mathewhe/aqua_rat huggingface dataset:
Question: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
(A) 55/119
(B) 55/221
(C) 55/223
(D) 55/227
(E) 56
Rationale: We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = \inline {\color{Black}26C_{2}} = = 325, n(B)= \inline {\color{Black}4C_{2}} = = 6 and n(A∩B) = \inline {\color{Black}2C_{2}} = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 =
B
Answer: (B) 55/221
Question: When the price of an article was reduced by 15% its sale increased by 80%. What was the net effect on the sale?
(A) 44% increase
(B) 44% decrease
(C) 53% increase
(D) 66% increase
(E) 66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 15%, the new price is 0.85p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.85p)(1.8n) = 1.53np, which is 1.53 times the old revenue, so is 53% greater.
ANSWER:C
Answer: (C) 53% increase
Question: Which number comes next in the series
5 12 24 36 ?
(A) 52
(B) 55
(C) 60
(D) 120
(E) 23
Rationale: A
52
sum of consecutive prime numbers
(2+3 , 5+7 , 11+13 , 17+19 , 23+29)
Answer: (A) 52
Question: How many ways are there to lay four balls, colored red, black, blue and green in a row?
(A) 11
(B) 33
(C) 44
(D) 23
(E) 77
Rationale: Answer:B
Answer: (B) 33
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200
(B) 210
(C) 120
(D) 1000
(E) 20000
Rationale: Required selection = select 3 consonants from 7 and 2 vowels frm 4
= 7C3 * 4C2
= 210
As we have to form 5 letter word the above combination of consonants and vowels can be done in 5! = 120 different ways
Required no. of ways = 210 * 120
= 25200
Ans - A
Answer: (A) 25200
Question: X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.
infer that
FOR any given # 1 and the # itself are the definite factors.
Knowing above concepts:
product of X,Y, and Z = XYZ
divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8
ANSWER "C"
Answer: (C) 8
Question: Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
(A) 10.2 Days
(B) 15.2 Days
(C) 16.2 Days
(D) 18 Days
(E) 20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane = 4 bricks per day
Ashley = 1 brick per day
Together = 5 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 16
Remaining bricks = 40 - 24= 16
So together, they would take 16/5 = 3.2
Total no. of days = 8 + 4 + 3.2 = 15.2
Answer is B
Answer: (B) 15.2 Days
Question: Evaluate 35 / .07
(A) 400
(B) 500
(C) 505
(D) None of these
(E) 506
Rationale: Explanation:
35/.07 = 3500/7 = 500
Option B
Answer: (B) 500
Question: The number N is 7,6H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: A
Answer: (A) 1
Question: Rs.585 is divided amongst A, B, C so that 4 times A's share, 6 times B's share and 3 times C's share are all equal. Find C's share?
(A) 260
(B) 150
(C) 817
(D) 716
(E) 616
Rationale: A+B+C = 5854A = 6B = 3C = xA:B:C = 1/4:1/6:1/3= 3:2:44/9 * 585= Rs.260Answer: A
Answer: (A) 260
Question: a = 2^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 1 different values and answer is B....
Answer: (B) One
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 360 meters
(C) 280 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 16 * 20 = 320 = Length of train
Length of platform = 600 - 320 = 280
Answer: C
Answer: (C) 280 meters
Question: IN Common Wealth Games an athlete runs 400 meters in 24 seconds. Hisspeed is ?
(A) 25 km/hr
(B) 27 km/hr
(C) 60.60 km/hr
(D) 32 km/hr
(E) None of these
Rationale: Explanation :
(400/1000)/(24/3600)=60.60 km/hr
Answer : C
Answer: (C) 60.60 km/hr
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^28, then n =
(A) 3
(B) 6
(C) 12
(D) 27
(E) 24
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^28
=> 4 x 2^2n = 4^28 = 2^56
=> 2^2 x 2^2n = 2^56
=> 2^(2n+2) = 2^56
=> 2n+2 = 56=> n =27
So. Answer will be D.
Answer: (D) 27
Question: It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minutes to prepare one omelet. It takes Mitch N/2 minutes to prepare 2 omelets. If Jim, Cole and Mitch together prepare a total of 30 omelets in 40 minutes, then how many minutes would it take Mitch alone to prepare 30 omelets?
(A) 70
(B) 120
(C) 140
(D) 160
(E) 280
Rationale: Cole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).
Say the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.
Then, from (time)(rate) = (job done):
(40 minutes)(x + 2x + 4x) = (30 omelets);
(40 minutes)(7x) = (30 omelets);
Since it takes 40 minutes to prepare 30 omelets at the rate of 7x omelet/minute, then it would take 40*7/4 = 70 minutes to prepare the same 30 omelets at the rate of 7x*4/7 = 4x omelet/minute (the rate of Mitch).
Or:
(40 minutes)(7x) = (30 omelets);
(40*7/4 minutes)(7x*4/7) = (30 omelets);
(70 minutes)(4x) = (30 omelets);
Answer: A.
Answer: (A) 70
Question: The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
(A) 2m
(B) 2.5m
(C) 1.5m
(D) 1.25m
(E) 1m
Rationale: The volume of the earth removed is 5*5*3 = 75 m^3.
The remaining area of the field is 10*10 - 5*5 = 75 m^2.
75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height) = (volume)/(area) = 75/75 = 1 m.
Answer: E
Answer: (E) 1m
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
(A) a)82
(B) b)84
(C) c)85
(D) d)87
(E) e)90
Rationale: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: B)
84=8^2+4^2+2^2
Answer: B.
Answer: (B) b)84
Question: A bag contains 8 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 2/3
(C) 5/8
(D) 1/4
(E) 5/7
Rationale: Total number of balls = 8+6 = 14
number of white balls = 8
Probability = 8/14 = 4/7
Answer is A
Answer: (A) 4/7
Question: A farmer planned to plough a field by doing 120 hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule. What is the area of the field?
(A) 1420
(B) 1430
(C) 1450
(D) 1440
(E) 1460
Rationale: First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is 25100⋅120=30 hectares, therefore 120+30=150 hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is 120⋅x hectares. On the other hand, we get the same area if we add 120⋅2 hectares to 150(x−4) hectares. Then we get the equation
120x=120⋅2+150(x−4)
x=12
So, the job was initially supposed to take 12 days, but actually the field was ploughed in 12 - 2 =10 days. The field's area is 120⋅12=1440 hectares.
Answer is D.
Answer: (D) 1440
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 28
(B) 27
(C) 22
(D) 34
(E) 20
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer:D
Answer: (D) 34
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 7 employees to 2 different offices?
(A) 215
(B) 310
(C) 343
(D) 243
(E) 123
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 7*7*7=7^3=343.
Answer: C.
Answer: (C) 343
Question: If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?
(A) x
(B) x^2
(C) x^3
(D) 3x
(E) x + x^2
Rationale: x + x^2 + x^3 = odd
Since each is a power of x, x has to be odd
On checking the options, only
x + x^2 = odd + odd = even
Correct option: E
Answer: (E) x + x^2
Question: If it would take one machine 15 minutes to fill a large production order and another machine 25 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 4 1/60
(B) 5
(C) 5 5/11
(D) 5 1/2
(E) 9 3/8
Rationale: Since , Machine 1-M1 take 15 mins to fill the order
The work done by M1 in a min = 1/15
Machine 2- M2 take 25 mins to fill the same order
and work done by M2 in a min = 1/25
Total work done by M1 and M2 in a min = 1/15 + 1/25 = 8/75
Time needed for M1 and M2 to complete the order = 75/8 = 9 3/8
Answer E
Answer: (E) 9 3/8
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
(A) 8
(B) 15
(C) 16
(D) 18
(E) 19
Rationale: Capacity of the tank = (12 x 13.5) liters = 162 liters.
Capacity of each bucket = 9 liters.
Numbers of buckets needed = (162/9) = 18
ANSWER:D
Answer: (D) 18
Question: Which of the following number will completely divide (36^9)-1?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 4
Rationale: x^n - 1 will be divisible by x+1 only when n is even.
36^9 - 1 = (6^2)^9 - 1 = 6^18 - 1 which is divisible by 6+1 i.e. 7
Answer is C
Answer: (C) 7
Question: If x is a positive number and 1/3 the square root of x is equal to 3x, then x =
(A) 1/3
(B) 1/9
(C) 1/81
(D) 1
(E) 81
Rationale: 1/3 of sqrt(x) = 3x, which means that sqrt(x) = 9x
or x = 81x^2 -> divide by x
1=81x
x=1/81
C.
Answer: (C) 1/81
Question: In a software company 4/10 of people know C++, 2/4 of them know java, 2/8 of them know neither,find the total possibility to know C++?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Assume 100 persons in a company
person knows c++=4/10=100*4/100=20 persons
person knows java=2/4=100*2/4=50 persons
neither=2/8=100*2/8=25 persons
according to our assumption 100 person=20+50+25=95 person covered(5 remaining)
so,total possibility=20 person(c++)+5(remaining)=25 persons
which is 25/100=1/4
ANSWER:A
Answer: (A) 1/4
Question: Percentage of profit earned by selling a book for $1380 is equal to the percentage loss incurred by selling the same book for $1020. What price should the book be sold to make 20% profit?
(A) $1260
(B) $1440
(C) $1500
(D) $1680
(E) $2000
Rationale: Let C.P. be Rs. x.
Then, (1380 - x)	x 100 =(x - 1020) x 100
1380 - x = x - 1020
2x = 2400
x = 1200
Required S.P. = 120% of 1200 = 1.20 x 1200 = $1440
Answer : B
Answer: (B) $1440
Question: In how many ways can five boys and three girls sit in a row such that all girls sit together?
(A) A)1972
(B) B)9022
(C) C)2880
(D) D)1097
(E) E)4320
Rationale: Treat all girls as one unit. Now there are six students and they can be arranged in 6! ways. Again three girls can be arranged among themselves in 3! ways.
Required number of arrangements
= 6! * 3! = 720* 6
= 4320.
Answer:E
Answer: (E) E)4320
Question: If (2^x)(3^y) = 216, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
(A) 12
(B) 24
(C) 48
(D) 96
(E) 144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=3, y=3. now quickly 2^2(3^1)=12. Than answer should be number 1.
A
Answer: (A) 12
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 2 1/5 Km
(B) 3 1/5 Km
(C) 3 2/5 Km
(D) 3 3/5 Km
(E) 4 1/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
B
Answer: (B) 3 1/5 Km
Question: Village A’s population is 300 greater than Village B's population. If Village B’s population were reduced by 600 people, then Village A’s population would be 4 times as large as Village B's population. What is Village B's current population?
(A) 900
(B) 1000
(C) 1100
(D) 1200
(E) 1300
Rationale: A = B+300.
A=4(B-600).
4(B-600)=B+300.
3B=2700.
B=900.
The answer is A.
Answer: (A) 900
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
(A) 39.55$
(B) 40.63$
(C) 41.63$
(D) 42.15$
(E) 43.15$
Rationale: Let x be the amount the most their food can cost.
x + 0.07x + 0. 15x = 50
Solving for x, x = 40.98$, this is the maximum amount that can be used for food.
Hence 40.63$ is the maximum value less than 40.98$
Hence Option B
Answer: (B) 40.63$
Question: The total of the ages of Mahesh, Suresh, Ramesh is 102 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
(A) 32years
(B) 42years
(C) 45years
(D) 35years
(E) 30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 102
x = 8
Ramesh present age = 4*8+10 = 42 years
Answer is B
Answer: (B) 42years
Question: How many digits will be there to the right of the decimal point in the product of 98 and .08216 ?
(A) 5
(B) 6
(C) 9
(D) 7
(E) 8
Rationale: Product of 98 and .08216 is 8.05168.
Therefore number of digits to right of decimal point is 5
Answer is A.
Answer: (A) 5
Question: If two numbers are in the ratio 5:6. If 10 is added to both of the numbers then the ratio becomes 6:7 then find the smallest number?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
5:6
5x + 10 : 6x + 10 = 6 : 7
7[5x + 10] = 6[6x + 10]
35x + 70 = 36x + 60
36x - 35x = 70 - 60
x = 10
Then smallest number is =5
5x = 50
Answer: Option E
Answer: (E) 50
Question: The king of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the king must sit in the center chair, how many different seating arrangements are possible for the 5 people?
(A)  4
(B)  5
(C)  24
(D)  20
(E)  120
Rationale: IMO C
Given that one chair is taken, i think the remaining 4 dignitaries can be arranged 4!=24.
Answer: (C)  24
Question: X, Y and Z, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2350, what will be Z's share of the earnings?
(A) $525
(B) $550.50
(C) $1080.02
(D) $522.3
(E) $1020.2
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of Z is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
Z's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2350 = $522.3
hence:D
Answer: (D) $522.3
Question: 3 no. leave remainders of 43, 47 & 49 on division by N. The sum of the three no.'s leaves a remainder 9 on division by N. What are the values N can take?
(A) 34
(B) 35
(C) 38
(D) 67
(E) More than one value is possible
Rationale: In this question, the sum of the three numbers should leave a remainder 43 + 47 + 49 = 139. Or, it should be of the form N * k + 139, where K is an integer.
However, it leaves a remainder 9, or it is of the form N * m + 9.
N * k + 139 = N * m + 9
N * (m - k) = 130
Or, N should be a factor of 130. Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.
The only factors of 130 that are greater than 49 are 65 and 130. So, N can take 2 values – 65 or 130
E
Answer: (E) More than one value is possible
Question: In how many ways can a group of 16 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 6 people?
(A) 15C5 * 9! *4!
(B) 15C3 * 8! *3!
(C) 15C4 * 9! *3!
(D) 16C4 * 9! *5!
(E) 16C5 * 10! *4!
Rationale: 10 people can be selected from 16 people in 16C10 ways.
Remaining 6 people can be selected from 6 people in 6C6 ways.
Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 6 people on a round table = (6-1) ! = 5!
Hence, total number of ways = 16C10 * 9! * 6C6 * 5!
= 16C4 * 9! * 5!
D
Answer: (D) 16C4 * 9! *5!
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only Ⅰ& Ⅲ
(E) only Ⅱ & Ⅲ
Rationale: If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, Ⅰ& Ⅲ are the answers. Therefore, D is the answer.
Answer: (D) only Ⅰ& Ⅲ
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $25?
(A) 45
(B) 49
(C) 53
(D) 57
(E) 61
Rationale: $25 = 4 * $6 + $1
The number of doughnuts is 4*12 + 1 = 49
The answer is B.
Answer: (B) 49
Question: Square A has an area of 65 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
(A) 0.25
(B) 0.5
(C) 0.75
(D) 0.1
(E) 0.3
Rationale: I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 65-16=48 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=48/64 = 0.75.
Answer: C
Answer: (C) 0.75
Question: 32 = a + 2b
|a| > 2
If ‘a’ and ‘b’ are both integers, then what is the smallest possible values of ‘a’ that can be used to solve the above equation.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Let us understand the meaning of |a| > 2
Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b' (i.e. current case).
Now come to the question. First its given |a| > 2 ==> a > 2 i.e. a can have any value bigger than 2 (i.e. 3, 4, 5…).
Now, lets move to equation a + 2b = 32 ==> b = (32 – a)/2 ==> b = 16 – (a/2). According to question, b is an integer, hence to make ‘b’ integer a must be divisible by 2. Minimum possible value of ‘a’ that is divisible by 2 is 4 (a is greater than 2 so the next number that is divisible by 2 is 4). So the answer is C (value 4).
Answer: (C) 4
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 4
(B) 5
(C) 34
(D) 7
(E) 9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Answer: (D) 7
Question: What is the dividend. divisor 20, the quotient is 8 and the remainder is 6
(A) A)145
(B) B)148
(C) C)150
(D) D)153
(E) E)166
Rationale: D = d * Q + R
D = 20 * 8 + 6
D = 160 + 6
D = 166
Answer : E
Answer: (E) E)166
Question: What is the greatest positive integer x such that 3^x is a factor of 9^9?
(A) 5
(B) 9
(C) 10
(D) 18
(E) 30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^9?
9^9 = (3^2)^9 = 3^18
D. 18
Answer: (D) 18
Question: each man in a gang of 100 investors has investments ineither equities or securities or both. Exactly 2525 of the investors in equities haveinvestments in securities, exactly 4040 of the investorsin securities have investments inequities. How many have investmentsin equities?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 120
Rationale: The investors can be categorized into three groups:
(1) Those who have investments in equities only.
(2) Those who have investments in securities only.
(3) Those who have investments in both equities and securities.
Let xx, yy, and zz denote the number of people in the respective categories. Since the total number of investors is 110, we have
x+y+z=110x+y+z=110 ------------- (1)
Also,
The number of people with investments in equities is x+zx+z and
The number of people with investments in securities is y+zy+z.
Since exactly 25%25% of the investors in equities have investments in securities, we have the equation
25100×(x+z)=z25100×(x+z)=z
25100×x=25100×z25100×x=25100×z
x=3zx=3z ------------------- (2)
Since exactly 40%40% of the investors in securities have investments in equities, we have the equation
40100×(y+z)=z40100×(y+z)=z
(y+z)=5z2(y+z)=5z2
y=3z2y=3z2
Substituting equations (2) and (3) into equation (1) yields
3z+3z2+z=1103z+3z2+z=110
11z2=11011z2=110
z=110×211=20z=110×211=20
Hence, the number of people with investments in equities is:
x+z=3z+z=3×20+20=60+20x+z=3z+z=3×20+20=60+20= 80
B
Answer: (B) 80
Question: An alloy is to contain copper and zinc in the ratio 5:3. The zinc required to be melted with 40kg of copper is?
(A) 15kg
(B) 20kg
(C) 8kg
(D) 24kg
(E) 32kg
Rationale: Let the required quantity of copper be x kg
5:3::40:x
5x = 40*3
x = 24kg
Answer is D
Answer: (D) 24kg
Question: Pipe A can fill a tank in 9 hours, pipe B in 18 hours and pipe C in 54 hours. If all the pipes are open,in how many hours will the tank be filled ?
(A) 5.1
(B) 5.4
(C) 5
(D) 5.2
(E) 5.5
Rationale: 1/9+1/18+1/54=10/54=1/5.4. so 5.4 hrs
ANSWER:B
Answer: (B) 5.4