationale: 20 broken glasses indicates that 10*10= 100 defected bulbs are present.
100 defected bulbs indicates that 100*600= 60,000 light bulbs are present.
A is the answer
Answer: (A) 60,000
Question: A train 450 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
(A) 30 sec
(B) 32 sec
(C) 36 sec
(D) 38 sec
(E) 60 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(450×2/15) sec=60 sec
ANSWER :E
Answer: (E) 60 sec
Question: If x is an even integer and y = 6x + 4, which of the following CANNOT be a divisor of y?
(A) 17
(B) 20
(C) 29
(D) 41
(E) 53
Rationale: x takes even values as 2,4,6,8.,
y=6x+5
x is an even term so 6x must be an even term when it adds with 4 so it must be a even integer
20 didn't follows this condition ans is B
Answer: (B) 20
Question: John spends $320 buying his favorite dolls. If he buys only small Monkey dolls, which are $4 cheaper than the large Monkey dolls, he could buy 40 more dolls than if he were to buy only large Monkey dolls. How much does a large Monkey doll cost?
(A) $7.2
(B) $7.5
(C) $8
(D) $9
(E) $10
Rationale: A and B is not an integer. So we start with C
If large doll costs $8, then he can buy 320/8 = 40 large dolls and 320/4 =80 small dolls.
Difference is 40, which is we wanted.
Answer C.
Answer: (C) $8
Question: At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 9/10 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
(A) 23/200
(B) 11/100
(C) 7/50
(D) 3/20
(E) 4/25
Rationale: Males who did not arrive on time are 1/8*3/5 = 3/40 of the attendees.
Females who did not arrive on time are 1/10*2/5 = 2/50 of the attendees.
The fraction of all attendees who did not arrive on time is 3/40 + 2/50 = 23/200
The answer is A.
Answer: (A) 23/200
Question: If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
(A) 35
(B) 45
(C) 55
(D) 65
(E) 75
Rationale: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
35 = 5*7, so this is a possible value for the original expression.
The answer is A.
Answer: (A) 35
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by C are?
(A) 11
(B) 18
(C) 45
(D) 17
(E) 12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
15/25 * 75 = 45
Answer:C
Answer: (C) 45
Question: A fruit seller had some oranges. He sells 40% oranges and still has 360 oranges. How many oranges he had originally?
(A) 700
(B) 710
(C) 600
(D) 730
(E) 740
Rationale: 60% of oranges = 360
100% of oranges =(360×100)/6=600
total oranges = 700
ANSWER : C
Answer: (C) 600
Question: The width of a rectangle is 10mtr and its area is 150 square meter. If length of the rectangle is increased, then its new area is 1(1/3) times of the original area. What is the new perimeter of the rectangle?
(A) 45
(B) 54
(C) 67
(D) 60
(E) 69
Rationale: Ans.(D)
Sol. Length of original rectangle = 150/10 = 15
(10*(15+x))/(10*15) = 4/3
x = 5
Perimeter of new rectangle = 2(10+20) = 60
Answer: (D) 60
Question: circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) 44
(B) 55
(C) 66
(D) 78
(E) 49
Rationale: π (152 - 132) = 176
176 * 1/4 = Rs.44.Answer: A
Answer: (A) 44
Question: Jagan went to another town covering 240 km by car moving at 60 kmph. Then he covered 400km by train moving at 100 kmph and then rest 200 km he covered by a bus moving at 50 kmph. The average speed during the whole journey was ?
(A) 80 kmph
(B) 60 kmph
(C) 10 kmph
(D) 70 kmph
(E) 90 kmph
Rationale: Explanation:
By car 240 km at 60 kmph
Time taken = 240/60 = 4 hr.
By train 240 km at 60 kmph
Time taken = 400/100 = 4 hr.
By bus 240 km at 60 kmph
Time taken = 200/50 = 4 hr.
So total time = 4 + 4 + 4 = 12 hr.
and total speed = 240+400+200 = 840 km
Average speed of the whole journey = 840/12 = 70 kmph.
Answer: D
Answer: (D) 70 kmph
Question: If a and b are integers and (a*b)^5 = 144y, y could be:
(A) 40
(B) 48
(C) 56
(D) 62
(E) 54
Rationale: Distribute the exponent.
a^5 * b^5 = 144 y
Find the prime factorization of 144. This is 2^4 *3^2.
We need 2^1 and 3^3 i.e 2*27 =54
The answer is E.
Answer: (E) 54
Question: What is the greatest number of three digits which is divisible by 8, 16, 32 ?
(A) 997
(B) 992
(C) 999
(D) 998
(E) 990
Rationale: Greatest number of 3 digits = 999
LCM of 8, 16, 32 = 32
999 ÷ 32 = 31, remainder = 7
Hence, greatest number of four digits which is divisible by 8,16,32
= 999 - 7 = 992
answer : B
Answer: (B) 992
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.5
(B) 31.3
(C) 31.6
(D) 31.1
(E) 31.9
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer:C
Answer: (C) 31.6
Question: The average of three numbers is 48. The average of two of these numbers is 56%. What is the third number?
(A) 64
(B) 32
(C) 46
(D) 75
(E) 47
Rationale: B
32
The total of three numbers must be 48 x 3 = 144. The total of two numbers must be 56 x 2 = 112.
Therefore, 144 - 112 = 32.
Answer: (B) 32
Question: When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?
(A) 13b/52
(B) b/26
(C) b/17
(D) b/12
(E) b/6
Rationale: According to Bunuel's solution, since "b" is not divisible by 13, "b" will not be divisible by any integer which has 13 as factor so that b/26 (i.e., 2 * 13) cannot result in an integer.
For option A, 13b/52, even though the denominator has 13 as factor, this is cancelled out by the 13 in the numerator, resulting in an integer.
Alternatively, you can also plug in numbers:
b
6
19 (= 6 + 13)
32 (= 19 + 13)
45 (= 32 + 13)
58 (= 45 + 13)
71 (= 58 + 13)
84 (= 71 + 13)
97 (= 84 + 13)
110 (= 97 + 13)
123 (= 110 + 13)
136 (= 123 + 13)
149 (= 136 + 13)
.
.
. etc
You realise that 6 and 84 are divisible by 6; 84 is divisible by 12; 136 is divisible by 17; but none of the numbers for integer "b" are divisible by 13 or an integer with 13 as a factor!
So b/26 will not result in an integer.
ANSWER:B
Answer: (B) b/26
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,711 minutes earlier? (Assume standard time in one location.)
(A) 6:22
(B) 6:24
(C) 6:27
(D) 6:36
(E) 6:32
Rationale: 6:27minus 2,880,711in any way must end with 6, the only answer choice which ends with 6 is D.
Answer: D.
Answer: (D) 6:36
Question: Anthony and Michael sit on the six-member board of directors for company E. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: Soln: Let the commitees be I and II
Assuming that Anthony and Michael E go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.
Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.
So in total = 8 ways
Now total number of ways of choosing 3 from 6 people is
= 6C3
= 6 * 5 * 4/3!
= 20 ways
Therefore Probability is = (8 /20) * 100 = 40%
Answer: (C) 40%
Question: What is the remainder when 23415 is divided by 3?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: If the sum of the digits of a number is divisible by 3, the number will be divisible by 3.
2+3+4+1+5 = 15
The nearest multiple of 3 is 15.
15-15= 0.
ANSWER:A
Answer: (A) 0
Question: 217 + 2.017 + 0.217 + 2.0017 = ?
(A) 229.3657
(B) 229.7563
(C) 229.6357
(D) 229.5637
(E) 221.2357
Rationale: 217
2.017
0.217
+ 2.0017
--------
221.2357
---------
Answer is E.
Answer: (E) 221.2357
Question: If x/(11p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?
(A)  22
(B)  33
(C)  44
(D)  66
(E)  99
Rationale: x/(11p) = even prime number
x = even prime number * 11p
Least value of x = Lowest even prime number * 11 * Lowest value of p
= 2 * 11* 2 = 44
Answer C
Answer: (C)  44
Question: ? x 40 = 173 x 240
(A) 545
(B) 685
(C) 1038
(D) 495
(E) 534
Rationale: Let y x 40 = 173 x 240
Then y = (173 x 240) / 40
= 1038
ANSWER :C
Answer: (C) 1038
Question: Pick a team of 3 people from a group of 10 people.
(A) a) 20
(B) b) 40
(C) c) 80
(D) d) 120
(E) e) 210
Rationale: 10c3 = 120
Answer is D.
Answer: (D) d) 120