mathewhe/aqua_rat huggingface dataset:
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.6 kg. the weight of the new student is ?
(A) 10.6 kg
(B) 10.8 kg
(C) 7 kg
(D) 14.9 kg
(E) None
Rationale: Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.6 - 19 x 15) kg
= 7 kg.
Correct Option: C
Answer: (C) 7 kg
Question: A man engaged a servant on the condition that he would pay him Rs.900 and auniform after 1year service. He served only for 9months and received uniform and Rs.650, find the price of the uniform?
(A) Rs.80
(B) Rs.100
(C) Rs.120
(D) Rs.145
(E) Rs.156
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
B
Answer: (B) Rs.100
Question: A lent Rs. 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest per annum is
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) None of these
Rationale: Explanation:
Let R% be the rate of simple interest then,
from question we can conclude that
(5000∗R∗2/100)+(3000∗R∗4/100)=2200
<=>100R+120R=2200
<=>R=10%
Option B
Answer: (B) 10%
Question: A child was looking for his father. He went 90 m in the east before turning to his right. he went 20 m before turning to his right afain to lok for his father at his uncles place 30 m from this point. His father was not there. From there he went 100m north before meeting hiss father in a street. How far did the son meet his father from the starting point.
(A) 137
(B) 100
(C) 2977
(D) 126
(E) 191
Rationale: From the diagram, AB = 90 - 30 = 60 and BD = 100 - 20 = 80
AD=AB2+BD2−−−−−−−−−−√=602+802−−−−−−−−√=100AD=AB2+BD2=602+802=100
Answer:B
Answer: (B) 100
Question: Enrollment in City College in 1980 was 85/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) 100%
(B) 16 2/3 %
(C) 200%
(D) 253%
(E) 183 1/3%
Rationale: Assume 100 enrollments present in 1990
85/3 % of 1990 = enrollments on 1980
enrollments on 1980 = 28.33
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 28.33) *100 / 28.333
= 7166.67 / 28.333
= 253 %
Ans - D
Answer: (D) 253%
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 12 homes?
(A) $200,000
(B) $210,000
(C) $215,000
(D) $220,000
(E) $230,000
Rationale: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 12 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 12x=120,000.
x=10,000.
The 12 houses are sold at $10,000 profit or at $210,000. (ANSWER B)
Answer: (B) $210,000
Question: Abbey's income is 30 percent more than Abigail's income, and Abigail's income is 35 percent less than Jenny's income. What percent of Jenny's income is Abbey's income?
(A) 84.5%
(B) 81.5%
(C) 82.5%
(D) 83.5%
(E) 86.5%
Rationale: Jenny's income = 100 (assume);
Abigail's income = 65 (40 percent less than Jenny's income);
Abbey's income = 84.5 (30 percent more than Abigail's income).
Thus, Abbey's income (84.5) is 84.5% of Juan's income (100).
Answer: A
Answer: (A) 84.5%
Question: Thirty percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 42
(B) 40
(C) 230
(D) 130
(E) 125
Rationale: Let the number be x.
Then, 4*x/5 â€“30% of x) = 21
4x/5 â€“30x/100 = 21
x = 42.
Answer A.
Answer: (A) 42
Question: In a company there are 5 partners A,B,C,D,E. They invested money in the ratio of 1:2:3:4:5. If after one year if there is a profit of Rs.15,000. Then share of E will be ?
(A) 3000
(B) 4000
(C) 5000
(D) 6000
(E) 7000
Rationale: 5 partners A,B,C,D,E are invested money in the ratio of 1:2:3:4:5
Total profit = 15000
share of E = Profit*ratio(E)/(ratio(A)+ratio(B)+ratio(C)+ratio(D)+ratio(E))
= 15000*5/(1+2+3+4+5)=5000
ANSWER:C
Answer: (C) 5000
Question: What is 15% of 2/3 of 0.4?
(A) 0.09
(B) 0.9
(C) 9
(D) 90
(E) None of the above
Rationale: The best way to solve these questions is to convert every term into fraction
(15/100)*(2/3)*(4/10) = 120/3000 = 0.04
Option A
Answer: (A) 0.09
Question: what is the remainder when 30^72^87 is divided by 11.
(A) 5
(B) 7
(C) 1
(D) 3
(E) 4
Rationale: let us take N=72^87
eq is..30^N/11=8^N/11
here cyclicity of 8 is 10
then N/10=72^87/10=2^87/10
here cyclicity of 2 is
then 87%4=3(3rd cycle of 2)....i.e2^3%10=8(8th cycle of8)
therefore final ans is 8^8%11=5
ANSWER:A
Answer: (A) 5
Question: A certain bakery baked a batch of 530 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
(A) 166
(B) 275
(C) 413
(D) 438
(E) 533
Rationale: Cookies which have both nuts and chocolate chips = 105
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(105+x)/(530+x) = 6/10
=>1050 + 10x = 3180 + 6x
=> 4x = 2130
=> x = 532.5
Therefore x = 533
Answer E
Answer: (E) 533
Question: Two friends want to buy a snack. They combine their money and find they have $3.45, consisting of quarters, dimes, and nickels. If they have 31 coins and the number of quarters is half the number of nickels, how many quarters do they have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 345. Then 7x + 2D = 69
(2) 3x + D = 31. Then 6x + 2D = 62
Let's subtract equation (2) from equation (1).
x = 7
The answer is C.
Answer: (C) 7
Question: The average age of a husband and a wife is 28 years when they were married eight years ago but now the average age of the husband, wife and child is 26 years(the child was born during the interval). What is the present age of the child?
(A) 2 years
(B) 6 years
(C) 9 years
(D) 4 years
(E) 1 years
Rationale: 36 * 2 = 72
26 * 3 = 78
-----------
6 years
Answer:B
Answer: (B) 6 years
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 36% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 4n/9
(D) 5n/6
(E) 8n/5
Rationale: total V G
1 ounce 0.36 0.6
n ounce 0.36n 0.6n -------------initial expression
lets say g ounces of gin is added to this mixture
n+g 0.36n 0.6n+g --------------final expression
given that after adding g ounces of gin , V should become 25% of the total volume.
=>Volume of V/total volume = 25/100
=> 0.36n /n+g = 1/4
=> 1.44n = n+g
=> g = 4n/9
Answer is C.
Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.36n=0.25(n+g) --> g=4n/9
Answer: C.
Answer: (C) 4n/9
Question: The difference between the compounded interest and simple interest on a certain sum at 10% per annum for 2 years is Rs.631. Find the sum.
(A) Rs. 52255
(B) Rs. 50000
(C) Rs. 63200
(D) Rs. 63100
(E) None
Rationale: Let the sum be Rs. X .Then, C.I.. = x( 1 + 10/100 )2 - x = 21x/100 S.I. = [ (x*10*2)/100] = x/5 (C.I.) – (S.I.) = [ (21x)/100 – (x/5) ] = x/100 => x/100 = 631 => x= 63100 Hence, the sum is Rs. 63100
Answer D
Answer: (D) Rs. 63100
Question: A waiter's salary consists of his salary and tips. During one week his tips were 3/4 of his salary. What fraction of his income came from tips ?
(A) 3/7
(B) 5/4
(C) 5/8
(D) 5/9
(E) 6/9
Rationale: Income = salary (s) +tips = s + s*3/4 = s*7/4
Tips = s*3/4
fraction of his income came from tips = (s*3/4)/(s*7/4)= 3/7
ANSWER:A
Answer: (A) 3/7
Question: A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^14, respectively, what is the value of A?
(A) -24(5^12)
(B) -23(5^12)
(C) -24(5^6)
(D) 23(5^12)
(E) 24(5^12)
Rationale: Ans : A
Assume that the numbers appear as shown below on the number line
A-----B-----C-----D-----E-----F-----G-----H
(5^12) (5^13)
As the values for G and H are given , we can calculate the difference between any two terms of the series .
Common Difference ,d = (5^13) - (5^12)
= (5^12) *[ 5-1 ]
= (5^12)*(4)
Also F + d = G as the terms are in equidistant and in increasing order.
So F + (5^12)*(4) = (5^12).
That is , F = (5^12) - (5^12)*(4)
= (5^12)[ 1-4]
= (5^12) (-3)
Similarly , E = F - d
= (5^12)[-3-4]
= (5^12)*(-7)
You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)
Following this pattern , A = (5^12)*(-24)
Answer: (A) -24(5^12)
Question: 10 people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10
Rationale: The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9
ANSWER:C
Answer: (C) 9
Question: When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
(A) 10/9 n
(B) 4/3 n
(C) 9/2 n
(D) 9/4 n
(E) 7/3n
Rationale: C is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 5/9
So 1/3 + n = 5/9
n = 5/9 - 3/9
n = 2/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/2
and total = 9/2n
Answer: (C) 9/2 n
Question: The price of a DVD Player is marked at $ 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
(A) $ 8721
(B) $ 6383
(C) $ 8739
(D) $ 8766
(E) $ 7739
Rationale: A
$ 8721
Actual price = 95% of 90% of 85% of $ 12000
= 95/100 * 90/100 * 85/100 * 12000 = $ 8721.
Answer: (A) $ 8721
Question: Three runners T, B and C run a race, with runner T finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?
(A) 36m
(B) 48m
(C) 60m
(D) 72m
(E) 84m
Rationale: Let distance of race be x mtrs. Then when T finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.
as speeds are constant, we have equation,
x-12/ x-18 = 12/10 > x = 48.
Answer B
Answer: (B) 48m
Question: Due to a reduction of 25/4% in the price of sugar, a man is able to buy 1 kg more for Rs. 120. Find the original rate of sugar.
(A) 7
(B) 8
(C) 8.5
(D) 9
(E) 9.5
Rationale: Rate reduced by 6.25%,
So amount Rs 120 reduced by= (6.25/100) * 120 = 7.5
So in Rs 7.5 extra sugar obtained is 1 kg
i.e. new rate is Rs. 7.5 per kg
Thus original rate = [7.5 / (100 – 6.25)]/100
= 7.5 / 0.9375 = Rs. 8
ANSWER :OPTION B
Answer: (B) 8
Question: A train is 360 meter long is running at a speed of 30 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 87
(B) 69
(C) 60
(D) 72
(E) 21
Rationale: Speed = 30 Km/hr = 30*(5/18) m/sec = 25/3 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (3/25) = 60 seconds
Answer: C
Answer: (C) 60
Question: A sum of Rs. 14,000 amounts to Rs. 22,400 in 12 years at the rate of simple interest. What is the rate of interest?
(A) 7%
(B) 6%
(C) 5%
(D) 4%
(E) 3%
Rationale: Explanation :
Simple Interest for 12 years (SI) = (22400 - 14000) = Rs.8400
R = ?
T = 12 years
P = Rs. 14000
R=100×SI/PT=100×8400/14000×12
=5%
Answer : Option C
Answer: (C) 5%
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 277 cm
(B) 800 cm
(C) 626 cm
(D) 245 cm
(E) 152 cm
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Answer: (B) 800 cm
Question: What is the remainder of E=3^19 when divided by 10?
(A) 0
(B) 1
(C) 5
(D) 7
(E) 9
Rationale: I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, E=when divided by 10, the remainder must be 7.D
Answer: (D) 7
Question: If a young child was 19 months old one year ago, how old was the child, in months, x months ago?
(A) x − 31
(B) x − 12
(C) 19 − x
(D) 24 − x
(E) 31 − x
Rationale: The child's age today is 19 months + 12 months = 31 months
x months ago, the child's age was (31 - x) months old.
The answer is E.
Answer: (E) 31 − x
Question: What is 1 percent of 12,356?
(A) 123.56
(B) 1.2356
(C) 12.356
(D) 0.012356
(E) 0.0012356
Rationale: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=1(1/100)12,356. The answer is 123.56. Hence, the correct answer is A.
Answer: (A) 123.56
Question: Jerry went to a shop and bought things worth Rs. 25, out of which 30 $ went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 21.3
(D) 21.5
(E) 21.7
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 $ is given as tax
=> Total tax incurred = 30 $ = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: (B) 19.7
Question: In what time will a train 140 m long cross an electric pole, it its speed be 108 km/hr?
(A) 2.5
(B) 4.7
(C) 2.9
(D) 2.3
(E) 2.1
Rationale: Speed = 108 * 5/18 = 30 m/sec
Time taken = 140/30
= 4.7 sec.
Answer: B
Answer: (B) 4.7
Question: The average of 50 numbers id 62. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
(A) 22.3
(B) 33.2
(C) 22.2
(D) 51.3
(E) 62.5
Rationale: Explanation:
Total of 50 numbers = (50×62)=3100
Total of 48 numbers =(3100-(45+55)]=3000
Required average = 3000/48=62.5
Answer:E
Answer: (E) 62.5
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by
(A) 2
(B) 8
(C) 1
(D) 1/8
(E) 1/64
Rationale: Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 2*V1.
Answer=A=2
Answer: (A) 2
Question: The average age of three boys is 40 years and their ages are in proportion 2:6:8. What is the age in years of the youngest boy?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 2x + 6x + 8x = 40
x =2.5
2x = 5
Answer:E
Answer: (E) 5
Question: Frank is 15 years younger then John. In 3 years John will be twice as old as Frank. How old will Frank be in four years?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Frank is 15 years younger then John --> F+15=J;
In 5 years John will be twice as old as Frank (in 3 year John will be J+3 years old and Frank will be F+3 years old) --> J+3=2*(F+3) --> (F+15)+3=2*(F+3) --> F=12;
In 4 years Frank will be 12+4=16 years old.
Answer: E.
Answer: (E) 16
Question: Abhijit started a business investing 60000. Anuja joined him after six months with an amount of 110000 and Sunil joined them with 1.2 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?
(A) 15 :18 :32
(B) 24 :32 :26
(C) 36 : 55 :48
(D) 26 :12 :24
(E) 15: 25 :35
Rationale: Ratio of their investments
= 60 × 36 : 110 × 30 : 120 × 24 = 36 : 55 : 48
Answer C
Answer: (C) 36 : 55 :48
Question: When a train moves at an average speed of 100 kmph it reaches its destination on time. When its average speed becomes 80 kmph, then it reaches its destination 20 minutes late. Find the length of journey rounded to two decimal places.
(A) 99.33 km
(B) 133.33 km
(C) 125.33 km
(D) 156.66 km
(E) None
Rationale: Sol.
Difference between timings = 20 min = 1/3 hr.
Let the length of journey be x km.
Then, x/80 - x/100 = 1/3
â‡” 5x - 4x = 133.33
â‡” x = 133.33 km.
Answer B
Answer: (B) 133.33 km
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 22678
(B) 26699
(C) 26788
(D) 19000
(E) 26711
Rationale: Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: D
Answer: (D) 19000
Question: There are 10 flavors of ice cream, 3 types of nuts and 5 types of fruit at an ice cream store. If a person can choose 2 ice cream flavors as base, 2 types of nuts and 2 types of fruit. How many different variations are possible if repetition is allowed ?
(A) 150
(B) 250
(C) 22500
(D) 225
(E) 225000
Rationale: Ice cream flavors: 10x10 = 100
Nuts: 3x3 = 9
Fruit: 5x5 = 25
Total = 22500
Answer: C
Answer: (C) 22500
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
(A) 38
(B) 42
(C) 45
(D) 46
(E) 48
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: (B) 42
Question: A number of 9 digits has the following properties: The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2
(A) 381654729
(B) 381654728
(C) 381655729
(D) 381754729
(E) 361654729
Rationale: 381654729
because 38 is divided by 2
381 is divided by 3
3816 is divided by 4
38165 is divided by 5
381654 is divided by 6
3816547 is divided by 7
38165472 is divided by 8
381654729 is divided by 9
ANSWER:A
Answer: (A) 381654729
Question: A room is a square of side 50 feet. A second room is of area
100 square yards. A third room is of area 200 square feet.
Which of these can seat maximum people? (Hint:1 yard=3
feet)
(A) 200 sq feet
(B) 300 sq feet
(C) 400 sq feet
(D) 500 sq feet
(E) 600 sq feet
Rationale: first room because area 50*50=2500 sq feet
second room area 100 sq yard in feet 300 sq feet
third room area 200 sq feet
ANSWER:A
Answer: (A) 200 sq feet
Question: What is the price of a banana?
(a) 14 banana and 35 oranges cost Rs. 84
(b) with a 50% discount on banana, Rs. 12 can buy 4 bananas and 5 oranges
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 14X1+35X2=84
4XO.5+5X2=12
So price of banana =1 and orange=2
ANSWER:A
Answer: (A) 1
Question: The diference of two numbers is 20% of the larger number, if the smaller number is 20, then the larger number is :
(A) 33
(B) 25
(C) 76
(D) 28
(E) 19
Rationale: Explanation:
Let the large number be x.
Then x - 20 = 20x/100 <=> x - x/5 = 20 => x = 25.
Answer: B) 25
Answer: (B) 25
Question: In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 78% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 73.
(C) 53
(D) 91
(E) 108
Rationale: Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
78%of 250 = 195 are boys who play soccer.
Girls who play soccer = 55.
Total girls who do not play soccer = 108 - 55 = 53.
Correct option: C
Answer: (C) 53
Question: If an item that originally sold for w dollars was marked up by u percent and then discounted by v percent, which of the following expressions represents the final price of the item?
(A) (10,000w + 100w(u – v) – uvw)/10,000
(B) (10,000w + 100w(v – u) – uvw)/10,000
(C) (100w(u – v) – uvw)/10000
(D) (100w(v – u) – uvw)/10000
(E) 10000 /(u – v)
Rationale: Assume w=100, u=10, v=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Answer: (A) (10,000w + 100w(u – v) – uvw)/10,000
Question: A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 60%
Concentration of salt in the mixed solution = 20%
The pure solution and the salt solution is mixed in the ratio of --> (60 - 20)/(20 - 0) = 2/1
1/x = 2/1
x = 1/2
Answer: C
Answer: (C) 1/2
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: B
4
By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Answer: (B) 4
Question: In a bag, there are 5 green, 6 black and 7 red pens. One pen is picked up randomly. What is the probability that it is neither red nor green?
(A) 5/18
(B) 7/18
(C) 1/3
(D) 1/2
(E) 1/5
Rationale: Explanation :
Neither red nor green means the pen drawn is black.
Total number of outcomes = (5+6+7) = 18.
Number of Favourable outcomes = 6 = Number of black pens.
Hence, Probability of the event = 6/18 = 1/3.
Answer : C
Answer: (C) 1/3
Question: The ratio of earnings of A and B is 4:5. If the earnings of A increase by 20% and the earnings of B decrease by 20%, the new ratio of their earnings becomes 6:5. What are A's earnings?
(A) 375099
(B) 37500
(C) 27899
(D) 28778
(E) 19911
Rationale: Explanation:
Let length = x meters, then breadth = 0.6x
Given that perimeter = 800 meters
=> 2[ x + 0.6x] = 800
=> x = 250 m
Length = 250m and breadth = 0.6 * 250 = 150m
Area = 250 * 150 = 37500 \fn_jvn {\color{Blue}m^{2}}
Answer: B
Answer: (B) 37500
Question: Magnabulk Corp sells boxes holding z magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
(A) 100m/(bz)
(B) 100bz/m
(C) bz/(100m)
(D) m/(bz)
(E) bz/m
Rationale: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding Z magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
Z = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when Z=2, B=3 and M=12. There's only one answer that matches...
Answer is A
Answer: (A) 100m/(bz)