mathewhe/aqua_rat huggingface dataset:
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.3
(B) 52.2
(C) 52.1
(D) 52.5
(E) 52.4
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80
= 52.5
Answer:D
Answer: (D) 52.5
Question: What is the greatest prime factor of (10!9!) + (10!11!)?
(A) 23
(B) 29
(C) 31
(D) 37
(E) 41
Rationale: 10!9! + 10!11!
= 10!9! (1+10*11)
= 12!11!(111)
= 12!11!(3*37)
The greatest prime factor is 37.
The answer is D.
Answer: (D) 37
Question: In a box of 10 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 7/12
(B) 11/20
(C) 17/30
(D) 28/45
(E) 51/90
Rationale: # defective pens = 2
# good pens = 8
Probability of the 1st pen being good = 8/10
Probability of the 2nd pen being good = 7/9
Total probability = 8/10 * 7/9 = 28/45
The answer is D.
Answer: (D) 28/45
Question: If the probability of rain on any given day in City X is 20%, what is probability that it rains on exactly 3 days in a 4 day period?
(A) 16/625
(B) 8/125
(C) 6/125
(D) 4/25
(E) 3/25
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 1/5*1/5*1/5*4/5 = 4/625
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*4/625 =16/625
The answer is A.
Answer: (A) 16/625
Question: An article is bought for Rs.1280 and sold for Rs.900, find the loss percent?
(A) 28%
(B) 29%
(C) 16%
(D) 26%
(E) 32%
Rationale: 1280 ---- 380
100 ---- ? => 29%
Answer:B
Answer: (B) 29%
Question: If 41/88 = 0.46590, what is the 77th digit to the right of the decimal point of the fraction?
(A) 6
(B) 2
(C) 5
(D) 0
(E) 9
Rationale: we are not concerned what 41/88 means..
we have to look at the decimal..
0.6590means 0.465909090....
so leaving girst,second and third digit to the right of decimal, all ODD numbered are 0 and all EVEn numbered are 9..
here 77 is odd, so ans is 0
Answer is D
Answer: (D) 0
Question: Milk contains 10% water. What content of pure milk should be added to 20 liters of milk to reduce this to 5%?
(A) 20liters
(B) 25liters
(C) 30liters
(D) 15liters
(E) 18liters
Rationale: Quantity of water in 20 liters = 10% of 20 liters = 2 liters
Let x liters of pure milk be added.
Then, 2/(20+x) = 5/100
5x = 100
x=20 liters
Answer is A
Answer: (A) 20liters
Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by ?
(A) 25 m
(B) 75 m
(C) 85 m
(D) 05 m
(E) 15 m
Rationale: Explanation:
A:B = 200 : 169
A:C = 200 : 182
=
=> 182:169
When C covers 182 m , B Covers 169 m
When C covers 350 m , B Covers
=> 325 m
So C beats B by (350 - 325) = 25 m.
Answer: A
Answer: (A) 25 m
Question: A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 328
(B) 279
(C) 240
(D) 285
(E) 231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 15
x + 300 = 585
x = 285 m. Answer:D
Answer: (D) 285
Question: The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
(A) 126
(B) 156
(C) 190
(D) 300
(E) 260
Rationale: Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D
Answer: (D) 300
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 2t seconds, then what is the length of the platform?
(A) 0.5 L
(B) L
(C) 1.5 L
(D) 2 L
(E) 3
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 2t
(L+P) / (L/t) = 2t
P = L
The answer is B.
Answer: (B) L
Question: It takes 2 team of farm workers 12 days to completely prepare a piece of land for planting. if both team of workers were to work separately, one of them can complete the work 10 days earlier than the other, how many days will it take each of them to separately complete the work?
(A) 12 and 22
(B) 11 and 21
(C) 15 and 25
(D) 9 and 19
(E) 20 and 30
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two team of workers would complete a job in 12 days. This means that (individually) each of team would take MORE than 12 days to do the job.
Answers D, A and B are illogical, since the individual times must both be greater than 12 days.
so we can TEST the values for Answers C and E.
Using the values for Answers B and D...
Answer B: (15)(25)/(15+25) = 375/40 = 9.4 This is a match
Answer E: (20)(30)/(20+30) = 12
Final Answer:
E
Answer: (E) 20 and 30
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $7.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $7.50
(E) $5.60
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 7.80 - 3.20 = 4.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
4.6 = T(5.4x) -> T= (4.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*4.6/5.4 = 7.5
Answer D.
Answer: (D) $7.50
Question: If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) =
(A) 11x^2+4x+4
(B) 11x^2-12x+44
(C) 30x^3-24x+44
(D) 30x^3+4x+4
(E) 30x^3-12x+44
Rationale: g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>C
Answer: (C) 30x^3-24x+44
Question: By selling an article for $195, a person gains $45. What is the gain %?
(A) 25%
(B) 30%
(C) 50%
(D) 20%
(E) 10%
Rationale: S.P. = $195
Gain = $45
C.P. = 195-45 = 150
Gain% = 45/150 * 100% = 30%
Answer is B
Answer: (B) 30%
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/5 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 11/30
(E) 5/6
Rationale: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/5M =12 books
Total = 22 books
M' = 22 = 11/30*60
Ratio: 11/30
Ans:D
Answer: (D) 11/30
Question: A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -
(A) (A−B+C)/2
(B) (A−B−C)/2
(C) (A+B+C)/2
(D) (A+B−C)/2
(E) (2A−B+C)/2
Rationale: Male Goats = A
Female Goats = B
1/2 of Horn Goats = Females = x (say)
Therefore, other half will be Male = x
Now, Male Goats without horn = A -x -- (1)
Also, Total Goats without horn = C = (A -x) + (B-x)
or x = (A+B - C)/2
Substituting the value of x in equation (1)
We will have A - x =(A−B+C)/2.
Answer A.
Answer: (A) (A−B+C)/2
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
(A) 40 kg
(B) 50 kg
(C) 65 kg
(D) 66.5 kg
(E) 80 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: (D) 66.5 kg
Question: Find the value of 3 + 2 • (8 – 3)
(A) 25
(B) 13
(C) 17
(D) 24
(E) 15
Rationale: 3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 * 5
= 3 + 10
= 13
correct answer B
Answer: (B) 13
Question: If T = 5/9 * (K - 32), and if T = 35, then what is the value of K?
(A) 92
(B) 95
(C) 98
(D) 101
(E) 104
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(35)/5 + 32 = 95
The answer is B.
Answer: (B) 95
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 1/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 10% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
(A) $105
(B) b $100
(C) c $125
(D) d $130
(E) e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 1/3*1500 =500 ,Selling amount for 500 cabbage = 500 * 0.5 = $ 250
Remaining were sold at a price equal to 10% less than the price each head sold for on the day before i.e , (90/100)*0.5 = $ 0.45
Hence selling cost for the remaining cabbage = 1000 * 0.45 = $ 450
Total selling cost = 450 + 250 = $ 700
Gross profit = $ 700 - $ 600 = $ 100
Hence Answer is B
Answer: (B) b $100
Question: If 200 lb of a mixture contain 80% husk and 20% sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk?
(A) 1/4
(B) 20/3
(C) 1/2
(D) 40
(E) 60
Rationale: We need to extract 40 lb of husk.
80 % of 200 = 160
20 % of 200 = 40
Now we have t remove husk to have 75 % of Husk ( key point sand is not supposed to be removed)
Let X be the new quantity after removing husk
So, 40 = 25 % of X
X = 160
Husk will 120 lbs , hence we need to remove 1/4 of the total husk or 40 lbs
ANSWER:D
Answer: (D) 40
Question: The rational number for recurring decimal 0.125125.... is:
(A) 119/999
(B) 125/999
(C) 125/1000
(D) 125/999
(E) None of them
Rationale: 0.125125...
= 0.125
= 125/999
Answer is B.
Answer: (B) 125/999
Question: John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
(A) 201
(B) 301
(C) 401
(D) 101
(E) 501
Rationale: The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
Answer: (B) 301
Question: While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 3° east of north, in what direction was it originally flying?
(A) (a) 30° west of north
(B) (b) 30° east of north
(C) (c) 22° west of north
(D) (d) 22° east of north
(E) (e) 5° west of north
Rationale: If after a turn of 25° you are 3°NEast, with a 22° turn you would be perfectly pointing at north. So you were, before the turn, 22° to the other side (West).
Answer C)
Answer: (C) (c) 22° west of north
Question: Triangle ATriangle B are similar triangles with areas 1536 units square and 2166 units square respectively. The ratio of there corresponding height would be
(A) 9:10
(B) 17:19
(C) 23:27
(D) 13:17
(E) 16:19
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1536/2166
(x^2/y^2)=(16*16*6)/(19*19*6)
(x^2/y^2)=17^2/19^2
x/y=16/19
Ans=E
Answer: (E) 16:19
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
(A) 2 / 3
(B) 1 / 3
(C) 3 / 3
(D) 4 / 5
(E) 2 / 4
Rationale: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer B
Answer: (B) 1 / 3
Question: You collect balls. Suppose you start out with 7. John takes half of one more than the number of balls you have. Since his mother makes balls, Peter decides to triple your balls. How many balls do you have at the end?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Solution
Start with 7 balls.
John takes half of one more than the number of balls you have. So John takes half of 7 + 1 which is 4,
so you're left with 7 - 4 = 3.
Peter triples the number of balls you have: 3 × 3 = 9 balls.
So you have 9 at the end.
Correct answer : D
Answer: (D) 9
Question: A circular rim 21 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 48x
(D) 45x
(E) x/75
Rationale: Let's try the explanation. We have two wheels. One with 21pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 21pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 21pi*x=35pi*a.
(21pi*x)/(35pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 45x.
Ans:D
Answer: (D) 45x
Question: A group of men decided to do a work in 20 days, but 10 of them became absent. If the rest of the group did the work in 40 days, Find the original number of men?
(A) 20
(B) 50
(C) 40
(D) 100
(E) 25
Rationale: Original number of men = 10*40 / (40-20) =20
Answer is A
Answer: (A) 20
Question: Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.
(A) 1:9
(B) 2:9
(C) 3:9
(D) 5:9
(E) None of them
Rationale: Let their edges be a and b. Then,
=a^3/b^3 = 1/27 (or) (a/b)^3 = (1/3)3 (or) (a/b) = (1/3).
Therefore, Ratio of their surface area = 6a^2/6b^2 = a^2/b^2 = (a/b)^2 = 1/9, i.e. 1:9.
Answer is A.
Answer: (A) 1:9
Question: In a normal 5-day work week, each of 12 employees produces 300 items per day-last week, 1/3 of the employees were absent from work for 2/5 of the days in the week. how many total items were produced last week?
(A) 18000
(B) 14400
(C) 6000
(D) 15600
(E) 16,200
Rationale: 1 employee produces 300 items per day
1/3 of the employees were absent for 2/5 days of last week.
==> 4 employees were absent for 2 days.
Items produced by them in 3 days
= 300*3*4
=3600
Items produced by other employees
=8*5*300
=12000
Total items produced = 12000+3600
=15600
ANSWER:D
Answer: (D) 15600
Question: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men?
(A)  5/7
(B)  1/7
(C)  2/7
(D)  3/7
(E)  1/2
Rationale: Total ways to choose 4 employees from 8 employees = 8C3
Two men = 5C2
Two women = 3C1
P = (5C2 * 3C1)/8C2 = 5/7 hence A.
Answer: (A)  5/7
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A
Answer: (A) 11
Question: If f is a number such that –2 ≤ f ≤ 2, which of the following has the largest possible absolute value?
(A) 3f – 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 f = -2
Answer: (A) 3f – 1
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(A) 24
(B) 35
(C) 13
(D) 61
(E) 45
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 35
Ans: B
Answer: (B) 35
Question: The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accommodate?
(A) 2 metres
(B) 3 metres
(C) 4 metres
(D) 3√3metres
(E) None
Rationale: Solution
Required length	= Diagonal
‹=›√3 a
‹=›(√3×√3) m
‹=›3 m.
Answer B
Answer: (B) 3 metres
Question: The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?
(A) 7
(B) 10
(C) 4
(D) 6
(E) 8
Rationale: Cube volume = a(power)3 cubic units
Surface area = 6 a(power)2 sq.units
a(power)3 = 6 a(power)2
a = 6 m
Answer is D.
Answer: (D) 6
Question: The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, what is x?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Let the cost price = y
The cost price of 40 articles = 40y
The selling price of x articles = 1.25y*x
1.25y*x = 40y
x = 40 / 1.25 = 32
The answer is D.
Answer: (D) 32
Question: How long does a train 120 m long running at the speed of 70 km/hr takes to cross a bridge 145 m length?
(A) 13.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 13.9 sec
(E) 47.98 sec
Rationale: Speed = 70 * 5/18 = 19 m/sec
Total distance covered = 120 + 145 = 265 m.
Required time = 265/19 = 13.9 sec.
Answer:D
Answer: (D) 13.9 sec
Question: If a and b are integers and a≠0 which of the following cannot equal 0?
(A) ab
(B) a-b
(C) a+b
(D) ab-b^2
(E) a^2+b^2
Rationale: (A) ab
If b=0 , then ab=0
(B) a - b
If a=b , then a-b= =0
(C) a + b
If b=-a , then a+b=0
(D) ab - b^2
If a=b , then ab-b^2= 0
(E) a^2 + b^2
Can't be equal to zero .
If a=0 , then a^2 + b^2	=b^2
if a=-ve , then a^2 + b^2 not equal to 0
Answer E
Answer: (E) a^2+b^2
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 11
(B) 45
(C) 66
(D) 72
(E) 32
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Answer: (B) 45
Question: Which of the following is NOT a factor of 10! ?
(A) 1440
(B) 625
(C) 160
(D) 80
(E) 50
Rationale: 625=5*5*5*5 and we dont have four 5 in 10! answer is B
Answer: (B) 625
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
(A) 1,20,000
(B) 1,20,080
(C) 1,20,900
(D) 1,29,000
(E) 1,20,070
Rationale: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer:A
Answer: (A) 1,20,000
Question: A circular mat with diameter 22 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 5/12
(B) 2/5
(C) 3/2
(D) 3/4
(E) 5/8
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(11)(11)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(121/24)
I hope this is easy to follow, so with some simplification i get (1/8)(5) = (5/8) Answer is E
Answer: (E) 5/8
Question: There are 28 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
(A) 800
(B) 820
(C) 850
(D) 870
(E) 900
Rationale: The total number of stations= 30
From 30 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 30P2 ways.
30P2= 30*29= 870
ANSWER:D
Answer: (D) 870
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 75
(B) 267
(C) 299
(D) 266
(E) 21
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.Answer: A
Answer: (A) 75
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed, what is the minimum number of questionnaires that should be mailed?
(A) 400
(B) 500
(C) 600
(D) 700
(E) 800
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 240
x = 400
The answer is A.
Answer: (A) 400
Question: How many words can be formed by using all letters of the word 'PIG' ?
(A) 6
(B) 8
(C) 9
(D) 5
(E) 7
Rationale: The word PIG contains 3 different letters
Required number of words = 3P3 = 3! = 3*2*1 = 6
Answer is A
Answer: (A) 6
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 132 km
(B) 167 km
(C) 143 km
(D) 162 kilometres
(E) 245 km
Rationale: D
12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: (D) 162 kilometres
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value R of the product xy?
(A) 	-12
(B) 	-3
(C) 	0
(D) 	2
(E) 	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value R.
Hence, Answer Choice C is the one to go.
Answer: (C) 	0
Question: A cube is divided into 512 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
(A) 216
(B) 264
(C) 296
(D) 312
(E) 324
Rationale: Each face of the cube has 8 x 8 = 64 cubelets.
On each face, only the interior cubelets are painted one colour.
On each side, 6 x 6 = 36 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*36 = 216
The answer is A.
Answer: (A) 216