mathewhe/aqua_rat huggingface dataset:
Question: A school has received 40% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
(A) $200
(B) $300
(C) $100
(D) $400
(E) $250
Rationale: Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )
$16000 is 40% of total amount.
So total amount = 16000 * 100/40
Remaining amount is 60% of total amount.
60% of total amount = 16000 * (100/40) * (60/100) =24000
This amount has to be divided by 60 ( remaining people are 60 )
So per head amount is 24000 / 60 = $400
ANSWER:D
Answer: (D) $400
Question: x, a, z, and b are single digit positive integers. x = 1/7 a. z = 1/7 b. (10a + b) – (10x + z) could NOT equal
(A) 30
(B) 36
(C) 42
(D) 63
(E) 66
Rationale: a=7x , b =7z therefore(7x.10+7z) - (10x +z) = (7-1) (10x+z) =6.(10x+Z)
number should be divisible by 6
D
Answer: (D) 63
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
(A) Rs.20043.94
(B) Rs.18654.81
(C) Rs.20264.46
(D) Rs.19612.41
(E) None of these
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
ANSWER:A
Answer: (A) Rs.20043.94
Question: Two trains are moving in opposite directions @60kmph and 90kmph. Their length are 1.10km and 0.9km. The time taken by the slower train to cross faster train in second is?
(A) 25sec
(B) 30sec
(C) 48sec
(D) 36sec
(E) 40sec
Rationale: Relative speed = 60+90 = 150*5/18 = 125/3 m/s
Distance covered = 1.10+0.9 = 2km = 2000m
Required time= 2000*3/125 = 48sec
Answer is C
Answer: (C) 48sec
Question: A man buys an article for $15. and sells it for $20. Find the gain percent?
(A) 33 1/3%
(B) 50 1/3%
(C) 20 1/3%
(D) 15%
(E) 30%
Rationale: C.P. = $15
S.P. = $20
Gain = $5
Gain% = 5/15 *100 = 33 1/3%
Answer is A
Answer: (A) 33 1/3%
Question: A right circular cylinder has a height of 24 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
(A) 500(π – 3)
(B) 500(π – 2.5)
(C) 500(π – 2)
(D) 600(π – 1.5)
(E) 500(π – 1)
Rationale: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
24*25*pi - 15*sqrt(50)^2
=600(π – 1.5)
D. 500(π – 1.5)
Answer: (D) 600(π – 1.5)
Question: Two workers can type two pages in two minuets then how many persons can type 18 pages in 6 minuets
(A) 2Workers
(B) 3Workers
(C) 6Workers
(D) 7Workers
(E) 8Workers
Rationale: 2Worker 2pages 2minutes
1Worker 1page 2minutes
1worker 18pages 36minutes
Therefore to reduce the time by 6 times, workers should be increased by 6 times
ANSWER:C
Answer: (C) 6Workers
Question: A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 6 letters in its codes, and all letters can be repeated in any one code?
(A) A.321272406
(B) B.308915776
(C) C.11881376
(D) D.456976
(E) E.17576
Rationale: The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
# for 5 letters : 26 * 26*26*26*26 =11881376
# for 6 letters : 26 * 26*26*26*26*26 =308915776
The total : By adding all of them , 26+676+17576+456976+11881376+308915776=321272406
A
Answer: (A) A.321272406
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
(A) 1178
(B) 144
(C) 66
(D) 8
(E) 55
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B
Answer: (B) 144
Question: If the sum of 3 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 3
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Rationale: sum of 3 consecutive integers
= (n) + (n+1) + (n+2)
=3n + 3
= odd + odd = even
= 3(n+1) = divisible by 3
Hence, x is even and divisible by 3.
Answer: D
Answer: (D) I and III
Question: A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 80 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 20 minutes
(E) 2 hours 10 minutes
Rationale: v1 and V2 are speeds.
v1.t /80 = v2
v2.t/40 = v1
v1/v2 = 2
which train A would 80. 1/2 mins to cover the same distance
40 + 40 = 80 mins (ans D)
Answer: (D) 1 hour 20 minutes
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 8
(B) 9
(C) 7
(D) 5
(E) 2
Rationale: 3x + 5x + 7x = 45
x =3
3x = 9
Answer: B
Answer: (B) 9
Question: A certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 40 miles per hour? (1 mile = 5,280 feet)
(A)  1
(B)  2
(C)  4
(D)  6
(E)  7
Rationale: Distance: 4024 feet. This is (4024/5280) miles = 0.76 miles
Speed: 40 miles per hour
Time: (Distance / Speed) (0.76/40) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 1.14 minutes.
Answer to be 1 minutes.
Answer: (A)  1
Question: An investment of Rs.800 doubled in 4 years when compounded annually. How many more years will it take to get another Rs.1600 compound interest?
(A) 1 years
(B) 6 years
(C) 4 years
(D) 5 years
(E) 3 years
Rationale: Explanatory Answer
Rs.800 invested in compound interest becomes Rs.1600 in 4 years.
The amount will double again in another 4 years.
i.e., the amount will become Rs.1600 in another 4 years.
So, to earn another Rs.1600 interest, it will take another 4 years.
Answer C
Answer: (C) 4 years
Question: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: Explanation :
Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8	---(1)
3m + 7w = 1/10	---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 × (1/400) = 1/40
Ie, 10 women can complete the work in 40 days
Answer : Option B
Answer: (B) 40
Question: What is the probability of getting exactly 2 heads in a single throw of five fair coins?
(A) 1/4
(B) 3/8
(C) 3/16
(D) 5/16
(E) 11/32
Rationale: One possible case is HHTTT.
P(HHTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C2 = 10 possible cases.
P(2 heads) = 10*1/32 = 5/16
The answer is D.
Answer: (D) 5/16
Question: If −y ≥ x, and −x < −6, then which of the following must be true?
(A) y = −6
(B) y > −6
(C) −y > 6
(D) y ≤ −6
(E) y ≥ −6
Rationale: −y ≥ x, and −x < −6
y <= -x < -6
As '-x' is less than '-6' and Y is less than or equal to '-x'
we have y < -6 which is similar to -y > 6.
C) -y>6
Answer: (C) −y > 6
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 8100
interest only for the period. The principal amount borrowed by her was
(A) Rs. 22500
(B) Rs. 10000
(C) Rs. 15000
(D) Rs. 20000
(E) None of these
Rationale: Explanation :
Principal = Rs. (100×8100 / 12×3)
=> Rs. 22500.
Answer : A
Answer: (A) Rs. 22500
Question: Johnny makes $4.75 per hour at his work. If he works 6 hours, how much money will he earn?
(A) $30
(B) $54
(C) $28.50
(D) $12
(E) $9.60
Rationale: 4.75*6=28.50. Answer is C.
Answer: (C) $28.50
Question: A man spends 3/5 of his expenditure on house rent,2/5 of his expenditure on food and 1/6 of his expenditure on conveyence.if he spent total 12000 rs.,find his expenditure on food.
(A) 4800
(B) 4000
(C) 3500
(D) 7500
(E) 2800
Rationale: expenditure=12000 rs.
expenditure on food =12000*2/5=4800 rs.
answer A
Answer: (A) 4800
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.50, in which year will commodity X cost 90 cents more than the commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 30 + 90 = $1.20 cents on commodity Y, which will take 12 years.
The answer is D.
Answer: (D) 2013
Question: A began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally?
(A) 8 months
(B) 9 months
(C) 6 months
(D) 5 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12500 : (12 – x) × 25000
or 12 : 2(12 – x)
Since profit is equally divided so
12 = 2(12 – x) or x = 6. Thus B joined after 8 months.
Answer C
Answer: (C) 6 months
Question: The area of a square is equal to seven times the area of a rectangle of dimensions 25 cm * 343 cm. What is the perimeter of the square?
(A) 810 cm
(B) 800 cm
(C) 980 cm
(D) 718 cm
(E) 860 cm
Rationale: Area of the square = s * s = 7(343 * 25)
=> s = 5 * 7 * 7 = 245 cm
Perimeter of the square = 4 * 245 = 980 cm.
Answer: C
Answer: (C) 980 cm
Question: A cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 33
(B) 88
(C) 40
(D) 99
(E) 12
Rationale: 1/4 - 1/x = 1/6
x = 12
Answer: E
Answer: (E) 12
Question: If c^2 = d^2, which of the following must be true?
(A) c = d
(B) |c| = |d|
(C) c = |d|
(D) c = −|d|
(E) c=-d
Rationale: Since c^2=d^2 we have 0=c^2 – d^2 =(c-d)*(c+d). So c=d or c=-d.
So only (A) and only (E) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.
The answer is, therefore, (B).
Answer: (B) |c| = |d|
Question: Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
(A) 120
(B) 126
(C) 252
(D) 1200
(E) 1260
Rationale: My ans is 10C3 = 120
A
Answer: (A) 120
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) Rs.10000
(B) Rs.12800
(C) Rs.6000
(D) Rs.8000
(E) Rs.13000
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
ANSWER:B
Answer: (B) Rs.12800
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.125
(C) 0.128
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.5
Therefore, probability of no rain = 0.5
0.5*0.5*0.5 = 0.125
Hence B
Answer: (B) 0.125
Question: If 12 : 18 :: x : 9, then find the value of x
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Explanation:Treat 12:18 as 12/18 and x:9 as x/9, treat :: as = So we get 12/18 = x/9=> 18x = 108=> x = 6 Option C
Answer: (C) 6
Question: A reduction of 21% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) s.2.66
(B) s.2.4
(C) s.2.5
(D) s.2.2
(E) s.2.1
Rationale: 100*(21/100) = 21 --- 10
? --- 1 => Rs.2.1
100 --- 79
? --- 2.1 => Rs.2.66
Answer:A
Answer: (A) s.2.66
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8
Question: The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?
(A) 50%
(B) 40%
(C) 33 1⁄3%
(D) 25%
(E) 12 1⁄2%
Rationale: Product of x and y = xy
If the value of x is increased by 50% , value of y needs to be = xy/(1.5 x ) = 2/3 y
Decrease in value of y = y - 2/3 y = 1/3 y
% decrease in value of y = (1/3 y)/y * 100%
=33 1⁄3%
Answer C
Answer: (C) 33 1⁄3%
Question: The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
(A) 50
(B) 80
(C) 100
(D) 110
(E) 130
Rationale: Let the number of candidate who passed = y
Then, 39y + 15(120 - y) =120 x 35
⇒ 24y= 4200 -1800
∴ y= 2400 / 24 = 100
C
Answer: (C) 100
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,710 minutes earlier? (Assume standard time in one location.)
(A) 6:22
(B) 6:24
(C) 6:27
(D) 6:30
(E) 6:32
Rationale: 6:27minus 2,880,710in any way must end with 7, the only answer choice which ends with 7 is C.
Answer: C.
Answer: (C) 6:27
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.60 per metre.
(A) 2399
(B) 3888
(C) 2999
(D) 5808
(E) 6072
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.60) = Rs. 6072.
Answer: E) 6072
Answer: (E) 6072
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
(A) 50
(B) 88
(C) 77
(D) 66
(E) 51
Rationale: 5 * 46 – 4 * 45
= 50
Answer: A
Answer: (A) 50
Question: By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c?
(A) 38020
(B) 38000
(C) 38028
(D) 29400
(E) 38192
Rationale: CP + CP/2 = 45000
CP = 30000
SP = 30000*(98/100)
=29400
Answer:D
Answer: (D) 29400
Question: A is a set containing 8 different positive odd numbers. B is a set containing 7 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
(A) The range of B is even.
(B) The mean of A is even.
(C) The mean of B is even.
(D) The range of A is equal to the range of B.
(E) The median of B is equal to the mean of B.
Rationale: Given: A is a set containing 8 different positive odd numbers
Easily inferred: B is a set containing 7 differentoddnumbers
(A) The range of B is even. - Always even, since it is a difference of two odd numbers
(B) The mean of A is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of B is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of A is equal to the range of B.
(E) The median of B is equal to the mean of B
Option C.
Answer: (C) The mean of B is even.
Question: Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37!
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: 3,8 and 7 have a power cycle of 4, i.e. the units digit in each case will repeat after every 4th power.
For eg : 3^1 = 3, 3^2 = 9 , 3^3 = 27 , 3^4 = 81, 3^5 = 243
All the powers given(1!+2!+....), are multiples of 4. It is so because the last 2 digits of the total sum will be 00,for each one of them, which make them divisible by 4.
Thus, the given problem boils down to 3^4+8^4+7^4=1+6+1=8
Thus, the units digit is 8.
ANSWER:D
Answer: (D) 8
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (4/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
(A)  2/5
(B)  1/2
(C)  11/16
(D)  5/7
(E)  3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 4/8*c:
(b+c)/2 = (4/8)*c
b = 0
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (0)/2 = 0
Median = (a + c)/2 = (0 + c)/2 = c/2 = (1/2)*c (ANSWER B)
Answer: (B)  1/2
Question: The average height of 50 pupils in a class is250 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is __________ .
(A) 151 cm
(B) 351 cm
(C) 241 cm
(D) 251 cm
(E) 261 cm
Rationale: Total height = 250 * 50 = 12500 cm.
New average = [12500 - 5 * 146 + 5 * 156 ] / 50 =251 cm.
ANSWER:D
Answer: (D) 251 cm
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 17 years
(C) 97 years
(D) 27 years
(E) 29 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: (A) 20 years
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
(A) 84 degrees
(B) 64 degrees
(C) 54 degrees
(D) 44 degrees
(E) 24 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8.
Temperature on the 5th day = 8x = 64 degrees.
Answer: B
Answer: (B) 64 degrees
Question: In how many years will a sum of money double itself at 10% per annum?
(A) 2 years 4 months
(B) 4 years 2 months
(C) 8 years 4 months
(D) 10 years 8 months
(E) None
Rationale: Sol.
Let sum = x. Then, S.I. = x
∴ Time = [100 * S.I. / P*R] = [100 * x / x * 12] years
= 8 1/3 years = 8 years 4 months.
Answer C
Answer: (C) 8 years 4 months
Question: A certain car averages 35 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28
(B) 30
(C) 33
(D) 39
(E) 38
Rationale: Answer D
No of Miles per Gallon = Total no of miles/Total no of Gallons
=10+50/(10/35+50/40) ~ 39.06
Answer: (D) 39
Question: Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 10.1 sec
(C) 10.6 sec
(D) 11.88 sec
(E) 10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 190 = 330 m.
Required time = 330 * 9/250
= 11.88 sec.
Answer:D
Answer: (D) 11.88 sec
Question: A 12% stock yielding 10% is quoted at:
(A) 223
(B) 2778
(C) 277
(D) 120
(E) 288
Rationale: Explanation:
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 12, money invested = = Rs. 120.
Market value of Rs. 100 stock = Rs. 120.
Answer: D) 120
Answer: (D) 120
Question: What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
(A) 1/6
(B) 1/4
(C) 1/2
(D) 21/216
(E) 32/216
Rationale: The other way would be to list out each option.
The options for a sum of 8: (6,1,1) has 3 options ie (6,1,1), (1,6,1), (1,1,6); (5,2,1) has 6 options, (4,3,1) has 6 options, (4,2,2) has 3 options, (3,3,2) has 3 options. We have 21 options to get 8.
The options for a sum of 14: (6,4,4) has 3 options, (6,5,3) has 6 options, (6,6,2) has 3 options, (5,5,4) has 3 options. We have 15 options to get 14.
Total: 21+15= 36/216 = 1/6.
Answer A.
Answer: (A) 1/6
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $109.90, what was the total value of the item?
(A) $1940
(B) $2150
(C) $2360
(D) $2570
(E) $2780
Rationale: Let x be the value of the item.
0.07*(x-1000) = 109.90
x = 2570
The answer is D.
Answer: (D) $2570
Question: From a group of 17 astronauts that includes 8 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
(A) 248
(B) 258
(C) 268
(D) 278
(E) 288
Rationale: number of astronauts with previous experience = 8
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(8C1)*(9C2)
=8*36= 288
Answer : E
Answer: (E) 288
Question: At a local supermarket, a box of cereal usually costs 5 dollars. This week, the supermarket sells the box of cereal for 3 dollars. How much money will you save if you buy this cereal at this supermarket?
(A) 5 dollars
(B) 3 dollars
(C) 4 dollars
(D) 2 dollars
(E) 1 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 5 - 3 = 2 dollars
Option D
Answer: (D) 2 dollars
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 39000, then the share of B is?
(A) 18000
(B) 24000
(C) 24005
(D) 24009
(E) 24002
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 39000
Share of B = 6/13 (39000) = Rs. 18000
Answer: A
Answer: (A) 18000
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 7 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test?
(A) a 40
(B) b 400
(C) c 5^8
(D) d 8^5
(E) e 5^7
Rationale: different ways to solve each question is 5.
So, 5*5*5*5.. 7 times ----> 5^7
Answer will be E
Answer: (E) e 5^7