mathewhe/aqua_rat huggingface dataset:
Question: Pipe P can fill a tank in 3 hours, pipe Q in 9 hours and pipe R in 18 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2 hours
(B) 2.4 hours
(C) 3 hours
(D) 3.5 hours
(E) 4.5 hours
Rationale: Explanation:
Part filled by (P + Q + R) in 1 hour = (1/3 + 1/9 + 1/18) = 1/2
All the three pipes together will fill the tank = 2/1 = 2 hours
ANSWER A
Answer: (A) 2 hours
Question: 120 is what percent of 80?
(A) 0.2%
(B) 2%
(C) 5%
(D) 150%
(E) 500%
Rationale: 120= x*80/100
x = 150%
Ans; D
Answer: (D) 150%
Question: Someone on a skateboard is traveling 8 miles per hour. How many feet does she travel in 5 seconds? (1 mile = 5280 feet)
(A) 60 ft
(B) 52 ft
(C) 53 ft
(D) 55 ft
(E) 58.65 ft
Rationale: per second => 8*5280 ft/60*60 =11.73 ft
5 seconds => 11.73 * 5 = 58.65 ft
Answer : E
Answer: (E) 58.65 ft
Question: 1393 x 1393 = ?
(A) A)1951609
(B) B)1951601
(C) C)1940449
(D) D)1951603
(E) E)1951604
Rationale: 1393 x 1393	= (1393)2
= (1400 - 7)2
= (1400)2 + (7)2 - (2 x 1400 x 7)
= 1960000 + 49 - 19600
= 1960049 - 19600
= 1940449.
Answer:C
Answer: (C) C)1940449
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 375,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
(A) a) 500
(B) b) 750
(C) c) 1,000
(D) d) 1,250
(E) e) 1,500
Rationale: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 375,000 = 93,750
So required ratio = 93,750/75 =1,250
Answer D
Answer: (D) d) 1,250
Question: In a certain company, a third of the workers do not have a retirement plan. 40% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 137
(E) 210
Rationale: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (60*1 + 40*2)/3 = 140/3% are men
Total = 120*300/140 = 257
No. of women = 257 - 120 = 137
D
Answer: (D) 137
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 4.4 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
(A) 45
(B) 48
(C) 51
(D) 54
(E) 57
Rationale: (4.4 miles / 8 minutes)*60 minutes/hour = 33 mph
Let x be the original speed.
x - 4(3) = 33
x = 45 mph
The answer is A.
Answer: (A) 45
Question: The initial price of an article is Rs.4000 which increases 40% increse in its price in the first year,a 20% decrease in the second year and a 20% increase in the next year. What is the final price of the article ?
(A) Rs.2928
(B) Rs.5928
(C) Rs.3928
(D) Rs.R4928
(E) Rs.6928
Rationale: The initial price of the article is Rs.4000. In the 1st year, price of the article = 4000 + 1600 = Rs. 5600. In the 2nd year, price = 5600 - 20% of 5600 = 5600 - 1120 = Rs. 4480.
In the 3rd year, price = 4480 + 10% of 4480 = 4480 + 448 = Rs. 4928
Required price = = Rs.4928.
Answer:D
Answer: (D) Rs.R4928
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 3:7
(B) 1:5
(C) 2:6
(D) 3:4
(E) 3:2
Rationale: Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer:E) 3:2
Answer: (E) 3:2
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which part is not equal to the other four ? The number of that part is the answer.
(A) (x + 2y)(3x + 2y)
(B) (x + 2y)2 + 2x(x + 2y)
(C) (3x + 2y)2 – 2x(3x + 2y)
(D) 3x(x + 2y) + 2y(x + 2y)
(E) x(3x + 2y) – 2y(3x – 2y)
Rationale: Others are equal to 3x2 + 8xy + 4y2
Answer E
Answer: (E) x(3x + 2y) – 2y(3x – 2y)
Question: If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x?
(A) x - 8
(B) x - 5
(C) x - 2
(D) x + 2
(E) x + 6
Rationale: Answer: A
4^(x-4) = 4^(y+4)
Since the base is the same, I isolated the equations and solved for y.
x-4 = y+4
y=x-8
Answer: (A) x - 8
Question: A girl has 12 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
(A) A)100
(B) B)102
(C) C)108
(D) D)144
(E) E)112
Rationale: The girl can select one jeans in 12 ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 12 * 12 = 144 ways.
D
Answer: (D) D)144
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 4 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
(A) 20cm
(B) 25cm
(C) 26cm
(D) 100/3cm
(E) 23cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 4) - 2x * x = 75 => 3x - 25 = 75 => x = 100/3.
Length of the rectangle = 100/3 cm.
Answer: Option D
Answer: (D) 100/3cm
Question: The number 243 has been divided into three parts in such a way that one third of the first part, fourth of the second part and half of the third part are equal. Determine the largest part.
(A) 108
(B) 86
(C) 74
(D) 92
(E) 96
Rationale: Explanation:
It is given that 243 has been divided into 3 numbers x y and z for instance.
Second condition mentioned in the question is:
=> x/3 = y/4 =z/2
Clearly the biggest number is y. So let us solve w.r.t. y.
=> x = 3y/4
=> x =3z/2
=> z = y/2
=> x+y+z = 243
=> y/2 + 3y/4 + y = 243
9y/4 = 243
=> 243*4/9
=> 108
ANSWER A
Answer: (A) 108
Question: If a and b are positive integers and x = 9^a and y = 3^b, which of the following is a possible units digit of xy?
(A) 2
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: The units digit of 9^a is either 1 or 9.
The units digit of 3^b is 3, 9, 7, or 1.
We can multiply the units digits together to see that the units digits of xy could be 1, 3, 7, or 9.
The answer is D.
Answer: (D) 7
Question: Working together, printer A and printer B would finish the task in 30 minutes. Printer A alone would finish the task in 50 minutes. How many pages does the task contain if printer B prints 3 pages a minute more than printer A ?
(A) 200
(B) 400
(C) 600
(D) 800
(E) 900
Rationale: 30*A + 30*B = x pages
in 30 mins printer A will print = 30/50 * x pages = 3/5*x pages
thus in 30 mins printer printer B will print x - 3/5*x = 2/5*x pages
Also it is given that printer B prints 3 more pages per min that printer A. In 30 mins printer B will print 90 more pages than printer A
thus 3/5*x - 2/5*x = 90 => x = 400 pages
Answer: B
Answer: (B) 400
Question: What is the value of: -9^7 + 9^9 ?
(A)  9^2
(B)  -18^16
(C)  63(9^7)
(D)  -80(9^7)
(E)  80(9^7)
Rationale: -9^7 + 9^9 = 9^7 (-1 + 9^2) = 9^7 (-1 + 81) = 80 (9^7), Answer E.
Answer: (E)  80(9^7)
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19.9
(B) 19.3
(C) 19.1
(D) 19.5
(E) 19.4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer: Option D
Answer: (D) 19.5
Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank?
(A) 8
(B) 14
(C) 43
(D) 44
(E) 9
Rationale: Answer: Option B
This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.
Answer: (B) 14
Question: {1/(4+√15)}^2 =
(A) a. 16+16√15
(B) b. 31- 8√15
(C) c. 31+ 8√15
(D) d. 32- 4√15
(E) e. 32 + 4√15
Rationale: 1 / (16 - 8 root15 + 15)
= 1 / (31 + 8 root15)
Multiply numeratordenominator by (31 - 8 root15)
= (31 + 8 root15) / (961-960) = (31 - 8 root15)
Answer = B
Answer: (B) b. 31- 8√15
Question: Today John is twice as old as Sam and Sam is 4 years younger than Mike. If John, Sam, and Mike are all alive 5 years from today, which of the following must be true on that day. I. John is twice as old as Sam II. Sam is 4 years younger than Mike III. John is older than Mike
(A) I
(B) I, II
(C) II
(D) III
(E) I,II & III
Rationale: Say Mike age is 10
Sam age is 6
John age is 12
After 5 years
Mike age is 15
Sam age is 11
John age is 22
i.e ) after 5 years
Sam is 4 years younger than Mike
John is twice as old as Sam
John is older than Mike
Answer : E
Answer: (E) I,II & III
Question: Which of these must the factor G of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
(A) 1,2 only
(B) G=2,3 only
(C) G=1,2,3 only
(D) G=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) G=1,2,3,4 only
Question: If the simple interest on Rs. 2000 is less than the Simple Interest on Rs. 3000 at 5% by Rs. 50, find the time.
(A) 2.5 year
(B) 1 year
(C) 1.5 year
(D) 2 year
(E) 0.5 year
Rationale: Explanation :
Difference in principal = 3000-2000 = 1000
i.e., Simple Interest on Rs.1000 will be Rs.50
1000×5×T/100=50
50T=50
T=1 year
Answer : Option B
Answer: (B) 1 year
Question: What least number must be added to 3000 to obtain a number exactly divisible by 19 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Sol. On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2.
Option B
Answer: (B) 2
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 2x km.
(A) 16
(B) 18
(C) 24
(D) 19
(E) 12
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 2x/(x/8) = 16 kmph
Answer: A
Answer: (A) 16
Question: If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value?
(A) 3a – 1
(B) x^2 + 1
(C) 3 – x
(D) x – 3
(E) x^2 – x
Rationale: Ans is A .. leads to the max value of 7 for a = -2
Answer: (A) 3a – 1
Question: A woman bought a pack of 36 eggs, but the seller told her that there were 3 rotten eggs in the pack. She forgot it and begun to prepare a recipe that needs 2 eggs. What is the probability that both choosen eggs will be rotten?
(A)  1/210
(B)  2/210
(C)  3/210
(D)  1/119
(E)  2/119
Rationale: There are 3 rotten eggs in a pack of 36. Thus the probability of picking 2 rotten eggs is: (3/36)(2/35) = 1/210. The correct answer is A.
Answer: (A)  1/210
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 30m/h. what is the speed of the person while he was going to his office?
(A) 8km/h
(B) 9km/h
(C) 10km/h
(D) 11km/h
(E) 20km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=30
\inline \Rightarrow 1.5k = 30
\inline \Rightarrow k=20km/h
E
Answer: (E) 20km/h
Question: Three numbers are in the ratio 3 : 4 : 5 and their average is 36. The largest number is :
(A) 30
(B) 98
(C) 27
(D) 21
(E) 45
Rationale: Explanation:
Let the numbers be 3x, 4x and 5x, Then, (3x + 4x + 5x ) / 3 = 36
=> 12x = 36*3
=> x = 9
Largest number 5x = 5*9 = 45
Answer:E
Answer: (E) 45
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
(A) 1/2
(B) 3/4
(C) 3/8
(D) 5/16
(E) 7/16
Rationale: n(S)=36
n(E)=27
P(E)=n(S)/n(E)
=27/36
=3/4
Option B
Answer: (B) 3/4
Question: A bag contains 3red, 2blue and 4green balls. If 2 balls are picked at random, what is the probability that both are red?
(A) 1/12
(B) 1/13
(C) 1/14
(D) 1/15
(E) 1/18
Rationale: P(Both are red),
=3C2/9C2=1/12
A
Answer: (A) 1/12
Question: A father is now three times as old as his son. Four years back, he was four times as old as his son. The age of the son (in years) is
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-4 = 4*(S-4)
3S-4 =4S-16
S=12
F=36 years
ANSWER:A
Answer: (A) 12
Question: The average age of a husband and a wife is 23 years when they were married THREE years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
(A) 6
(B) 5
(C) 8
(D) 4
(E) 2
Rationale: 26 * 2 = 52
20 * 3 = 60
-----------
8 years.Answer: C
Answer: (C) 8
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 5 and 6hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 8hrs 25min. (AM)
(B) 8hrs 54min. (AM)
(C) 7hrs 45min. (AM)
(D) 7hrs 15 min. (AM)
(E) 7hrs 30min. (AM)
Rationale: 1 to 2 = 1/5
2 to 3 = 1/5 + 1/6 = 11/30
After 3 AM = 1/5 + 1/6 - 1/2= -4/30
1/5 + 11/30 = 17/30
1 h ---- 4/30
? ----- 17/30
7hrs 15 min. (AM)
Answer:D
Answer: (D) 7hrs 15 min. (AM)
Question: If 3^x*4^y = 531,441 and x – y = 12, then x = ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since 531,441 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 12 and y = 0, then x = 12.
The answer is C.
Answer: (C) 12
Question: How many different sets of positive square integers S, each greater than 1, add up to 75?
(A)  1
(B)  4
(C)  7
(D)  11
(E)  13
Rationale: E= 13 is the correct answer.
Answer: (E)  13
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 28%
(B) 40%
(C) 68%
(D) 70%
(E) 72%
Rationale: Let initial price be 1000
Price in day 1 after 10% discount = 900
Price in day 2 after 15% discount = 765
Price in day 3 after 20% discount = 612
So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68%
Answer will definitely be (C)
Answer: (C) 68%
Question: How many times hour hand covers full circle in a day?
(A) 3 times
(B) 2 times
(C) 4 times
(D) 5 times
(E) once
Rationale: 2 times
ANSWER:B
Answer: (B) 2 times
Question: To save money, Branded company Cheese will reduce each dimension of its rectangular box container (which is entirely full of cheese) by 50%, and reduce the price it charges its consumers by 50% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cheese?
(A) 1. No change
(B) 2. 50%
(C) 3. 100%
(D) 4. 200%
(E) 5. 300%
Rationale: If the current volume is L * W * H, then the new volume is 12 (L) * 12 (W) * 12 (H), or 18 * LWH. So the new portion is 1/8 the size of the old portion. But the new cost is only ½ the cost, meaning that if the old price-per-unit was 1:1, now it’s 12 : 18, or 4:1. So the consumer is paying 400% of what it used to, or 300% more than it used to. The answer is therefore E.
Answer: (E) 5. 300%
Question: A board of length L feet is cut into two pieces such that the length of piece A is 3 feet less than twice the length of piece B. Which of the following is the length, in feet, of piece A?
(A) (L - 1)/2
(B) (2L + 3)/3
(C) (L + 1)/3
(D) (2L + 2)/3
(E) (2L - 3)/3
Rationale: A+B = L so we know that B = L - A.
A = 2B-3
A = 2(L-A) - 3
3A = 2L - 3
A = (2L-3) / 3
The answer is E.
Answer: (E) (2L - 3)/3
Question: A man’s current age is of the age of his father. After 8 years, he will be of the age of his father. What is the age of father at now ?
(A) 50
(B) 40
(C) 33
(D) 30
(E) 35
Rationale: Explanation:
Let, father’s current age is A years.
Then, Man’s current age = years.
2/5A+8=1/2(A+8)= A= 40. Answer: B
Answer: (B) 40
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 3 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^3
(D) 1 + (0.05)^4
(E) 1 + 4(0.05)
Rationale: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 3 years would be
1(1.05)^3
1.05^3
C. (1.05)^3
Answer: (C) (1.05)^3
Question: Four kids having five rocks each were playing a game in which they need to throw the rock at solid area in the water.
Kid1: Succeeded in throwing three rocks at solid area but one of the rock sunk.
Kid3: His aim was so bad that all rocks got sunk.
Kid4: He was awesome and none of the rocks got sunk.
Kid2 was the winner but was struck by a rock in the head and died.
Who killed Kid2 ?
(A) Kid1
(B) Kid2
(C) Kid3
(D) Kid4
(E) None of above
Rationale: A
Kid1, he was left with one rock.
Answer: (A) Kid1
Question: If a - b = 3 and a(power 2) + b(power 2) = 25, find the value of ab.
(A) 5
(B) 8
(C) 4
(D) 10
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 25 - 9 = 16
ab = 8.
Answer is B.
Answer: (B) 8
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
(A) 2281
(B) 2771
(C) 1500
(D) 2777
(E) 1711
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500
Answer: C
Answer: (C) 1500
Question: The total number of digits used in numbering the pages of a book having 366 pages is
(A) 732
(B) 990
(C) 1098
(D) 1305
(E) 1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
ANSWER:B
Answer: (B) 990
Question: 6 noun, 3 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
(A) 294
(B) 310
(C) 324
(D) 360
(E) 440
Rationale: we have to choose one from each set. 1 from 6 nouns and 1 from 3 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
6c1*3c1*3c1*3!=324
ANSWER:C
Answer: (C) 324
Question: A box contains 2 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
(A) 1/2
(B) 4/3
(C) 7/12
(D) 2/3
(E) 7/10
Rationale: Total selection ways: 4C2=4!/2!2!=6
Selecting one blue chip out of two: 2C1=2!/1!1!=2
Selecting one red chip out of four: 2C1=2!/1!1!=4
Thus, (2C1*2C1)/4C2=(2*4)/6=8/6=4/3=B
Answer: (B) 4/3
Question: What is the probability of getting only 1 head in a single throw of four fair coins?
(A) 1/2
(B) 3/8
(C) 1/4
(D) 1/5
(E) 5/8
Rationale: One possible case is HTTT.
P(HTTT) = 1/2*1/2*1/2*1/2 = 1/16
There are 4C1 = 4 possible cases.
P(1 head) = 4*1/16 = 1/4
The answer is C.
Answer: (C) 1/4
Question: Can you find the missing number in the series below?
1 5 9 2 6 10 3 ? 11 4 8 12
(A) 5
(B) 6
(C) 3
(D) 8
(E) 7
Rationale: Series given in the problem :
1 5 9 2 6 10 3 ? 11 4 8 12
Let us break the series as :
1 5 9
2 6 10
3 ? 11
4 8 12
Now, read the numbers from left, top to bottom. The missing number is obviously 7.
correct answer is E)7
Answer: (E) 7
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 250
(B) 280
(C) 240
(D) 270
(E) 230
Rationale: Explanation:
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer D
Answer: (D) 270
Question: in a class of 25 students, 15 play hockey and 16 play basketball. if there are 4 students who play neither sport, determine the number of students who play both hockey and basketball?
(A) 10
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: Let the number of who play both be x
Number of students who play sports 25-4=21
Use Venn diagram
(15-x)+x+(16-x)=21
Which gives x=10
Answer is A
10 play both sport
Answer: (A) 10
Question: A clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
(A) 01:54:40 PM
(B) 01:56:24 PM
(C) 12:46:40 PM
(D) 11:54:24 AM
(E) 01:20:48 PM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×48×60 minutes
1% gain = ( 6×24×60)/100 = 172.8 minutes
so, total gain = 172.8 - 32 = 140.8 min = 140 + 0.8 min = 2 Hours 20 minutes + 0.4 × 60 seconds = 2 Hours 20 min + 48 seconds
10 days later the clock should be 2 Hours 20 min + 48 seconds
so time , 01:20:48 pm (Answer E)
Answer: (E) 01:20:48 PM
Question: Which of the following is equal to the average (arithmetic mean) of (x+5)^2 and (x-5)^2?
(A) x^2
(B) x^2+2
(C) x^2 +30
(D) x^2+20
(E) x^2+25
Rationale: Avg = [(x+5)^2 + (x-5)^2] / 2
Expanding and simplifying, (x^2 + 10x + 25 + x^2 - 10x + 25) / 2 = x^2 + 25
Answer E.
Answer: (E) x^2+25
Question: How many multiples of 9 are there between 1 and 50, exclusive?
(A) 5
(B) 4
(C) 6
(D) 7
(E) 3
Rationale: 5
multiples of 9 between 1 and 50 exclusive.
from 9 * 1 upto 9*5, (1,2,3,4,5). Hence, 5 multiples !
correct option is A
Answer: (A) 5
Question: A certain number of workers can do a work in 85 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
(A) 75
(B) 30
(C) 28
(D) 24
(E) 32
Rationale: number of workers = 10* (85-10)/10 = 75
Answer is A
Answer: (A) 75
Question: If two of the four expressions x + y , x + 4y , x - y , and 4x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/6
(B) 1/8
(C) 1/7
(D) 1/5
(E) 1/4
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 4x and 4y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : A
Answer: (A) 1/6
Question: In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
(A) 19
(B) 85
(C) 120
(D) 624
(E) 1024
Rationale: A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.
Answer: D.
Answer: (D) 624