mathewhe/aqua_rat huggingface dataset:
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 14 sec. What is the length of the platform?
(A) 287 m
(B) 350 m
(C) 267 m
(D) 535.71 m
(E) 656 m
Rationale: Speed = 300/14= 150/7 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 150/7
=> x = 535.71 m.
Answer:D
Answer: (D) 535.71 m
Question: Circles X and Y are concentric. If the radius of circle X is six times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
(A) 13
(B) Pi/3
(C) Pi/2
(D) 35/36
(E) 8/9
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 6a, so area = 9. PI a ^ 2
Area of shaded region = 36PI a^2 - PI a^2 = 35 PI a^2
So, probability = ( 35 PI a^2 ) / (36 PI a^2 )
= 35/36 = Answer = D
Answer: (D) 35/36
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 35 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
(A) 80
(B) 90
(C) 95
(D) 121.5
(E) 108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 35% = 90*1.35 = 121.5
Thus ratio = 121.5/100 = 1.215 (in % terms = 121.5%). Thus D is the correct answer.
Answer: (D) 121.5
Question: How many Kg of rice at Rs.6.60 per Kg. be mixed with 56Kg of rice at Rs.9.60 per Kg to get a mixture
worth Rs.8.20 per Kg
(A) 56 Kg
(B) 52 Kg
(C) 44 Kg
(D) 49 Kg
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind rice Cost of 1 kg of 2nd kind rice
6.6 9.6
Price of 1Kg of the mixture
8.2
9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6
Quantity of 1st kind rice : Quantity of 2nd kind rice = 1.4 : 1.6 = 7 : 8
Quantity of 1st kind rice : 56 = 7 : 8
=>Quantity of 1st kind rice = 56×78=49
Answer : Option D
Answer: (D) 49 Kg
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) 17/22
(B) 17/29
(C) 17/98
(D) 17/20
(E) 17/27
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: A one-foot stick is marked in 1/2 and 1/4 portion. How many total markings will there be, including the end points?
(A) 8
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: LCM of 8 = 4
1/2 marking are (Table of 2) 0...... 2 ........... 4
(Total = 3)
1/4 marking are (Table of 1) 0 ....... 1 ...... 2...... 3........ 4 (Total = 5)
Overlapping markings are 0 ........ 2 ......... 4 (Total = 3)
Total markings = 3+5-3 = 5
Answer = C
Answer: (C) 5
Question: Find a two digit number, given that the sum of the digits is 13 and the difference of the digits is 5.?
(A) 74
(B) 82
(C) 95
(D) 76
(E) 94
Rationale: Using elimination method find which of the options fit the description of the number
... from the option only 94 meets this description
sum of digits---9+4 = 13
difference of digits ---9-4 = 5
Answer E.
Answer: (E) 94
Question: john bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that john paid, including sales tax?
(A) 3%
(B) 4%
(C) 7%
(D) D.10%
(E) 12%
Rationale: For john
Cost of Computer = $2000
Sales tax = (5/100)*2000 = $100
Total Cost of Computer = 2000 + 100 = 2100
For Henry
Cost of Computer = $1800
Sales tax = (12/100)*1800 = $216
Total Cost of Computer = 1800 + 216 = 2016
% that Henry paid less than john = (2100 - 2016)*100/2100 =4%
Answer: Option B
Answer: (B) 4%
Question: In how many ways can 5 boys and 2girls be arranged ata table if 2 girls are never together?
(A) 234
(B) 256
(C) 345
(D) 367
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in h hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of h?
(A) 3/4
(B) 1[1/5]
(C) 1[2/5]
(D) 1[3/4]
(E) 2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * h = 1 => X = 1/h
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/h = 4/3
=> 1/h = (8-3)/6 = 5/6
=> h = 6/5 = 1[1/5]
Answer B
Answer: (B) 1[1/5]
Question: The L.C.M. of 2 numbers is 54. The numbers are in the ratio 2:3. Find their sum?
(A) 36
(B) 40
(C) 45
(D) 32
(E) 56
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 54
x = 9
The numbers are = 18 and 27
Required sum = 18+27 = 45
Answer is C
Answer: (C) 45
Question: Set A contains all the even numbers between 22 and 70 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 600
(B) 800
(C) 1000
(D) 1200
(E) 1400
Rationale: Each term in set B is 40 more than the corresponding term in set A.
The difference of the sums = 25 * 40 = 1000.
The answer is C.
Answer: (C) 1000
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 74% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 58% problems right. How many more questions he would have to answer more to get
passed
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 58% = 58% of total quations
= 58 % of 74 = 43.
He would have to answer 43 - 40 = 3
Answer: Option A
Answer: (A) 3
Question: If Jake loses 5 pounds, he will weigh thrice as much as his sister. Together they now weigh 285 pounds. What is Jake's present weight, in pounds?
(A)  131
(B)  135
(C)  139
(D)  147
(E) 215
Rationale: This problem can be solved as a simple word problem in which we must convert words to math. Before we create our equations, we want to define some variables.
J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 5 = 3S
J = 3S + 5 (Equation 1)
Next, we are told that “Together they now weigh 275 pounds.” We can also put this into an equation.
J + S = 285 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
3S + 5 = 285-S
4S = 280
S = 70
J + 70 = 285
J = 215
Answer: E
Answer: (E) 215
Question: A and B started a business with their capitals Rs. 24,000 and 36,000 respectively. Annual profit will be distributed between them in the ratio
(A) 1:3
(B) 2:3
(C) 4:3
(D) 2:1
(E) 2:5
Rationale: 24,000:36,000
Ans. 2:3
ANSWER:B
Answer: (B) 2:3
Question: Which of the following numbers is between 1⁄2 and 1⁄3?
(A) .55
(B) .38
(C) .29
(D) .22
(E) .20
Rationale: 1/3 = .333...
1/2 = .5
The only number between these two is 0.38.
The answer is B.
Answer: (B) .38
Question: How much time does a train 125 metres long running at 60 km/hr take to pass a pole?
(A) 6s
(B) 2.08s
(C) 7.5s
(D) 8s
(E) 9s
Rationale: Explanation:
60 km/hr = 60 * 5/18 = 16.67 m/s
Speed = distance/time; v = d/t
16.67 = 125/t
t = 7.5s
ANSWER C
Answer: (C) 7.5s
Question: What is the smallest number which, when increased by 7, is divisible by 7, 8, and 24?
(A) 154
(B) 161
(C) 168
(D) 175
(E) 182
Rationale: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-7=161.
The answer is B.
Answer: (B) 161
Question: In how many ways can a group of 2 men and 2 women be made out of a total of 7 men and 5 women?
(A) 240
(B) 270
(C) 230
(D) 210
(E) 280
Rationale: We need to select 2 men from 7 men and 2 women from 5 women. Number of ways to do this= 7C2 × 5C2210 D)
Answer: (D) 210
Question: Two cars start from the opposite places of a main road, 140 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
(A) 65
(B) 38
(C) 20
(D) 55
(E) 21
Rationale: Answer: D) 55 km
Answer: (D) 55
Question: Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
(A) Rs. 610
(B) Rs. 612
(C) Rs. 614
(D) Rs. 616
(E) None of these
Rationale: Explanation:
Amount=[7500×(1+4100)2]=(7500×2625×2625)=8112
So compound interest = (8112 - 7500) = 612
Answer: B
Answer: (B) Rs. 612
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
(A) 1/31
(B) 1/35
(C) 1/37
(D) 2/35
(E) 3/37
Rationale: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
B)
Answer: (B) 1/35
Question: An increase of Rs 3 in the selling price of an article turn a loss of 15/2% into a gain of 15/2%.The cost price of the article is??
(A) 10 rs
(B) 20 rs
(C) 25 rs
(D) 30 rs
(E) 40 rs
Rationale: let cost price= x rs
and selling price = y rs
now condition (1)-
if we sell at y loss occurs 15/2%
so by formula
selling price ={(100-%loss)/100}* cost price
so put values
y={(100-15/2)/100}x
y=(185/200)*x
x*182/200 - y=0---------(1)
condition 2-
if we increase selling price by 3 we get profit by 15/2%
so by formula
selling price={(100+%profit)/100}*cost price
put values
y+3={(100+15/2)/100}*x
x*(215/200)-y=3 --------(2)
now on solving equation 1 and 2 we get
x= 20 rs
ANSWER:B
Answer: (B) 20 rs
Question: A and B complete a work in 6 days. A alone can do it in 8 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.43 days
(C) 2.99 days
(D) 2.98 days
(E) 2.44 days
Rationale: 1/6 + 1/8 = 7/24
24/7 = 3.43 days
Answer: B
Answer: (B) 3.43 days
Question: The addition 742586 + 829430 = 1212016 is incorrect. It can be corrected by changing
one digit d, wherever it occurs, to another digit e. Find sum of d and e.
(A) 1316016
(B) 1416016
(C) 1516016
(D) 1616016
(E) 1716016
Rationale: let's choose 8=2+6. So,
Consider d=2 and e=6
Therefore, changing every occurrence of 2 with 6 in the whole statement(i.e both R.H.S and L.H.S), we get
746586+869430=1616016
ANSWER:D
Answer: (D) 1616016
Question: If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
(A) −48
(B) −5
(C) 2
(D) -7
(E) 48
Rationale: i.e. if a = 2 then b = -9
or if a = -9 then b = 2
But in each case a+b = -9+2 = -7
Answer: option D
Answer: (D) -7
Question: How long will it take for a sum of money to grow from Rs.1000 to Rs.5,000, if it is invested at 20% p.a simple interest?
(A) 8 years
(B) 20 years
(C) 72 years
(D) 56 years
(E) None
Rationale: In this case, Rs. 1000 has become Rs.5000.
Therefore, the interest earned = 5000 – 1000 =4000
Interest for Rs 1000 @ 20% for 1 year = 200
200 - 1
4000 - ? => 20 years
Answer : B
Answer: (B) 20 years
Question: 45 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
(A) 24
(B) 77
(C) 30
(D) 25
(E) 13
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 45 :: 18 : x
[Please pay attention, we have written 27 : 45 rather than 45 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
{\color{Blue} x=\frac{45\times 18}{27}}
x = 30
So 30 days will be required to get work done by 27 men.
Answer: C
Answer: (C) 30
Question: The greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively, is:
(A) 123
(B) 127
(C) 235
(D) 4
(E) 505
Rationale: Explanation:
Required number = H.C.F. of (1642 - 6) and (1856 - 4)
= H.C.F. of 1636 and 1852 = 4. Answer: D
Answer: (D) 4
Question: Indu gave Bindu Rs.7500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 5
(B) 2
(C) 9
(D) 5
(E) 12
Rationale: 7500
= D(100/4)2
D = 12
Answer: E
Answer: (E) 12
Question: A store sells brand X pens for 5 dollars each, brand Y pens for $4 each and brand Z pens for $3 each. There are a total of 36 of these three types of pens in the store, the number of brand X pens is twice sum of the number of brand Y pens and brand Z pens, and the difference of the number of brand Y pens and the number of brand Z pens is 2. What is the largest possible total amount that three types of pens will be sold for?
(A) $163
(B) $159
(C) $156
(D) $148
(E) $125
Rationale: Max price = 5X+4Y+3Z -------(1)
Given: X+Y+Z = 36 -------(2)
Given: X = 2(Y+Z) --------(3)
Substitute (3) in (2) Y+Z = 12 -----(4)
Given: Y-Z = 2 ----(5)
Using equations (4) and (5) Y = 7 and Z = 5.
Substitute Y and Z in 3 we get X = 24
Substitute X, Y and Z in (1) we get answer = 163 i.e.
ANSWER:A
Answer: (A) $163
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 33 1/7%
(B) 33 1/6%
(C) 33 1/3%
(D) 33 1/4%
(E) 33 5/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: Working at their respective constant rates, machine A makes 100 copies in 8 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
(A)  250
(B)  425
(C)  675
(D)  825
(E)  750
Rationale: Machine A can produce 100 *30/8= 375 copies
And, Machine B can produce 150* 30/10= 825 Copies
Total producing 700 Copies.
D is the answer
Answer: (D)  825
Question: a,b and c are three sides of a right angled triangle . a,b and c are all integers . Area of the triangle is T1. From all three sides a,b and c , we draw a square having areas as S1, S2 and S3 . Now, Total area ( T1+S1+S2+S3) is :
(A) a fractional value
(B) may be even or odd
(C) odd only
(D) even only
(E) None of these
Rationale: Take any of the pythagorean triplets (3,4,5),(5,12,13),(7,24,25)..e.t.c
I will consider the first one.. a=3,b=4,c=5
then T1= 1/2*3*4= 6(always be even for right angle triangle)
S1= 9(odd)
S2=16(even)
S3=25(odd)
Now T1+S1+S2+S3= 56(even).
also even+even=even, odd+odd=even
ANSWER:D
Answer: (D) even only
Question: How much space, in cubic units, is left vacant when maximum number of 3x3x3 cubes are fitted in a rectangular box measuring 6x9x11 ?
(A) 112
(B) 111
(C) 110
(D) 109
(E) 108
Rationale: No of cubes that can be accommodated in box = (6*9*11)/(3*3*3)
6*9 in numerator can be perfectly divided by 3*3 in denominator.
side with length 11 can't be perfectly divided by 3 and hence is the limiting factor. Closet multiple of 3 less that 11 is 9. so vacant area in cube =
=6*9*(11-9)
=6*9*2
=108
Ans - E
Answer: (E) 108
Question: A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?
(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16
Rationale: Total possible outcomes when coined is tossed 6 time=2^6=4*4*4=64
Total possible outcomes getting 2 or 3 or 4 or 5 tails= 6C2+6C3+6C4+6C5=(6*5)/2+(6*5*4)/(3*2)+(6*5)/2+6=15+20+15+6=56
Probability of getting at least 2 but not more than 5 times tails=56/64=7/8
Ans=C
Answer: (C) 7/8
Question: Find the value of m from given 72519 x 9999 = m?
(A) 455666576
(B) 565476563
(C) 567642887
(D) 725117481
(E) 658899003
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: A tradesman by means of his false balance defrauds to the extent of 12%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 26.4
(B) 25.44
(C) 27.5
(D) 28.54
(E) 27
Rationale: Explanation:
g% = 12 + 12 + (12*12)/100
= 25.44%
Answer: B
Answer: (B) 25.44
Question: John was thrice as old as Tom 6 years ago. John will be 2 times as old as Tom in 4 years. How old is Tom today?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: J-6 = 3(T-6), so J = 3T-12
J+4 = 2(T+4)
(3T-12) + 4 = 2T + 8
T = 16
The answer is C.
Answer: (C) 16
Question: A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 200m
(B) 776 m
(C) 400 m
(D) 187 m
(E) 1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.
Answer:C
Answer: (C) 400 m
Question: there are sixty markings on a clock, minutes hand was exactly on one of those markings. nine markings away from the minutes hand was hours hand. what could be the time.
(A) 5:14
(B) 6:20
(C) 7:48
(D) 3:09
(E) 3:19
Rationale: given angle diff=9mins
we know
1min=6 deg
therefore 9mins=9*6=54 deg
so the angle diff must be 54 deg
better to go through the options
let us consider
A.5hrs 14mins
find angle
angle traced by hour hand=(5*30)+(14/2)=157
angle traced by minute hand=(14*6)=84
angle diff=157-84=73
similarly for option C.
angle traced by hour hand=(7*30)+(48/2)=234
angle traced by minute hand=(48*6)=288
angle diff=(288-234)=54
ANSWER:C
Answer: (C) 7:48
Question: The total cost of 100 paper plates and 200 paper cups is $8.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
(A) $.90
(B) $1.00
(C) $1.20
(D) $1.50
(E) $1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $8.00
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $1.60
Therefore OA is E
Answer: (E) $1.60
Question: In a certain city, 60 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
(A) 15,000 to 75,000 inclusive
(B) 15,000 to 90,000 inclusive
(C) 30,000 to 75,000 inclusive
(D) 60,000 to 90,000 inclusive
(E) 75,000 to 120,000 inclusive
Rationale: The maximum percentage with both is 50% which is 75,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 10% which is 15,000 households.
This means that 40% of households have only recorders but not cable television.
The other 10% of households with recorders have cable television.
The answer is A.
Answer: (A) 15,000 to 75,000 inclusive
Question: Rohit paid $4,000 for 100 shares of stock X and $2,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/5 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) A Gain of 1.4 times as much
(B) A Gain of 3 times as much
(C) A Gain of 2 times as much
(D) A Gain of 1.5 times as much
(E) A Loss of 2 times as much
Rationale: A = 4000; B = 2000; Profit = (3/5)*2000 = 1200
After prices are reversed:
A = 2000; B =4000; Profit = (3/5)*4000 = 2400
2400 --> Gain of 2 times 1200
Answer: C
Answer: (C) A Gain of 2 times as much
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 hours
(B) 6 hours
(C) 8 hours
(D) 9 hours
(E) 3 hours
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
14. If I walk at 3 kmph, I miss
Answer: A
Answer: (A) 2 hours
Question: Of the 60 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
(A)  15
(B)  18
(C)  20
(D)  25
(E)  30
Rationale: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B
The larger diff is
70 want team A so diff is 70-40=30. At least 30 people will NOT get their wish, so for 60 researchers the same number is 18.
Answer choice B
Answer: (B)  18
Question: Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
(A) k/m %
(B) (k – m) %
(C) [100(k – m)] / (100 + k) %
(D) [100(k – m)] / (100 + m) %
(E) [100(k – m)] / (100 + k + m) %
Rationale: One way of doing this is assuming some value for y. Say, y = 60. So x is greater than 20 but less than 30. Say x could be 25.
Not put y = 60 and x = 25 in the options:
(A) y < x < 2y -----> 60 < 25 < 2*120 ( does not hold)
(B) 2y < 6x < 3y ------> 2*60 < 6*25 < 3*60 (holds so could be the answer)
Mind you, you need to check every option to ensure that the relation holds for only one option. If it holds for more than one options, you will need to check for some other values too.
The point is that we assume values and then plug them in the options to see which relation works.
Last Year:
Price per share (PPS) increased by k%. Let's say k = 20. So if the price was 100, it increased by 20% to become 120 (New PPS).
Earnings per share increased by m%. Let's say m = 10 (m must be less than k). So if earnings per share was also 100, it increased by 10% to become 110 (New EPS).
By what percent did the ratio of price per share to earnings per share increase?
Ratio of PPS/EPS was 100/100 = 1
New ratio = New PPS/ New EPS = 120/110 = 1.0909
%Increase = [(1.0909 - 1)/1] * 100 = 9.09%
Now, in the options, put k = 20, m = 10
Only (D) will give you 9.09%. Let me show you calculations of some of the options.
B. (k – m) %
(20 - 10)% = 10% (Not the answer)
C. [100(k – m)] / (100 + k) %
[100(20 - 10)]/(100 + 20) % = 1000/120 % = 8.3% (Not the answer)
D. [100(k – m)] / (100 + m) %
[100(20 – 10)] / (100 + 10) % = 1000/11 % = 9.09% (Answer) answer is D
Answer: (D) [100(k – m)] / (100 + m) %
Question: Line m lies in the xy-plane. The y-intercept of line m is -5, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
(A) -3
(B) -1
(C) -1/3
(D) 0
(E) Undefined
Rationale: Ans: A
Solution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)
as we can see that the y axis of intercept point is (0,-5) means line m is parallel to x axis
slope M= -3
Ans: A
Answer: (A) -3
Question: How many different subsets of the set {11, 14, 17, 24} are there that contain an odd number of elements?
(A)  3
(B)  6
(C)  10
(D)  8
(E)  12
Rationale: Answer = D = 8
{11}
{14}
{17}
{24}
{11, 14, 17}
{14, 17, 24}
{11, 17, 24}
{11, 14, 24}
Answer: (D)  8
Question: You need to print a document of the area 216 sq cm. Condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides. What is the optimized size of your paper?
(A) 60sq.cm
(B) 70sq.cm
(C) 95sq.cm
(D) 80sq.cm
(E) 90sq.cm
Rationale: let us consider it is a rectangle.
so area=24*9=216sq.cm
now (24-3*2)*(9-2*2)=18*5=90sq.cm
ANSWER:E
Answer: (E) 90sq.cm