mathewhe/aqua_rat huggingface dataset:
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 44, what will be his grade at the end of the third year?
(A) 44
(B) 56
(C) 82
(D) 75
(E) 80
Rationale: Cool question!
There's a lot of information given here, so let's eat slow here.
Joey scores a 44 at the end of his first year. That means that he's currently 22 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).
Now, come next year, or his second year at this psychology school, he's technically 23 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.
Well, his second year is then going to be 23(2) + 22 = 68.
Now let's tackle the main question: what's his grade going to be the third year?
Well, he will be at an age of 22 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (24x2), plus half of his previous year's grade (as calculated for his second year, his grade is 68; therefore, 68/2)
Having said that, the final answer would be 24(2) + 68/2 = 48 + 34 = 82 --> (C)
Answer: (C) 82
Question: 2^(2x/3) = 2^(x/2)
What is the value of x ?
(A) 2
(B) 2/3
(C) 1
(D) 0
(E) -2
Rationale: 2x/3 = x/2
4x = 3x
4x-3x=0; x=0
Ans: D
Answer: (D) 0
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 370440, then population in 1978 was?
(A) 120000
(B) 228788
(C) 266891
(D) 267689
(E) 320000
Rationale: X * (105/100) * (105/100) * (105/100) = 370440
X = 370440/1.157625
X = 320000
Answer:E
Answer: (E) 320000
Question: The product of the prime integers between 33 and 40, inclusive, is:
(A) 50! – 40!
(B) 99,029
(C) 1,221
(D) 2,021
(E) 2,000
Rationale: only prime number bet ween 43 and 50 inclusive are 43 and 47
thus 33*37 = 1221
Ans: C
Answer: (C) 1,221
Question: Simplify: 896 x 896 - 204 x 204
(A) 716200
(B) 761200
(C) 712600
(D) 710612
(E) 710262
Rationale: = (896)^2 - (204)^2
= (896 + 204) (896 - 204)
= 1100 x 692 = 761200.
Answer is B
Answer: (B) 761200
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -
(A) 1/26
(B) 3/52
(C) 15/26
(D) 11/26
(E) 1/13
Rationale: Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 âˆ© E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
ANSWER IS A
Answer: (A) 1/26
Question: Of the 45 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
(A) 15
(B) 20
(C) 30
(D) 40
(E) 45
Rationale: This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 15 30
Other 1 15 15
Total 3 15 45
Answer is 30. i.e C
Answer: (C) 30
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 5
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: (B) 4
Question: A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
ANSWER:D
Answer: (D) 10
Question: 1024 people in village 720 speak tamil,562 speak english while 346 speak both. person who don not speack english or tamil speak hindi. what is probibility that person speak hindi
(A) 13/128
(B) 12/128
(C) 11/126
(D) 11/127
(E) 11/128
Rationale: n(t)=720
n(e)=562
n(t^e)=346
n(tUe)=720+562-346=936
Now, n(h)=1024-936=88
p(h)=88/1024=11/128=0.085
ANSWER:E
Answer: (E) 11/128
Question: If a2+b2=177and ab=54 then find the value of a+b/a-b?
(A) 5
(B) 4
(C) 2
(D) 1
(E) 3
Rationale: (a+b)2=a2+b2+2ab=117+2*24=225
a+b=15
(a-b)2=a2+b2-2ab=117-2*54
a-b=3
a+b/a-b=15/3=5
Answer is A.
Answer: (A) 5
Question: The area of rhombus is 150 cm square. The length of one of the its diagonals is 10 cm. The length of the other diagonal is:
(A) 15 cm
(B) 20 cm
(C) 25 cm
(D) 30 cm
(E) None of these
Rationale: Explanation:
We know the product of diagonals is 1/2*(product of diagonals)
Let one diagonal be d1 and d2
So as per question
1/2∗d1∗d2=150
1/2∗10∗d2=150
d2=150/5=30
Option D
Answer: (D) 30 cm
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
(A) 4.5 gallons
(B) 8 gallons
(C) 9.5 gallons
(D) 10 gallons
(E) 11 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 / 40 = 4.5 *1 gallon correct answer A
Answer: (A) 4.5 gallons
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 8 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 45
(B) 65
(C) 75
(D) 89
(E) 80
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 8 = 76
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 76 + 4 = 80
E
Answer: (E) 80
Question: A man can row upstream at 7 kmph and downstream at 33 kmph, and then find the speed of the man in still water?
(A) 11
(B) 77
(C) 30
(D) 20
(E) 34
Rationale: US = 7
DS = 33
M = (33 + 7)/2 = 20
Answer:D
Answer: (D) 20
Question: (1+0.0001)/(0.04+100)
The value of the expression above is closet to which of the following?
(A) 0.0001
(B) 0.01
(C) 0.1
(D) 1
(E) 10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 1 and the denominator is very close to 10, hence the value of the fraction is very close to 1/100=0.01.
Answer: B.
Answer: (B) 0.01
Question: The price of a certain painting increased by 20% during the first year and decreased by 25% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
(A) 102%
(B) 90%
(C) 120%
(D) 85%
(E) 95%
Rationale: Easiest thing to do: Assume that price is 100
Price at the end of yr 1: 100+ 20 = 120
Price at the end of year 2 = 120 - 120*0.25 = 120*0.75 = 90
Hence required answer = (90/100)*100% = 90%
Answer is B.
Answer: (B) 90%
Question: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 9
Rationale: For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?
Used brute force on this one to calculate. Not sure if there is a quicker way.
1+3=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out
Answer: B
Answer: (B) 2
Question: 1/4+[(2/3*3/8)+4]-9/16=
(A) 63/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Rationale: 1/4+[(2/3*3/8)+4]-9/16=
1/4+[(1/4)+4]-9/16=
1/4+[17/4]-9/16=
4/16 + 68/16 - 9/16 = 63/16
A
Answer: (A) 63/16
Question: Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 16 sec
(B) 13 sec
(C) 17 sec
(D) 21 sec
(E) 23 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 12 + 6 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer: B
Answer: (B) 13 sec
Question: A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1 and 2, how many palindromes are possible?
(A) 8
(B) 12
(C) 16
(D) 24
(E) 32
Rationale: There are 2 choices for each of the first three digits.
The number of possible palindromes is 2^3=8.
The answer is A.
Answer: (A) 8
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many E digits does this integer consists of?
(A) 150
(B) 339
(C) 342
(D) 359
(E) 362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer E= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: (C) 342
Question: If |y−12|<112|y−12|<112, which of the following could be a value of y?
(A) -11
(B) -11/2
(C) 11/2
(D) 11
(E) 22
Rationale: |y−12|<112|y−12|<112, is equivalent to −112<y−12<112−112<y−12<112.
Add 1212 to each part of the inequality: −112+12<y<112+12−112+12<y<112+12 --> −5<y<6−5<y<6.
Only answer C is from this range.
Answer: C.
Answer: (C) 11/2
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 88
(D) 66
(E) 23
Rationale: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2 = 10 kmph. Answer:A
Answer: (A) 10
Question: The sum of two numbers is 40 and their product is 1050. What will be the sum of their reciprocals?
(A) (4/105)
(B) (11/210)
(C) (35/4)
(D) (75/8)
(E) None
Rationale: Solution
x+y=40 xy=1050 1/x+1/y=x+y/xy 40/1050 = (4/105).
Answer A
Answer: (A) (4/105)
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
(A) 16:15
(B) 15:16
(C) 12:11
(D) 11:13
(E) 13:18
Rationale: Let the Face Value of Stock giving dividend 9% be Rs. x, whose Market Value is Rs.96.
Let the Face Value of Stock giving dividend 12% be Rs. y, whose Market Value is Rs.120.
By given formula,
Face Value * Dividend % / Market Value = Annual income.
Annual Income from 1st Stock = 9x/96.
Annual Income from 2nd Stock = 12y/120.
To obtain equal dividends from both,
Annual Income from 1st Stock = Annual Income from 2nd Stock.
= 9x/96 = 12y/120.
= x/y = 96/90.
We find GCD of 96, 90 = 6.
= x/y = 16*6 / 15*6.
= Required ratio = x:y = 16:15.
answer : A
Answer: (A) 16:15
Question: 0.05 x 0.03 = ?
(A) 0.00015
(B) 0.015
(C) 0.0015
(D) 0.15
(E) 1.5
Rationale: 5 x 3 = 15.
Sum of decimal places = 4
0.05 x 0.03 = 0.0015
Answer: Option C
Answer: (C) 0.0015
Question: Dan's age after 18 years will be 8 times his age 3 years ago. What is the present age of Dan?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Let Dan's present age be x.
x+18 = 8(x-3)
7x = 42
x = 6
The answer is B.
Answer: (B) 6
Question: 81,162,49,98,25,50,55
(A) 110
(B) 127
(C) 129
(D) 128
(E) 131
Rationale: 81*2=162
49*2=98
25*2=50
55*2=110
ANSWER:A
Answer: (A) 110
Question: A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 3 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
(A) 2.4 kg or 80%
(B) 1.4 kg or 88%
(C) 3.4 kg or 60%
(D) 4.9 kg or 81.4%
(E) 1.4 kg or 60%
Rationale: Right Answer Explanation:
x : 6
y : 100
90
10 : 90 – y
(90-y)/6 = 10/x = ………..(1)
In the second case,
x 3
y 90
84
6 84-y
Therefore (84-y)/3 = 6/x ………..(2)
Dividing (1) and (2)
=
270 – 3y = 840 – 10y
7y = 570
y = 81.4
x = 60/(90-80) = 60/10 = 6 kg
Quantity of zinc in x = 81.4% of x
= 0.814 6
= 4.9 kg
Weight and percentage of zinc is 4.9 kg or 81.4%
D
Answer: (D) 4.9 kg or 81.4%
Question: A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
(A) 12 min
(B) 34 min
(C) 32 min
(D) 45 min
(E) 29 min
Rationale: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 ÷ 150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8 × 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
We can also find the final answer as follows
4.5 x 8 = 32 minutes
correct answer is C) 32 min
Answer: (C) 32 min
Question: Set G consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set G by 50, set Y is derived by multiplying each term in set G by 1.5, and set Z is derived by dividing each term in set G by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
(A)  X, Y, Z
(B)  X, Z, Y
(C)  Y, Z, X
(D)  Y, X, Z
(E)  Z, Y, X
Rationale: Set G - {2, 4, ..., 100};
Set X - {-48, -46, ..., 50};
Set Y - {3, 6, ..., 150};
Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.
If we add or subtract a constant to each term in a set the SD will not change, so sets G and X will have the same SD.
If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set G and set Z will have 4 times less SD than set G (note SD can not be negative so SD of Z wil be SD of G divided by 4 not by -4).
So, the ranking of SD's in descending order is: Y, G=X, Z.
Answer: D.
Answer: (D)  Y, X, Z
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer C
Answer: (C) 15
Question: A military garrison in a wild frontier has 60 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 30 men. How long will the provisions last?
(A) 13 1/3
(B) 12 1/3
(C) 11 3/3
(D) 12 1/2
(E) 12 3/4
Rationale: Total provisions=600*26*7=10920
Provisions used for in 6 weeks=6*7*600=2520
remaining provisions=8400
remaining provisions need to be split between 90(60+30) people.
Number of provisions per person= 8400/90
we need to find the answer in terms of weeks=(8400/90)/7=40/3
Answer:A
Answer: (A) 13 1/3
Question: By selling an article at Rs.900, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) s.600
(B) s.480
(C) s.500
(D) s.540
(E) s.550
Rationale: SP = 900
Profit = 25%
CP = (SP)*[100/(100+P)]
= 900 * [100/125]
= 720
Loss = 25% = 25% of 720 = Rs.180
SP = CP - Loss = 720 - 180 = Rs.540
ANSWER:D
Answer: (D) s.540
Question: xy=2 then what is (2^(x+y)^2) / (2^(x-y)^2)
(A) 2
(B) 4
(C) 8
(D) 16
(E) 256
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
8
2^8 = 256
Answer E
Answer: (E) 256
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value A of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
A=z-x = x+9-x= 9
Ans:D
Answer: (D) 9
Question: I have 150 pieces of cake. There are 50 friends in my house. I would like to give each friend the same amount of cake, how much should I give to each friend?
(A) 12
(B) 7
(C) 9
(D) 15
(E) 3
Rationale: 150/50 = 3
The answer is E.
Answer: (E) 3
Question: Working together, Jose and Jane can complete an assigned task in 12 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 48 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
(A) 25 days
(B) 30 days
(C) 60 days
(D) 65 days
(E) 36 days
Rationale: Assume:
Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day
Together, they does (x+y)/xy job in a day. This is equals to 1/20. So
(x+y)/xy = 1/12
12(x+y) = xy
Next, we're told 1 job takes 48 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.
x/2 + y/2 = 48
x+y = 96
So
xy = 1152
The answer choices are:
25 days
30 days
60 days
65 days
36 days
From the answer choices, So I'll go for 36 days for Jose and 32 days for Jane.
Answer : E
Answer: (E) 36 days
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ?
(A) 127.5 m
(B) 254 m
(C) 184 m
(D) 212 m
(E) 314 m
Rationale: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 x 212.5)/1000 = 127.5 m.
ANSWER IS A
Answer: (A) 127.5 m
Question: There are a total of 11 students in Mr. Michael's gym class. Over the course of a badminton unit, each of the 11 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
(A) 58
(B) 51
(C) 52
(D) 55
(E) 59
Rationale: there are 11 students , if each play with all other members .
then total games can be calculated as 10+9....+1 = 55.
alternate approach is to choose 2 distinct out of 11 = 11c2 = 55
Answer is D.
Answer: (D) 55
Question: J is faster than P. J and P each walk 24 km. Sum ofthe speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let j's speed is x then p's speed would be 7-x.
and given,
sum of time taken by them is 14 hours
=>(24/x)+(24/(7-x)=14
=>x=4,3
therefore j's speed will be 4 as j walks faster than p.
ANSWER:A
Answer: (A) 4
Question: A box contains 2 red balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 1/4
(B) 7/5
(C) 1/2
(D) 5/8
(E) 2/3
Rationale: My complicated version of your simple approach
Let the 5 black balls be BBBBB and 2 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (7!)/ (5!x2!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 6 slots and 4 Black (BBBB) and 2 Red (RRR)
They can be arranged in (7!)/ (4!x2!)
Hence required probability = [(7!)/ (5!x2!)]/[(6!)/ (4!x2!)]=7/5
B
Answer: (B) 7/5
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 55%. Staff are allowed a further 50% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.275D
(B) 0.225D
(C) 0.265D
(D) 0.245D
(E) 0.205D
Rationale: Effective discount = a + b + ab/100 = - 55 - 50 + (-55)(-50)/100 = 77.5
Sale price = D * ( 1 - 77.5/100)
Sale price = .225 * D
Answer (B)
Answer: (B) 0.225D
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will b
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
C)
Answer: (C) 7
Question: Two trains of equal length, running with the speeds of 60 and 90 kmph, take 50 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) 3.2
(B) 2.6
(C) 6.6
(D) 32.2
(E) 42.2
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 90 = 150 * 5/18
T = 2500/9 * 18/750 = 6.6 sec.Answer: C
Answer: (C) 6.6
Question: If a^2x = b^y, then
(A) log a/b= x/y
(B) log a/ log b = x/y
(C) log a/ log b = y/2x
(D) log b/a = x/y
(E) log b/a = y/x
Rationale: a^2x = b^y => log a^2x = log b^y => 2x log a = y log b
=> log a/ log b = y/2x
ANSWER:C
Answer: (C) log a/ log b = y/2x
Question: A can complete the job in 4 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
(A) 1/7
(B) 3/10
(C) 1/2
(D) 5/6
(E) 8/9
Rationale: A=1/7
Answer: (A) 1/7
Question: A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $20,000, what is the total profit?
(A) $38,000
(B) $42,000
(C) $46,000
(D) $50,000
(E) $54,000
Rationale: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.
Let the total profit be x.
x * 8/20 = 20000
x = 20000*20/8 = 50,000.
The answer is D.
Answer: (D) $50,000
Question: the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: t2 + t19 = t8 + t15 + t12
=> a+d + a+18d = a+7d + a+14d + a+11d
=> a + 13d = 0
=> t14 = 0 i.e. 14th term is zero.
ANSWER:C
Answer: (C) 14
Question: A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?
(A) 15%
(B) 5%
(C) 10%
(D) 25%
(E) 19%
Rationale: let the market price of each pen be Rs 1
then,C.P of 40 pens = Rs 36
S.P of 40 pens =99% of Rs 40=Rs 39.60
profit %=((3.60*100)/36) %=10%
Answer is C.
Answer: (C) 10%
Question: In an examination 80% failed in Math and 20% failed in French. If 24% failed in both. What % of students passed in both.
(A) 25%
(B) 24%
(C) 20%
(D) 30%
(E) 10%
Rationale: Passed in Math = 100 - 80 = 20%
Passed in French = 100 - 20 = 80%
Students who passed Math or French = 100 -24 = 76%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 20+80-76 =24%
ANSWER:B
Answer: (B) 24%
Question: The grade point average of the entire class is 80. If the average of one fourth of the class is 92, what is the average of the rest of the class?
(A) 73
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
80x = (1/4)92x + (3/4)(P)x
320 = 92 + 3P
3P = 228
P = 76.
The answer is D.
Answer: (D) 76
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 66, and the three numbers in order are?
(A) 116,58,36
(B) 98,49,33
(C) 126,63,36
(D) 108,54,36
(E) None of these
Rationale: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 66
By solving we will get x = 108.
Hence A= 108
B= 108/2= 54
C= 108/3 = 36
Answer : D
Answer: (D) 108,54,36
Question: A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
(A) ⁹C₂
(B) ³C₂
(C) ¹⁶C₂
(D) ¹²C₂
(E) ¹⁴C₂
Rationale: Explanation:
Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.
ANSWER IS C
Answer: (C) ¹⁶C₂
Question: Given a unit square, two points are chosen uniformly at random within the square. Compute
the probability that the line segment connecting those two points touches both diagonals of the
square.
(A) 1/4
(B) 2/4
(C) 3/4
(D) 4/4
(E) 5/4
Rationale: If we draw both diagonals, then the desired event happens if and only if the two
points appear in dierent triangles that do not share an edge. Given the triangle where one
point lands, the other point has probability
1/4
of landing in the other triangle.
correct answer A
Answer: (A) 1/4