mathewhe/aqua_rat huggingface dataset:
Question: What will be the difference between simple and compound interest @25% per annum on a sum of $3600 after 2 years?
(A) $150
(B) $220
(C) $225
(D) $182
(E) $189
Rationale: S.I. = 3600*25*2/100 = $1800
C.I. = 3600 * (1 + 25/100)^2 - 3600 = $2025
Difference = 2025-1800 = $225
Answer is C
Answer: (C) $225
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 24 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has how many candies initially?
(A) 36
(B) 48
(C) 54
(D) 36
(E) 60
Rationale: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Answer : D
Answer: (D) 36
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure m in inches of the width of the foil covered prism?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 m= 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =10
Ans E.
Answer: (E) 10
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 09
(B) 10
(C) 05
(D) 02
(E) 06
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: (B) 10
Question: Suppose 12 points lie on a circle. How many cyclic quadrilaterals can be made by using these points?
(A) 440
(B) 454
(C) 495
(D) 486
(E) None
Rationale: For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495. Therefore, we can draw 495 quadrilaterals.
Answer C
Answer: (C) 495
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 277
(B) 888
(C) 228
(D) 860
(E) 911
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Answer: (D) 860
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 887
(C) 167
(D) 197
(E) 230
Rationale: Length of the train be ‘X’
X + 130/15 = X + 250/20
20X + 2600 = 15X + 3750
5x=1150
X = 230m
Answer: E
Answer: (E) 230
Question: The total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?
(A) 7,500
(B) 8,000
(C) 9,000
(D) 6,500
(E) None of these
Rationale: 4M + 2W = 46000;
Again, W = M + 500
or, M = W – 500
∴ (W – 500) + 2W = 46000
or, 6W = 46000 + 2000 = 48000
∴ W = 8000
Answer B
Answer: (B) 8,000
Question: A sun is divided among X, Y and Z in such a way that for each three rupees X gets, Y gets two rupees and Z gets 80 paisa. If the share of Y is RS. 55, what is the total amount of X and Y?
(A) 120
(B) 124.5
(C) 104.5
(D) 114.5
(E) 100
Rationale: x:y:z = 300:200:80
15:10:4
10 --- 55
19 --- ? => 104.5
Answer: C
Answer: (C) 104.5
Question: The grade point average of one third of the classroom is 30; the grade point average of the rest is 33. What is the grade point average of the whole class?
(A) 44
(B) 41
(C) 38
(D) 35
(E) 32
Rationale: Let n=total students in class
total points for 1/3 class=30n/3=10n
total points for 2/3 class=33*2n/3=22n
total points for whole class=10n+22n=32n
32n total class points/n total students=32 grade point average for total class
Answer : E
Answer: (E) 32
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 8 seconds, the speed of each train (in km/hr) is
(A) 42
(B) 36
(C) 28
(D) 20
(E) 54
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/8 = 30 m/s
Speed of each train = v = 30/2 = 15 m/s
= 15×36/10 km/hr = 54 km/hr
Answer: Option E
Answer: (E) 54
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 20% profit and remaining 50% at 30% profit. Find his % profit on total.
(A) 23%
(B) 25%
(C) 26%
(D) 28%
(E) 35%
Rationale: If the total quantity was 100
Then 40X 20% + 50 X30%= 23
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'A' is the answer
Answer: (A) 23%
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 15 a.m
(B) 10 a.m
(C) 12 a.m
(D) 02 a.m
(E) 05 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: (B) 10 a.m
Question: two branch of tree bird sit in way if one bird of the first branch goes to second branch there ratio become equal and if bird from second branch goes to first branch ratio become double than first. what are there ratio in sitting ?
(A) 7:5
(B) 6:5
(C) 8:5
(D) 5:7
(E) 5:8
Rationale: if birds on 1st branch=x, 2nd branch=y
Ist condition, x-1=y+1, x-y=2 ---(i) &
2nd condition, x+1=2(y-1), x-2y=-3 ---(ii)
Solving (i) & (ii), x=7, y=5
ANSWER:A
Answer: (A) 7:5
Question: The value of x.320 Ã· 2 Ã· 3 = X
(A) 53.33
(B) 46.33
(C) 15.36
(D) 15.45
(E) 15.48
Rationale: 320Ã·2Ã·3
=320Ã—1/2Ã—1/3
=160/3
=53.33
CORRECT ANSWER : A
Answer: (A) 53.33
Question: In a race with 30 runners where 3 trophies will be given to the top 5 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
(A) 5^3 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
Rationale: 5 people can be prized with 3 distinct prizes in 5^3 ways
ANSWER:A
Answer: (A) 5^3 ways
Question: How many keyboards do you need if you have to place 1024 keys into keyboards that each hold 32 keys?
(A) A)28
(B) B)30
(C) C)32
(D) D)34
(E) E)None of the above
Rationale: Sol.
1024 keys of 32 each
= 1024 / 32
= 32
Answer : C
Answer: (C) C)32
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction R of all babies born who were NOT part of a set of twins or triplets?
(A) z - 2x - 3y
(B) (2x+3y)/z
(C) (x+y)/z
(D) 1 - (2x+3y)/z
(E) 1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
R= 1- (2x+3y)/Z. Hence answer is D.
Answer: (D) 1 - (2x+3y)/z
Question: What positive number, when squared, is equal to the cube of the positive square root of 16?
(A) 64
(B) 32
(C) 8
(D) 4
(E) 2
Rationale: Let the positive number be x
x^2 = ((16)^(1/2))^3
=>x^2 = 4^3 = 64
=> x = 8
Answer C
Answer: (C) 8
Question: 0.002 x 0.5 = ?
(A) 0.1
(B) 0.0001
(C) 0.01
(D) 1.0
(E) 0.001
Rationale: 2 x 5 = 10.
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Answer is E.
Answer: (E) 0.001
Question: How many different values of positive integer x, for which |x+6|<x, are there?
(A) 0
(B) 2
(C) 3
(D) 8
(E) 16
Rationale: Answer D
I opted to put the random value option.
i used 0 , 6 , -6 and the the extreme of 20 and -20..
i was able to solve it in 1:09
D
Answer: (D) 8
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) 46.5 kg
(B) 54 kg
(C) 65 kg
(D) 66.5 kg
(E) 76.5 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: A trailer carries 3, 4 and 5 crates on a trip. Each crate weighs no less than 120 kg. What is the maximum weight of the crates on a single trip?
(A) 1250
(B) 625
(C) 600
(D) 7500
(E) 375
Rationale: Max No. of crates=5.
Max Weight=120Kg
Max. weight carried = 5*120=600Kg=C
Answer: (C) 600
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:121
(B) 81:126
(C) 81:189
(D) 81:176
(E) 81:117
Rationale: Ratio of the sides
= ³√729 : ³√1331 = 9 : 11
Ratio of surface areas
= 92 : 112 =81:121
Answer:A
Answer: (A) 81:121
Question: If 0 < m < 1 < n< 6, which of the following must be less than 1? I.m/n II. mn III. n - m
(A) I only
(B) III only
(C) II,III only
(D) II only
(E) I,II only
Rationale: n > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : A
Answer: (A) I only
Question: A and B undertake to do a piece of work for $500. A alone can do it in 5days while B alone can do it in 10days. With the help of C, they finish it in 2days. Find the share of C?
(A) $200
(B) $150
(C) $300
(D) $25
(E) $100
Rationale: C's 1day work = (1/2)-(1/5 + 1/10) = 1/5
A:B:C= 1/5 : 1/10: 1/5 = 2:1:2
B's share = 500*2/5 = $200
Answer is A
Answer: (A) $200
Question: Light glows for every 13 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
(A) 380 times
(B) 381 times
(C) 382 times
(D) 392 times
(E) 482 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/13)=382 times.
ANSWER:C
Answer: (C) 382 times
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 360 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Explanation:
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 72 kmph * 12 seconds
Convert 72 kmph into m/sec
1 kmph = 518518 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 72 kmph = 518∗72518∗72 = 20 m/sec
Therefore, length of the platform = 20 m/s * 12 sec = 240 meters.
Correct answer: A
Answer: (A) 240 meters
Question: 120 is what percent of 40?
.
(A) 0.2%
(B) 2%
(C) 5%
(D) 300%
(E) 500%
Rationale: 120= x*40/100
x = 300%
Ans; D
Answer: (D) 300%
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?
I. c < t < h
II. 0 < t < h
III. (c/2) < t < (h/2)
(A) a) I only
(B) b) II only
(C) c) III only
(D) d) I and II
(E) e) II and III
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 2, 3 are valid.Therefore E is the best answer
Answer: (E) e) II and III
Question: The average age of a group of 10 students was 20. The average age increased by 3 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 38 years
(D) 44 years
(E) None of these
Rationale: The total age of 10 students with average 20 = 200
The total age of 12 students with average 23 = 276
The total age of 2 new students = 76
Their average =38
Correct Option C
Answer: (C) 38 years
Question: If x and y are positive integers, Choose which of the following CANNOT be the greatest common divisor of 35x and 20y?
(A) 5
(B) 5(x-y)
(C) 10x
(D) 20y
(E) 35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 35x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 35x/5 = 7x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 10x when x = 1 its 10 and 10 cannot be the greatest common divisor of 35x and 20y ...
or 35x/10x = 3.5 which is not a integer.
so answer is C.
Answer: (C) 10x
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
(A) 386
(B) 378
(C) 396
(D) 395
(E) 394
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 1638 = Rs. 378
Answer: B
Answer: (B) 378
Question: Calculate the dividend from Caleb's stock, if Caleb he invested Rs. 2500 at 79 to obtain an income of Rs. 200.
(A) 6.32
(B) 5.32
(C) 7.32
(D) 2.32
(E) 1.32
Rationale: By investing Rs.2500, income = Rs.200
By investing Rs.79, income = 200Ã—79/2500=6.32
ie, dividend = 6.32%
Answer is A.
Answer: (A) 6.32
Question: X does a work in 40 days. Y does the same work in 60 days. In how many days they together will do the same work?
(A) 10
(B) 12
(C) 24
(D) 30
(E) 15
Rationale: X's 1day's work= 1/40
Y's 1 day's work=1/60
(X+Y)'s 1day's work= (1/40+1/60)=1/24
both together will finish the work in 24 days.
correct option is C
Answer: (C) 24
Question: Eighteen years ago,a father was three times as old as his son.Now the father is only twice as old as his son.Then the sum of the present ages of the son and the father is :
(A) 54
(B) 72
(C) 105
(D) 108
(E) None of these
Rationale: Solution
Let the present ages of the father and son be 2x and x years respectively.
Then,(2x - 18)=3 (x - 18) ⇔ x = 36.
∴ Required sum = (2x + x) = 3x =108 years. Answer D
Answer: (D) 108
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 18%
(B) 19%
(C) 12%
(D) 32%
(E) 17%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: (C) 12%
Question: 12 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work?
(A) 23
(B) 27
(C) 36
(D) 27
(E) 11
Rationale: 12 * 30 = 10 * x => x = 36 days
Answer:C
Answer: (C) 36
Question: If m is an integer such that (-2)^2m=2^(12-m) then m=?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 2m = 12-m
3m = 12
m = 4
The answer is D.
Answer: (D) 4
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
(A) 50
(B) 40
(C) 20
(D) 30
(E) 10
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
answer is B.
Answer: (B) 40
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 70 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.70=42 Democrats are expected to vote for Candidate A;
40*0.20=8 Republicans are expected to vote for Candidate A.
Thus total of 42+8=50 registered voters are expected to vote for Candidate A, which is 50% of the total number of registered voters.
Answer: A
Answer: (A) 50%
Question: A family consists of two grandparents, two parents, and three grandchildren. The average age of the grandparents is 65 years, the average age of the parents is 36 years, and the average age of the grandchildren is 5 years. What is the average age (in years) of the family?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Total age of the grandparents = 65 Ã— 2 = 130
Total age of the parents = 36 Ã— 2 = 72
Total age of the grandchildren = 5 Ã— 3 = 15
Average age of the family = (130+72+15)/7 = 217/7 = 31 years
The answer is A.
Answer: (A) 31
Question: What is 992*992?
(A)  974,169
(B)  974,219
(C)  984,064
(D)  985,219
(E)  985,369
Rationale: if you take a base of 1000 then 992 is 8 less than 1000
to get the product of 992 x 992 write like this
992- 8( as 8 less than base1000)
992- 8
now 8 x 8 = 64
and 992-8 = 984
so 992 x 992 = 984064 ... (bingo the answer is C . you can even have a shortcut ...... 8 x 8 = 64 ... only answer choice has last three digits as 64.. so no need to calculate 992-8 . after you get 8 x 8 you can straight way pick answer choice C.
Answer: (C)  984,064
Question: A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.40 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?
(A) $94.03
(B) $96.75
(C) $98.75
(D) $102.07
(E) $105.3
Rationale: there can be 2 cases
1)25+25+10+5=$98.75 or
2)25+25+25=$96.75
C
Answer: (C) $98.75
Question: If the 15th day of a month is three days earlier than Saturday, What day will it be on the 24th day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that 15th day of a month is three days earlier than Saturday
=> 15th day is Wednesday
=> 22nd is Wednesday
=> 24th is Friday
Answer: Option E
Answer: (E) Friday
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120
(B) 775
(C) 555
(D) 288
(E) 278
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
Answer: (A) 120
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) Rs. 720
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: (C) Rs. 698
Question: An woman sitting in a train which is travelling at 25 kmph observes that a goods train travelling in a opposite direction, takes 3 seconds to pass him. If the goods train is 140 m long, find its speed.
(A) 141
(B) 142
(C) 143
(D) 144
(E) 145
Rationale: Relative speed = (140/3)m/s = (140/3)*(18/5) = 168 kmph
speed of goods train = 168-25 = 143 kmph
Answer is C
Answer: (C) 143
Question: Q as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P.
(A) 62%
(B) 50%
(C) 75%
(D) 66%
(E) 65%
Rationale: Explanation :
IF P+Q=62%
ANSWER IS A
Answer: (A) 62%
Question: Find the least number must be subtracted from 899830 so that remaining no.is divisible by 16?
(A) 5
(B) 8
(C) 7
(D) 6
(E) 9
Rationale: On dividing 899830 by 16 we get the remainder 6, so 6 should be subtracted
D
Answer: (D) 6
Question: A candidate who gets 20% of the marks fails by 40 marks. But another candidate who gets 30% marks gets 20 marks more than necessary for passing. Find the number of marks for passing?
(A) 100 Marks
(B) 200 Marks
(C) 280 Marks
(D) 160 Marks
(E) 827 Marks
Rationale: 20% ------------ 40
30% ------------ 20
----------------------
10% ------------- 60
20% -------------- 120
120 + 40 = 160 Marks
Answer:D
Answer: (D) 160 Marks
Question: Find how many positive integers less than 10,000 are there such thatthe sum of the digits of the no. is divisible by 3?
(A) 2468
(B) 2789
(C) 2987
(D) 3334
(E) 3568
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: (D) 3334
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 5 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
(A) 20cs
(B) cs/2
(C) 60cs
(D) (2cs)/12
(E) (24c)/s
Rationale: Ans: C
Solution: simple multiplication s students , c classes , 5 books/ month= 60 books a year
total number of books = 60cs
Answer: (C) 60cs
Question: Which of the following is a multiple of 6!-120?
(A) 5!+80
(B) 6!+320
(C) 5!+380
(D) 5!+480
(E) 4!+24
Rationale: The factorial 6! mean 6*5*4*3*2
Therefore 6!-120 =(6*5*4*3*2)-120
This gives you 720-120=600
valculating all the options the only option that gives a factor of 6!-120 is option D) 5!+480
Answer: (D) 5!+480
Question: A chef cuts a watermelon along its horizontal diameter once and then along its vertical diameter twice at right angle to each other. A slice is removed (other pieces remains intact). What will be the total surface area of the remaining portion?
(A) 4*pi*r^2
(B) 4*pi*r^3
(C) 4*pi*r^4
(D) 4*pi*r^5
(E) 4*pi*r^6
Rationale: surface area of sphare is (4*pi*r^2)
if 1/4th parth is removed (4*pi*r^2)-(pi*r^2)= 3*pi*r^2
and the cut surface is (1/2*pi*4^2)*2
so total surface area is 4*pi*r^2
ANSWER:A
Answer: (A) 4*pi*r^2
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 28!
(A) 13
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18,21,24,27
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
21=3x7->1
24=3x8->1
27=3x3x3->3
---- count 3's =13 so answer is 13
Answer : A
Answer: (A) 13
Question: How many integers between 1000 and 10000 have
no digits other than 4, 5 or 6?
(A) 91
(B) 51
(C) 81
(D) 71
(E) 61
Rationale: Any number between 1,000 and 10,000 is of 4 digits. The unit’s place can be filled up by 4,5 or 6, that is, in 3 ways.
Similarly, the ten’s place can be filled up by 4 or 5 or 6, that is in 3 ways. The hundred’s place can be filled up by 4, 5 or 6, that is in 3 ways and the thousand’s place can.be filled up by 4 or 5 or 6, that is, in 3 ways.
Hence the required numbers = 3 x 3 x 3 x 3 = 81
ANSWER:C
Answer: (C) 81
Question: United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
(A) 200 minutes
(B) 100 minutes
(C) 120 minutes
(D) 140 minutes
(E) 160 minutes
Rationale: Lets take number of minutesx.
Given that, 7+0.25x=12+0.2x ->0.05x=2 -> x=100minutes
ANS B
Answer: (B) 100 minutes