mathewhe/aqua_rat huggingface dataset:
Question: Dhoni has x dollars more than Rahul has, and together they have a total of y dollars. Which of the following represents the number of dollars that Rahul has?
(A) (y – x)/3
(B) (y – x)/2
(C) (y – x)/4
(D) (2y – x)/2
(E) (y – x)/5
Rationale: To solve, we will set up two equations. Let's start by defining two variables.
R = number of dollars Rahul has
D= number of dollars Dhoni has
We are given that Dhoni has x dollars more than Rahul. We set up an equation:
D= x + R
We are next given that together they have a total of y dollars. We can set up our second equation:
R + D = y
Since we know that D = x + R, we can substitute x + R for D into the second equation R+ D = y.
Notice that, after the substitution, we will only have variables of R, x, and y. Thus, we have:
R + x + R = y
2R + x = y
2R = y – x
R = (y – x)/2
Answer : B
Answer: (B) (y – x)/2
Question: If the 9th day of a month is two days earlier than Monday, What day will it be on the nineteenth day of the month?
(A) Saturday
(B) Tuesday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that 9th day of a month is two days earlier than Monday
=> 9th day is Saturday
=> 16th is Saturday
=> 19th is Tuesday
Answer: Option B
Answer: (B) Tuesday
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median T of x, y, and z?
I. 9
II. 10
III. 11
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median T.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: (E) I and III only
Question: If s and t are positive integers such that s/t = 64.24, which of the following could be the remainder when s is divided by t?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: 0.24 = 24/100 = 6/25
The remainder must be divisible by 6.
The answer is D.
Answer: (D) 30
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 8 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
(A) 11:00am
(B) 10:30am
(C) 9:30am
(D) 10:00am
(E) 11:30am
Rationale: In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 16/4 = 4 hours.
Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 4 hours = 11:30am.
Answer: E
Answer: (E) 11:30am
Question: Set A: 3, q, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – q?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(q+8)/2= (y+9)/2
y - q= -1
Answer B
Answer: (B) -1
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10 sec
(B) 16 sec
(C) 19 sec
(D) 7.2 sec
(E) 13 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 36
D = 36 * 100/18 = 200
RS = 60 + 40 = 100 * 5/18
T = 200 * 18/500 = 7.2 sec
Answer: D
Answer: (D) 7.2 sec
Question: $500 will become $1000 in 5 years find the rate of interest?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 50%
Rationale: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*5 =20%
Answer is B
Answer: (B) 20%
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) 11.9
(B) 11.6
(C) 11.4
(D) 11.5
(E) 11.2
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: 9 men went to a restaurant for taking their snacks. Eight of them spent Rs.15 each on their snacks and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them.
(A) Rs 115
(B) Rs116
(C) Rs 144
(D) Rs 178
(E) Rs 168
Rationale: Explanation :
Let the average expenditure of all the nine be RS.x
Then, 15 8 + (x + 8) = 9x
Therefore x = 16
Total money spent = 9x = RS.(9 16) = Rs.144
Answer : C
Answer: (C) Rs 144
Question: The sum of present age of Abe and the age before 7 years is 27. Find the present age of Abe. What will be his age after 7 years?
(A) 25
(B) 24
(C) 27
(D) 28
(E) 29
Rationale: Present age = x
Before 7yrs, y=x-7
After 7yrs, z=x+7
By the qn,
x+(x-7)=27
2x-7=27
2x=27+7
x=34/2
x=17
z=x+7
=17+7
=24
ANSWER:B
Answer: (B) 24
Question: If 42.18 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 42.18 = 14K + Km/50...we can rewrite the number as follows:
42+ 0.18= 14K + Km/50........Since K is integer, then 42=14K..........K=3
0.18=Km/50......18/100=3m/50......m=3
k+m=3+3=6
Answer: A
Answer: (A) 6
Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 90, how many horses are there ?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: legs 18*4 = 72
now half on their horses so remaining on the walk so 9 men
9 men has 18 legs
so, 18+ 72 = 90 legs walking
ANSWER:E
Answer: (E) 18
Question: How many 5 digit number can be formed out of digits 0,2,4,6,8 that is divisible by 8.
(A) 26
(B) 30
(C) 38
(D) 98
(E) 85
Rationale: For a number to be divisible by 8, its last three digits must divisible by 8.
So, last three digits can be from the following group
(024), (048), (064), (208), (240), (248), (264), (280), (408), (480), (608), (624), (640), (648), (680), (824), (840), (864),
There are 18 such groups.
Consider these 12 groups in which zero is there
(024), (048), (064), (208), (240), (280), (408), (480), (608), (640), (680), (840)
With each of these 12 groups, first digit can be any of the remaining 2 digits and second digit can be the remaining one digit
Therefore, 12×2 = 24 such numbers
Consider the 6 groups in which zero does not come
(248), (264), (624), (648), (824), (864),
With each of these 6 groups, first digit can be the one remaining digit(because zero cannot be the first digit)
Second digit can be zero
Therefore, 6×1 = 6 such numbers
Therefore, total count of 5 digit numbers = 24 + 6 = 30
So, Ans is 30
ANSWER:B
Answer: (B) 30
Question: The length, breadth and height of a room are in the ratio 9 : 4 : 2. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
(A) (a) remain the same
(B) (b) decrease by 13.64%
(C) (c) decrease by 15%
(D) (d) decrease by 23.08%
(E) (e) decrease by 30%
Rationale: Length (L) = 9
Breadth (B) = 4
Height (H) = 2
Total Area of Walls = 2(BH + LH) = 2*(4*2 + 9*2) = 2*(8+18) = 52
Then, Finally
Length (L) = 2*9 = 18
Breadth (B) = 4/2 = 2
Height (H) = 2/2 = 1
Total Area of Walls = 2(BH + LH) = 2*(2*1 + 18*1) = 2*(2+18) = 40
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (40-52)*100 /52=- 23.08% (Decrease)
Answer: Option D
Answer: (D) (d) decrease by 23.08%
Question: A chair is bought for Rs.500/- and sold at a loss of 10% find its selling price
(A) Rs.450/-
(B) Rs.451/-
(C) Rs.440/-
(D) Rs.455/-
(E) Rs.445/-
Rationale: Loss = 500*10/100 = 50
S.P = C.P - Loss
= 500- 50
=Rs.450/-
Answer : A
Answer: (A) Rs.450/-
Question: A person purchased a TV set for Rs. 13000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 16.82%
(B) 87.82%
(C) 61.82%
(D) 17.82%
(E) 18.82%
Rationale: The total CP = Rs. 13000 + Rs. 6250 = Rs. 19250 and SP
= Rs. 31150
Profit(%) = (31150 - 19250)/19250 * 100
= 61.82%
Answer:C
Answer: (C) 61.82%
Question: A cistern of capacity 40 litres has an inlet and an outlet pipe. When both the pipes are opened at once, it takes 8 minutes to fill the cistern. However, if the outflow rate is increased 1.5 times, the cistern never gets filled. Which of the following can be the outflow rate?
(A) 8 litres/minute
(B) 6 litres/minute
(C) 12 litres/minute
(D) 9 litres/minute
(E) 10 litres/minute
Rationale: DETAILED SOLUTION
Initially, net flow in the tank = 40 litres/ 8 minutes = 5 litres/minute
Now, the increase in outflow should be greater than 5 litres/min for the tank to fill up
Increase in outflow = 1.5x – x = 0.5x
Only in option c) 0.5 X 12 = 6 litres/min > 5 litres/min
CORRECT ANSWER C
Answer: (C) 12 litres/minute
Question: Of the 24 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
(A) 225
(B) 45
(C) 65
(D) 95
(E) 200
Rationale: M under 18 - 6
F above 18 - 6
How many distinct groups can be formed now: 6c2 * 6c2 = 225
Answer : A
Answer: (A) 225
Question: The speed of a boat in still water is 30kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Speed downstream = 30+ 20 = 50 kmph
Speed upstream = 30 - 20 = 10 kmph
Answer:B
Answer: (B) kmph
Question: In how many different F ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
(A) 70
(B) 288
(C) 576
(D) 10,080
(E) 20,160
Rationale: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer F= (4!)^2 = 576 or C
Answer: (C) 576
Question: 16384, 8192, 2048, 256, 16, ?
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 2.5
Rationale: Terms are continuously divided by 2,4,8,16, and so on
16384
16384 ÷ 2 = 8192
8192 ÷ 4 = 2048
2048 ÷ 8 = 256
256 ÷ 16 = 16
16 ÷ 32 = 0.5
Answer is A.
Answer: (A) 0.5
Question: George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 5% of the money for taxi fare and buys 25 mangoes. How many oranges can he buy?
(A) 25
(B) 30
(C) 20
(D) 22.5
(E) 12
Rationale: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 5
He decides to retain 5% of 200 = 10 for taxi fare, so he is left with 190
He buys 20 mangoes ( @ 5) so he spends 100
Money left is 90 (190 - 100)
No of oranges he can buy = 90/4 =>22,5
So, George can buy 20 Oranges.
D
Answer: (D) 22.5
Question: A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is?
(A) 33
(B) 29
(C) 17
(D) 10
(E) 16
Rationale: Explanation:
Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.
125/100 * 120/100 * 118/100 * x = 3009/100
177/100 x = 3009/100 => x = 17
Answer:C
Answer: (C) 17
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
(A) Rs. 10,500, Rs. 13,500, Rs. 16,500
(B) Rs. 10,500, Rs. 13,500, Rs. 16,509
(C) Rs. 10,500, Rs. 13,500, Rs. 16,506
(D) Rs. 10,500, Rs. 13,500, Rs. 16,588
(E) Rs. 10,500, Rs. 13,500, Rs. 16,512
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500.Answer: a
Answer: (A) Rs. 10,500, Rs. 13,500, Rs. 16,500
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
(A) 5%
(B) 10%
(C) 23%
(D) 25%
(E) 30%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: (B) 10%
Question: In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?
(A) 25%
(B) 33.33%
(C) 40%
(D) 20%
(E) 10%
Rationale: DETAILED SOLUTION
For questions of this type, it is best to go from the final step. In the final state, the number of girls should be 1.5 * the number of boys.
When 50% of the boys are taken as girls, let the number of boys = x
Number of girls = 1.5x
total number of students = 2.5x
Original number of boys = 2x (50% of boys = x)
Original number of girls = 0.5x
Girls form 20% of the overall class.
CORRECT ANSWER D.
Answer: (D) 20%
Question: The ratio of two quantities is 2 to 5. If each of the quantities is increased by 8, what is the ratio of these two new quantities?
(A) 2/5
(B) 5/8
(C) 7/13
(D) 22/25
(E) It cannot be determined from the information given.
Rationale: Correct Answer: E
Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.
For example, if x = 2 and y = 5, then (x+8)/(y+8) = (2+8)/(5+8) = 10/13. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+8)/(y+8) = (4+8)/(10+8) = 12/18 =6/9. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).
Answer: (E) It cannot be determined from the information given.
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 65 days
(B) 45 days
(C) 10 days
(D) 16 days
(E) 18 days
Rationale: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days.Answer: C
Answer: (C) 10 days
Question: Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?
(A) 5/M+K hours
(B) 6(M+K) hours
(C) 300/M+K hours
(D) 300/M−K hours
(E) 60/M−K hours
Rationale: Consider k=1,m=2
Then per the question,
500 - 1x = 200 + 2x
x=100
Check answer options for No. of hours (x)=100 for k=1 and m=2
ANSWER:C
Answer: (C) 300/M+K hours
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
(A) 720
(B) 740
(C) 760
(D) 790
(E) 800
Rationale: Option 'A'
Answer: (A) 720
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
(A) 0.5919
(B) 0.5904
(C) 0.5929
(D) 0.5928
(E) 0.594
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: (B) 0.5904
Question: 2x + y = 13
|y| <= 13
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
(A) 7
(B) 10
(C) 12
(D) 13
(E) 14
Rationale: Hi - The questions says |y| <=13 so the values of y will range from 0 to 13. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13. So 14 (E) is the answer. remember sign doesn't matter for y as y will always be positive.
Answer: (E) 14
Question: Find the cost of fencing around a circular field of diameter 12 m at the rate of Rs.3.50 a meter?
(A) 131.95
(B) 132.9
(C) 140.33
(D) 123.4
(E) 190.4
Rationale: 2 * 22/7 * 6 = 37.7
37.7 * 3 1/2 = Rs.131.95
Answer: A
Answer: (A) 131.95
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even nine-digit numbers are palindromes?
(A) 40
(B) 40000
(C) 500
(D) 5,000
(E) 100,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 222212222,444414444.
The middle number in the nine-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers
, the 3rd and 5th and 4th and 6th could must also be same i.e 0-9( 10 ways) e.g 242343242, 648565846
we thus have, 4 *10*10*10*10=40000 B
Answer: (B) 40000
Question: The population of a bacteria colony doubles every day. If it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 1024
(D) 2048
(E) 128
Rationale: 2^6(2) = 2^7 = 128
The answer is E.
Answer: (E) 128
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
(A) 3
(B) 4
(C) 9
(D) 3
(E) 5
Rationale: Explanation:
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer: Option B
Answer: (B) 4
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 200
(C) 250
(D) 300
(E) 500
Rationale: Answer: Option A
Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
ANSWER A
Answer: (A) 230
Question: What is the total number of integers between 20 and 100 that are divisible by 9?
(A) 5
(B) 15
(C) 12
(D) 7
(E) 9
Rationale: 27, 36, 45, ..., 90,99
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (99 - 27) / (9) + 1 = 8 + 1 = 9
Answer is E
Answer: (E) 9
Question: In shop there are 10 bulbs, a total of 4 are defective. If a customer buys 4 bulbs selected at random from the box, what is the probability that neither bulbs will be defective?
(A) 2/19
(B) 3/29
(C) 4/15
(D) 1/15
(E) 1/2
Rationale: First, there are 6C4 ways you can select 6 good bulbs from 4 good ones.
Second, there are 10C4 ways you select 4 bulbs from 10 ones in the box.
Then, the probability that neither bulb will be defective is: 6C4/10C4=15/210 = 1/15
Answer is D
Answer: (D) 1/15
Question: A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $556, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
(A) $150
(B) $290
(C) $365
(D) $715
(E) $730
Rationale: Total weekly income over 5 weeks=$556+$413+$420+$436+$395=$2220
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2220=$1280
From this, we subtract base salary for 2 weeks i.e $350*2=$700
Therefore, commission=$1280-$700=$580 for 2 weeks
Avg weekly commission=$290
Answer B
Answer: (B) $290
Question: The population of a town is 216400. If it increase at the rate of 4% per annum. What will be its population for 3years hence?
(A) 200000
(B) 243420
(C) 194582
(D) 194481
(E) 215460
Rationale: population after 3years = 216400*(1+ 4/100)^3 = 243420
Answer is B
Answer: (B) 243420
Question: If u and v are positive integers, and 3 is not a factor of v, then v may be which of the following?
(A) (u−1)·u·(u+1)
(B) (u−3)·(u−1)·(u+1)
(C) (u−2)·u·(u+2)
(D) (u−1)·u·(u+2)
(E) (u−3)·(u+1)·(u+2)
Rationale: Plugged in values :
let u=5
A. (u−1)·u·(u+1) --> divisible by 3
B. (u−3)·(u−1)·(u+1) --> divisible by 3
C. (u−2)·u·(u+2) --> divisible by 3
D. (u−1)·u·(u+2) --> not divisible. Hence the answer.
Answer: (D) (u−1)·u·(u+2)
Question: In how many different ways can 2 identical blue balls and 2 identical red balls be shared among 4 children such that each child receives a ball?
(A) 10
(B) 24
(C) 34
(D) 20
(E) 21
Rationale: GGG RRR
Therefore total number of ways is
4! but there are two groups of 2 identical things.
Therefore total number of "different" ways is
4!/ (2!) (2!) = 24 ANS:B
Answer: (B) 24
Question: If x^2 + y^2 = 20 and xy = 3, then (x − y)^2 =
(A) 8
(B) 11
(C) 14
(D) 17
(E) 20
Rationale: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 20-2*3=14..
Answer C
Answer: (C) 14
Question: If k, l, and m are distinct positive prime numbers, then (k^3)(l)(m) has how many different positive factors greater than 1?
(A) a. 8
(B) b. 9
(C) c. 12
(D) d. 10
(E) e. 27
Rationale: Let Number is (k^3)(l)(m) = (1^3)(4)(20) = 80
We can write 80 as product of two numbers in following ways
1*80
2*40
4*20
5*16
8*10
5 cases = 5*2 i.e. 10 factors (including 1)
Factors greater than 1 = 9
Answer: Option D
Answer: (D) d. 10
Question: A man can row a boat at 18 kmph in still water. If the speed of the stream is 12 kmph, what is the time taken to row a distance of 90 km downstream?
(A) 6 hours
(B) 4 hours
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: Speed downstream = 18 +12 = 30 kmph.
Time required to cover 90 km downstream = d/s = 90/30 = 3 hours.Answer:C
Answer: (C) 3 hours
Question: Ayisha's age is 1/6th of her father's age. Ayisha's father's age will be twice Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
(A) 5
(B) 10
(C) 7
(D) 9
(E) 4
Rationale: Shankar's present age =8+2=10
Ayisha's father's age after 10 years =2(10+10)=40
Ayisha's father's present age =40−10=30
Ayisha's present age =16×30=5
Answer is A.
Answer: (A) 5
Question: 3 years ago, the average age of P and Q was 20years. With R joining them, theiraverage age becomes 23years. What is the age of R?
(A) 18 years
(B) 20 years
(C) 21years
(D) 23 years
(E) 30 years
Rationale: Three years ago, the average age of P and Q was 20 years.
Three years ago, their sum of the ages was 2x20= 40 years
Present age of P+Q+R = 3 X23 =69
Present age of P+Q=40+( 2 x 3)= 46
Present age of R = ( P+Q+R)- (P+Q)= 69-46 =23 years
D
Answer: (D) 23 years
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <2>*<3>?
(A)  210
(B)  116
(C)  212
(D)  263
(E)  478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <3> is the sum of all integers from 1 to 2*3=6 and <2> is the sum of all integers from 1 to 2*2=4 --> <3>=21 and <2>=10 --> <3>*<2>=21*10=210.
Answer: A
Answer: (A)  210
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.173 per kg, the price of the third variety per kg will be
(A) Rs.169.50
(B) Rs.1700
(C) Rs. 195.50
(D) Rs. 180
(E) None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-173/22.50 = 1 =â€º x - 173 = 22.50 =â€º x=195.50.
Hence, price of the third variety = Rs.195.50 per kg.
Answer C
Answer: (C) Rs. 195.50
Question: A man rows his boat 78 km downstream and 56 km upstream, taking 4 hours each time. Find the speed of the stream?
(A) 6
(B) 5
(C) 7
(D) 8
(E) 3
Rationale: Speed downstream = d/t = 78/(4) = 20 kmph
Speed upstream = d/t = 56/(4) = 14 kmph
The speed of the stream = (20 - 14)/2 = 3 kmph
Answer:E
Answer: (E) 3