mathewhe/aqua_rat huggingface dataset:
Question: A 30% solution of barium chloride is mixed with 10 grams of water to form a 20% solution. How many grams of original solution did we start with ?
I am trained to complete above problem as per following technique. Is it possible to solve in following manner.
30%_________100%
______20%
ratio is 100-20 : 20-30, which is wrong. There should not be 20. Instead, value in the middle should be in between 30% to 100%.
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: We're told that 10g of water are mixed with an unknown amount of 30% barium mixture to form a 20% barium final mixture. We're asked to figure out how much barium mixture we have....
Logically, if we had 10g of water mixed with 10g of barium mixture, we'd end up with a 15% overall mixture, so 10 is NOT the answer. We need MORE barium mixture to raise the final mixture up to 20%. Since the numbers in the prompt are allroundnumbers, it's highly likely that the correct answer will ALSO be a round number....
Let's TEST Answer C = 20g
(20g of barium mixture)(30% barium) = 6g barium
+ 10g water.....
(6g barium)/(30g total liquid) = .2 = 20% final barium mixture.
So, the initial barium mixture MUST be 20g
ANSWER C
Answer: (C) 20
Question: Find the greatest number that will divide 205, 626 and 588 leaving 5, 6 and 8 as remainders respectively
(A) 19
(B) 17
(C) 13
(D) 9
(E) 20
Rationale: Explanation:
Answer will be HCF of (205-5, 626-6, 588-8)
HCF of (200, 626, 580) = 20
Option E
Answer: (E) 20
Question: 30 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
(A) 87
(B) 18
(C) 17
(D) 36
(E) 10
Rationale: Binders Books Days
30 1400 21
x 1600 20
x/30 = (1600/1400) * (21/20) => x = 36
Answer:D
Answer: (D) 36
Question: A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 1500. He sold both the items together for Rs. 4000. What percentage of profit did he make?
(A) 14.28%
(B) 1.20%
(C) 15.21%
(D) 14.20%
(E) 10.32%
Rationale: The total CP = Rs. 2000 + Rs. 1500
= Rs. 3500 and SP = Rs. 31150
Profit(%) = (4000 - 3500)/3500 * 100
= 14.28%
Answer: A
Answer: (A) 14.28%
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 299
(C) 797
(D) 179
(E) 642
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100
=600
Answer:A
Answer: (A) 600
Question: A city with a population of 97,500 is to be divided into 6 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
(A) 15,000
(B) 15,500
(C) 16,000
(D) 16,500
(E) 17,000
Rationale: The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 97,500 = p + 5(1.1)p
6.5p=97,5000
p = 15,000
The answer is A.
Answer: (A) 15,000
Question: Hillary and Tenzing are climbing to the summit of Mt. Everest from a base camp 4,800 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Tenzing lagging behind at a slower rate of 500 ft/hr. If Hillary stops 800 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Tenzing pass each other on her return trip?
(A) 12.0
(B) 11.0
(C) 10.0
(D) 13.0
(E) 14.0
Rationale: Solution:H stopped 800 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
A
Answer: (A) 12.0
Question: In a BCCI meeting there are 12 people. All shake hands with each other once. How many handshakes will be there altogether?
(A) 28
(B) 11
(C) 12
(D) 19
(E) 18
Rationale: There will be n-1 handshakes as A person will shake hands with all the other members.
=12-1=11
Answer:B
Answer: (B) 11
Question: If a and b are positive integers, and a=4b+16, the greatest common divisor of a and b CANNOT be
(A) 2
(B) 9
(C) 4
(D) 8
(E) 16
Rationale: If b is 2, 4, 8, or 16, then GCD of a and b is 2, 4, 8, and 16 respectively. So, by POE the answer must be B.
Still: if b is a multiple of 9, then a is 16 greater than a multiple of 9, so not a multiple of 9, so both of them cannot be divisive by 9.
Answer: B.
Answer: (B) 9
Question: Find the 21th term of an arithmetic progression whose first term is 3 and the common difference is 5.
(A) 100
(B) 102
(C) 103
(D) 150
(E) 46
Rationale: n th term of A.P = a +(n-1) *d
= 3+(21-1)*5 , = 3 + 100 = 103.
ANSWER:C
Answer: (C) 103
Question: What is the next number of the following sequence
7,0,1,8,5,12,9,2,6,3,2,?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: sum of alternate terms is same i.e:
( 7,0,1,8)= 7+1=8 & 0+8=8
(5,12,9,2)=5+9=14 & 12+2=14
likewise ( 6,3,2,x)= since 6+2=8 , so 3+x=8,
hence x=5
ANSWER:B
Answer: (B) 5
Question: Complete the numerical sequence by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ??????
(A) 3
(B) 588447
(C) 845668
(D) 454585
(E) 544586
Rationale: Series if formed as (a*b)(b*c)(c*a)
(9*5)(9*5)(9*5+9*5-5) => 454585
the number we take is 454585
Correct answer is: D)454585
Answer: (D) 454585
Question: One man selling a lottery there are 10 prizes and 25 no prizes. if a lottery is drawn randomly, What is the probability of getting a prize?
(A) 1/5
(B) 2/7
(C) 2/9
(D) 3/11
(E) 4/11
Rationale: P (getting a prize) =	10	=	10	=	2/7
(10 + 25)	35
B
Answer: (B) 2/7
Question: What least number should be subtracted from 642 so that the remainder when divided by 5, 7, and 9 will leave in each case the same remainder 4 ?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The LCM of 5, 7, and 9 is 315. The next multiple is 2*315 = 630.
630 + {remainder} = 630 + 4 = 634, which is 8 less than 642.
Answer: C.
Answer: (C) 8
Question: If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"RAM" would be
(A) 312
(B) 128
(C) 632
(D) 122
(E) 156
Rationale: R-1
A-2
M-8
so for mango the code is 128
ANSWER:B
Answer: (B) 128
Question: If 123xy is divisible by 40, then the value in place of x+y is :
(A) 1
(B) 7
(C) 4
(D) 3
(E) 9
Rationale: 123xy
1 + 0 = 1/4 ≠ 40
7 + 0 = 70/4 ≠ 40
4 + 0 = 40/4 = 10
Answer: C
Answer: (C) 4
Question: In a sample of associates at a law firm, 25 percent are second-year associates, and 75 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100
Rationale: 75 percent are not first-year associates --> This means 75 percent associates are either two or more than two years
Already, we know % of second-year associates = 25 %
So, % of associates there for more than two years = 75 % - 25 % = 50 % .. => (C).. Is it correct ?
Answer: (C) 50
Question: Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 9 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score?
(A) 22
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: One way to do this would be weighted average method..
1) let the average of 5 mocks be x...
so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...
By alligation/weighted average..
the difference in 760 and 726.67 is 5/6 of difference of 760 and x..
760-726.67 = 5/6 * (760-x)
760-x= 33.33*6/5=40...
so x = 720..
the last of mock test will be 720+9+9=738...
so ans = 760-738=22
A
Answer: (A) 22
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
(A) 3x^3
(B) x(x+1)(x+2)
(C) 9x
(D) 9x^2
(E) x+3
Rationale: *any number multiplied by 3, will be divided by 3
for option E if we put value x=7, 7+3=10 is not divisible by 3
Answer : E
Answer: (E) x+3
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 32 kmph
(B) 34 kmph
(C) 30 kmph
(D) 45 kmph
(E) 65 kmph
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: (C) 30 kmph
Question: If 15!/3^x is an integer, what is the greatest possible value of x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^6 is allowed. IMO D.
Answer: (D) 6
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length R of the fence including the fence posts on each end?
(A) mn
(B) m(n + x)
(C) R=m(n + x) + x
(D) m(n + x) + 2x
(E) 2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: (C) R=m(n + x) + x
Question: A 20% stock yielding 8% is quoted at?
(A) 165
(B) 170
(C) 250
(D) 180
(E) 185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.20, money invested = 100×20/8 = Rs.250
ie, market value of the stock = Rs.250
Answer is C.
Answer: (C) 250
Question: Jim bought edging to go around a circular garden with a radius of 6 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
(A) 28.84' additional edging
(B) 48.84' additional edging
(C) 38.84' additional edging
(D) 18.84' additional edging
(E) 37.68' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 6 = 37.68'
double of the circumference of small garden = 2 x 37.68' = 75.36'
More feet to be buy =75.36 - 37.68 = 37.68
Answer : E
Answer: (E) 37.68' additional edging
Question: Find the amount of rs.7500 at compound interest at 4%per annum for 2 years?
(A) 8112
(B) 9110
(C) 7160
(D) 6210
(E) 8021
Rationale: Compound interest=[7500*(1+(4/100))^2]
=7500*((104/100)^2)
=(7500*104*104)/(100*100)
=Rs.8112
Option A
Answer: (A) 8112
Question: 10^196 - 10^9 = Which of the following best approximates the value of the expression above?
(A) 10^186
(B) 10^196
(C) 10^100
(D) 10^150
(E) 10^170
Rationale: 10^196 - 10^9 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^196 is correct. Note that we need approximate value of the given expression and as 10^(196) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(196)-10^(9)=~10^(196).
Answer : B
Answer: (B) 10^196
Question: After decreasing 20% in the price of an article costs Rs.600. Find the actual cost of an article?
(A) 775
(B) 620
(C) 53
(D) 530
(E) 220
Rationale: CP* (80/100) = 600
CP= 7.75 * 100 => CP = 775
Answer: A
Answer: (A) 775
Question: The cost price of 25 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ?
(A) 12.8
(B) 18
(C) 16
(D) 15
(E) 14
Rationale: let S.P. of X books = Rs 100 = C.P. of 25 books
Therefore, C.P. of one book = Rs 6.25
Profit = 25 %
Therefore, S.P of one book = 7.8
S.P of X articles = 7.8 X
7.8 X = 100 => X = 12.8
ANSWER:A
Answer: (A) 12.8
Question: total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
(A) 21.84
(B) 50.96
(C) 53.84
(D) 24.84
(E) 50.26
Rationale: dinner bill of 3 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/3 = $ 50.96
ANSWER:B
Answer: (B) 50.96
Question: The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs. 3. The ratio of the two selling prices is?
(A) 52:56
(B) 52:53
(C) 52:50
(D) 22:56
(E) 51:53
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 102% of x / 106% of x
= 102/106 = 51/53 = 51:53
Answer: E
Answer: (E) 51:53
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?
(A) 25x^2 + 4 = y^2
(B) 75x^2 = 3y^2 - 12
(C) 25x^2 = (y + 2)(y - 2)
(D) 5x = y - 4
(E) x^2 = (y^2 - 4)/25
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 2
If we square both sides, we end up with....
(5X)^2 = (Y-4)^2
(5X)(5X) = (Y-4)(Y-4)
25X^2 = Y^2 - 8Y + 16
This is NOT a match for the original equation, so it's the answer that is NOT equivalent. D
Answer: (D) 5x = y - 4
Question: A vessel of capacity 45 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 28.8
(B) 72.9
(C) 38.3
(D) 78.3
(E) 79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 45, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(45 - 9)/45]^2 (45) = 28.8 litres.
Answer: Option A
Answer: (A) 28.8
Question: Three distinct single digit no A,B,C are in G.P. If abs(x) for real x is the absolute value of x(x if x is positive or zero, and x if x is negative),then the no. of different possible values of abs(A+B-C) is
(A) 6
(B) 4
(C) 3
(D) 5
(E) 2
Rationale: if a=1,r=2 then a=1,b=2,c=4 then abs(a+b-c)=1
if a=1,r=3 then a=1,a=3,a=9 then abs(1+3-9)=5
if a=2,r=2, then a=2,b=4,c=8 then abs(2+4-8)=2
if a=1,r=-2 then a=1,b=-2,c=4 the abs(1-2-4)=5
if a=1,r=-3 then a=1,b=-3,c=9 then abs(1-3-9)=11
if a=2,r=-2 then a=2,b=-4,c=-8 then abs(2-4-8)=10
so total 5 abs() values
ANSWER:D
Answer: (D) 5
Question: 15 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
(A) 55 days
(B) 18.75 days
(C) 20 days
(D) 88 days
(E) 44 days
Rationale: 15 * 25 = 20 * x => x
= 18.75 days
Answer: B
Answer: (B) 18.75 days
Question: What is the sum of the digits of integer k, if k = (10^45- 46)
(A) 356
(B) 366
(C) 363
(D) 396
(E) 408
Rationale: There are 46 digits in 10^45
When we subtract 46 from it, there will be 45 digits left.
10^45 can be written as 9999999....(45 times) + 1
So,
10^45 - 46 = 9999999....(45 times) + 1 - 46 = 9999999....(45 times) -45
Consider the last 2 digits,
99-45 = 54
The last 2 digits will be 54.
And our number would be 99999......99954 with 2 less 9s after subtraction.
Number of 9s left are 43 and the last two digits are 54
The sum of the digits will be
(43*9) + 5 + 4 =396
Answer:- D
Answer: (D) 396
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 5 for a dollar and the other at a rate of 5 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
(A) 1:1
(B) 1:5
(C) 2:3
(D) 1:2
(E) 2:5
Rationale: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/5 - 1/5 = 0 dollars.
The selling price of a mango from the second stack = 1/5 dollars --> the loss from one mango = 1/5 - 1/5 = 0 dollars.
no profit as whole 1:1
Answer: A.
Answer: (A) 1:1
Question: Given
A+B+C=100
60A+40B+C=2000
Find A+B=?
(A) 76
(B) 74
(C) 40
(D) 44
(E) can't determine
Rationale: (60A+40B+C=2000)-(A+B+C=100)
59A+39B=1900
So if we take A+B=40 so if A=17 and B=23 then 17+23=40 and 59*17+39*23=1900
it satisfy the condition so correct answer is=40
ANSWER:C
Answer: (C) 40
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
Answer: Option B
Answer: (B) 50%
Question: The average of a couple was 18Yrs when they were married 20Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 26Yrs now. How old is the
child now ?
(A) 2 Yrs
(B) 4 Yrs
(C) 3 Yrs
(D) 1 Yrs
(E) None of these
Rationale: (a+b-20-20)/2=18;
a+b=76;
a+b+c/3=26;
solving both c=2
ANSWER:A
Answer: (A) 2 Yrs
Question: If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?
(A) 8
(B) 21
(C) 25
(D) 44
(E) 47
Rationale: The answer is B - 21 because 21/0.375 yields an integer (= 56) and none of the other options does
x/y = Integer + Remainder
=> x/y = 33 + 0.375
Multiplying both sides by 56,
56(x/y) = 56*33 + 21
ALTERNATIVELY,you may calculate as follows:
x/y = 33.375
=> x/y = 33375/1000 = 267/8 = (33*8 + 3)/8
Multiply both sides by 7 to get
x/y = (33*56 + 21)/8 which can be written as 33*56/8 + 21/8
Once we know that we can get 3 as a remainder, we can select the answer choice that is a multiple of 3 (21 in this case)
The answer is therefore choice (B)
Answer: (B) 21
Question: An artist wishes to paint a circular region on a square poster that is 3 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
(A) 1/pi
(B) sqrt(2/pi)
(C) sqrt(4.5/pi)
(D) 2/sqrt(pi)
(E) pi/2
Rationale: Area of the poster is 3x3 = 9
1/2 the area = 4.5
pi*r^2 = 4.5
r^2 = 4.5/pi
r = sqrt(4.5/pi) answer (C)
Answer: (C) sqrt(4.5/pi)
Question: Train A is stopped at a railway station and train B is passing the train A with a speed of 62kph. Train A and B are having lengths of 200m and 185m respectively. How long it will take the train B to pass train A?
(A) 14.45
(B) 19.82
(C) 22.36
(D) 28.38
(E) 31.91
Rationale: Relative speed of train B with respect to train A = 62-0=62kph=17.22m/s
Distance needs to be covered by train B=200+185=385m
Time taken by the train B to pass train A = 385/17.22 = 22.36s
Answer: C
Answer: (C) 22.36
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
(A) 20.88%loss
(B) 20.98%loss
(C) 20.78%loss
(D) 20.38%loss
(E) 10.98%loss
Rationale: 81 ---- 17
100 ----- ? è 20.98%loss
Answer:B
Answer: (B) 20.98%loss
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, sam's new income would be what fraction of Quentin's new income?
(A) 	11/12
(B) 	12/11
(C) 	13/19
(D) 	12/19
(E) 	11/19
Rationale: MAKE R = 10
P = 0.6R = 6
Q = 0.8P = 4.8
S= 0.6P = 3.6
FOR THAT WE GET S = 9.6
AND Q 8.8
SO 9.6/8.8= 1.2/1.1
Ans:B
Answer: (B) 	12/11
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
(A) 1/2
(B) 16/19
(C) 4/5
(D) 17/20
(E) 3/5
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
ANSWER:D
Answer: (D) 17/20
Question: Find the odd man out 17, 39, 171, 347
(A) 18
(B) 18
(C) 83
(D) 82
(E) 39
Rationale: 6 x 2+5=17
17 x 2+5=39
39 x 2+5=83
83 x 2+5=171
ANSWER:C
Answer: (C) 83
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 32.7
(B) 32.4
(C) 32.5
(D) 32.9
(E) 32.2
Rationale: 36/7 r = 6.3
=32.4
Answer: B
Answer: (B) 32.4
Question: In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 72,030,000, how many red beads were removed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 72,030,000
= 2^4 * 5^4 * 7203
= 2^4 * 3 * 5^4 * 2401
= 2^4 * 3 * 5^4 * 7 * 343
= 2^4 * 3 * 5^4 * 7^4
The answer is D.
Answer: (D) 4
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 3 “low” cards?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: To get a 5, you need one high and three lows (you could have had 2 highs and one low, but the constraint is that you must have three low cards)
HLLL = 4!3! =4
4! is the number of ways you can arrange these four spaces. divide by 3! because you you repeat three low cards
ANS:D
Answer: (D) 4
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855. the total profit is
(A) Rs. 1425
(B) Rs. 1500
(C) Rs.1537
(D) Rs.1576
(E) None
Rationale: Solution
Let the total profit be Rs.100
After playing to charity, A's share	= Rs. (95 x 3/5)
If A's share is Rs.57, total profit	= Rs. 100.
If A's share is 855, total profit	= (100/57 x 855)
‹=›1500
Answer B
Answer: (B) Rs. 1500
Question: Evaluate: 35 - 12*3*2 = ?
(A) 62
(B) 52
(C) 32
(D) 27
(E) 22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
35 - 12*3*2 = 35 - 8 = 27
correct answer D
Answer: (D) 27
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
(A) 10080
(B) 4989600
(C) 120960
(D) 180960
(E) None of these
Rationale: The given words contain 8 letter MTHMTCS(AEAT), so 8!.
Then the 4 vowels can be formed differently, 4!.
But there are three words have repeated in the given words. So it should be divided by 2!*2!*2!.
Hence the solution is (8! * 4!) / (2! * 2! * 2!) = 120960
ANSWER:C
Answer: (C) 120960
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 34 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
(A) 33
(B) 2^4*3
(C) 24
(D) 38
(E) 47
Rationale: Working backward from the day it's covered:
day 34: fully covered
day 33: half covered
So 33 days
ANSWER:A
Answer: (A) 33
Question: Murali travelled from city A to city B at a speed of 4 kmph and from city B to city C at 6 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
A. 48 kmph
(A) 33
(B) 5
(C) 28
(D) 7
(E) 16
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/4 + (3x)/6 = (6x + 6x)/12 = 12x/12 = x Average speed = (2x + 3x)/(x) = 5 kmph.
Answer: B
Answer: (B) 5
Question: There are 134 toys coloured red and white in a box. Two red toys are removed from the lot and now there are twice as many red ones as white ones. How many of red colour toys are there now?
(A) 76
(B) 86
(C) 90
(D) 88
(E) 78
Rationale: r+w=134
Two red toys are removed from the lot and now there are twice red ones as white ones
r-2=2w sub 1st one we get
134-w-2=2w
132=3w
w=44
r=88
actually red will be 90
now 88
ANSWER:D
Answer: (D) 88
Question: 8 and 2 are the first two terms in a geometric sequence. What is the arithmetic difference between the 3rd term and the 4th term?
(A) (3) * (1/4)^3
(B) (6) * (1/4)^3
(C) (6) * (1/8)^3
(D) (6) - (1/4)^3
(E) (6) / (1/4)^3
Rationale: Common ratio = 2/8 =1/4
3rd term = 8*(1/4)^3
4th term = 8*(1/4)^4
Difference = 8 * ((1/4)^3 - (1/4)^4)
= 8 * (1/4)^3 *(1 - (1/4))
= 8 * (1/4)^3 * (3/4)
= (1/4)^3 * (3/4) * 8
= (6) * (1/4)^3
B
Answer: (B) (6) * (1/4)^3