mathewhe/aqua_rat huggingface dataset:
Question: x2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for 'b'?
(A) 3
(B) 12
(C) 6
(D) 24
(E) 8
Rationale: Explanatory Answer
In any quadratic equation of the form ax2 + bx + c = 0, represents the value of the sum of the roots and c/a represents the value of the product of the roots.
In the equation given in the question, the product of roots = 72/1 = 72.
We have been asked to find the number of values that 'b' can take.
If we determine all possible combinations for the roots of the quadratic equation, we can find out the number of values that 'b' can take.
The question states that the roots are integers.
If the roots are r1 and r2, then r1 * r2 = 72, where both r1 and r2 are integers.
Combinations of integers whose product is 72 are : (1, 72), (2, 36), (3, 24), (4, 18), (6, 12) and (8, 9) where both r1 and r2 are positive. 6 combinations.
For each of these combinations, both r1 and r2 could be negative and their product will still be 72.
i.e., r1 and r2 can take the following values too : (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12) and (-8, -9). 6 combinations.
Therefore, 12 combinations are possible where the product of r1 and r2 is 72.
Hence, 'b' will take 12 possible values.
Alternative Method
If a positive integer 'n' has 'x' integral factors, then it can be expressed as a product of two number is x/2 ways.
So, as a first step let us find the number of factors for 72.
Step 1: Express 72 as a product of its prime factors. 23 * 32
Step 2: Number of factors = (3 + 1)*(2 + 1) = 12 (Increment the powers of each of the prime factors by 1 and multiply the result)
i.e., 72 has a 12 positive integral factors.
Hence, it can be expressed as a product of two positive integers in 6 ways. For each such combination, we can have a combination in which both the factors could be negative. Therefore, 6 more combinations - taking it to total of 12 combinations.
Choice B
Answer: (B) 12
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs.16.57
(B) Rs.16.29
(C) Rs.16.20
(D) Rs.16.50
(E) Rs.16.27
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs.16.50
Answer: D
Answer: (D) Rs.16.50
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.50 per metre.
(A) 2399
(B) 3888
(C) 2999
(D) 5940
(E) 2888
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.50) = Rs. 5940.
Answer: D) 5940
Answer: (D) 5940
Question: A can do a work in 3 days. B can do the same work in 6 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?
(A) 600,400
(B) 500,500
(C) 300,700
(D) 800,200
(E) 200,400
Rationale: Ratio of their works A:B = 3:6
Ratio of their wages A:B = 1:2
A's share = (1/5)1000 = 200
B's share = (2/5)1000 = 400
correct option is E
Answer: (E) 200,400
Question: The price of a T.V. set worth Rs. 15000 is to be paid in 20 installments of Rs. 2000 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) 29997
(B) 28088
(C) 27098
(D) 13000
(E) 2799
Rationale: Money paid in cash = Rs. 2000
Balance payment = (15000- 2000) = Rs. 13000.Answer:D
Answer: (D) 13000
Question: In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n times)?
(A) 27,0
(B) 54,2
(C) 49/2, 54
(D) 49, 27
(E) 49, 29
Rationale: Given equation: 2*x^4 +0*x^3 - 49*x^2 +0*x +54
let x1 and x2 be two roots of the equation then
sum of roots is x1+x2= (-b)/a= 0/2=0
and product is given by x1 * x2 = c/a=54/2=27
ANSWER:A
Answer: (A) 27,0
Question: A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
(A) 116
(B) 132
(C) 148
(D) 164
(E) 180
Rationale: 3/10*P are ponies with horseshoes, so P is a multiple of 10.
5/8*3/10*P = 3/16*P are Icelandic ponies with horseshoes, so P is a multiple of 16.
The minimum value of P is 80. Then H = P+4 = 84.
The minimum number of horses and ponies is 164.
The answer is D.
Answer: (D) 164
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is?
(A) 44%
(B) 45%
(C) 50%
(D) 55%
(E) 60%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120	x	m	= 6	x	m.
100	5
New breadth = 120	y	m	= 6	y	m.
100	5
New Area = 6	x x	6	y	m2	= 36	xy	m2.
5	5	25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11	xy x	1	x 100	%	= 44%.
A)
Answer: (A) 44%
Question: In Town X, 65 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 27%
(C) 32%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 65%, out of which 48 are employed males, hence 17% are employed females.
(employed females)/(total employed people)=17/64=27%
Answer: B.
Answer: (B) 27%
Question: If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?
(A) -12
(B) -18
(C) -24
(D) -36
(E) -48
Rationale: we are given |x - y| = 12,
minimum possible value of xy would be maximum numeric value with a -ive sign..
so one of x or y will be negative and other negative..
|x-y|=12 in this case means that the numeric sum of x and y is 12..
various combinations could be -1 and 11, -2 and 10, -6 and 6, -11 and 1 and so on..
when the sum of two numbers is given, the max product is when both x and y are same numeric value...
so xy will have max numeric value when numeric value of x and y=12/2=6..
so numeric value of xy=36 but one of x and y is -ive..
so answer is -36
ANSWER:D
Answer: (D) -36
Question: A train crosses a post in 15 seconds and a platform 100 m long in 25 seconds. Its length is
(A) 75
(B) 100
(C) 125
(D) 175
(E) 150
Rationale: Assume x is the length of the train and v is the speed
x/v = 15 => v = x/15
(x+100)/v = 25 => v = (x+100)/25
Ie, x/15 = (x+100)/25
=> 5x = 3x+ 300
=> x = 300/2 = 150
Answer is E.
Answer: (E) 150
Question: John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
(A) 5 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days
B)
Answer: (B) 8 days
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
(A) 3!*8!*4!*4! Ways
(B) 8!*4!*4! Ways
(C) 3!*8!*4!*Ways
(D) 3!*4!*4! Ways
(E) 4!*4! Ways
Rationale: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Option A
Answer: (A) 3!*8!*4!*4! Ways
Question: Find the number of ways in which 5 different beads can be arranged to form a necklace.
(A) 30
(B) 20
(C) 12
(D) 60
(E) 80
Rationale: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,5 beads can be arranged to form a necklace in(5-1)! /2ways
= 4*3*2/2 = 12 ways
Answer is C
Answer: (C) 12
Question: What is the difference between the local value of 7 and 5 in the number 2574?
(A) 430
(B) 377
(C) 288
(D) 277
(E) 112
Rationale: Explanation:
500 â€“ 70 = 430
Answer: A
Answer: (A) 430
Question: A teacher randomly selects 3 students to clean the classroom. There are 6 girl and 4 boy students in the class. What is the probability the teacher will select exactly 2 girls?
(A) 3/7
(B) 7/11
(C) 1/3
(D) 2/5
(E) 2/3
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 3 students from 10 students = 10C3 = 10!/[3!(10 - 3)!] = 120.
To have 2 girls there must be 1 boy, select 1 boy from 4 = 4C1 = 4.
And, select 2 girls from 6 = 6C2 = 15.
2 girls and 1 boy = (4)(15) = 60
Probability = (number outcomes favorable)/(total number outcomes) = 60/120 = 2/3
Answer: E
Answer: (E) 2/3
Question: This year, MBB Consulting fired 6% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
(A) 98.5%
(B) 100.0%
(C) 102.8%
(D) 103.4%
(E) 105.0%
Rationale: 100 employees getting 1000$ avg, so total salary for 100 ppl = 100000
6% reduction in employees lead to 94 employees and a salary increase of 10% of previous avg salary
Thus the new avg salary is = 10%(1000)+1000 = 1100
so total salary of 94 employees is 94*1100 = 103400
Now the new salary is more than previous salary by x%. x = (103400/100000)*100 = 103.4%
So the Answer is D
Answer: (D) 103.4%
Question: In one can of mixed nuts, 20% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
(A) 16 2/3%
(B) 26 2/3%
(C) 25%
(D) 33 1/3%
(E) 35%
Rationale: Can 1: size 1; 30% nuts
Can 2: size 0.5 and 40% nuts
(1x0.2+0.5x0.4)/1.5=26.667= 26 2/3
B
Answer: (B) 26 2/3%
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 50%
(C) 65%
(D) 70%
(E) 75%
Rationale: 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 %
B
Answer: (B) 50%
Question: The speed of a boat in still water is 40kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 22 kmph
(B) 40 kmph
(C) 20 kmph
(D) 15 kmph
(E) 23 kmph
Rationale: Speed downstream = 40 + 20 = 60 kmph
Speed upstream = 40 - 20 = 20 kmph
Answer:C
Answer: (C) 20 kmph
Question: On increasing the price of T.V. sets by 40%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
(A) 4
(B) 5
(C) 56
(D) 12
(E) 7
Rationale: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(140 × 80) = Rs.11200
Increase% = 1200/10000 × 100 = 12%
Answer: D
Answer: (D) 12
Question: If 4log(4*5^2) = x, find x
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 4(log2^2*5^2)=x
4log(5*2)^2=x
4*2log(5*2)=x
8log10=x
log10 base 10=1
so
8*1=x
x=8
ANSWER:D
Answer: (D) 8
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 12 %
(B) 8 %
(C) 9 %
(D) 10%
(E) 4%
Rationale: Explanation:
65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer:E
Answer: (E) 4%
Question: A sum of money is sufficient to pay P's wages for 24 days and Q's wages for 40 days. The same money is sufficient to pay the wages of both for?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let the total money be $x
P's 1day work = $ x/24
Q's 1day work = $ x/40
P+Q 1day work = $ x/15
Money is sufficient to pay the wages of both for 15days
Answer is D
Answer: (D) 15
Question: 6 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2candidates. In how many ways can one cast his vote?
(A) 11
(B) 12
(C) 25
(D) 36
(E) 47
Rationale: There are 9 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 9C2 = 36.
D
Answer: (D) 36
Question: A bat is bought for Rs.400 and sold at a gain of 20% find its selling price?
(A) Rs.460/-
(B) Rs.480/-
(C) Rs.500/-
(D) Rs.520/-
(E) Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
Option 'B'
Answer: (B) Rs.480/-
Question: A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 10 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?
(A) 72
(B) 110
(C) 220
(D) 495
(E) 1096
Rationale: student government + the student advisory board consists of 10 + 8 = 18 members.
6 students hold membership in both, so they were counted twice.
The total number of people to choose from is 18 - 6 = 12
The number of ways to choose 8 members from 12 is 12C8 = 495
The answer is D.
Answer: (D) 495
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50
(B) 99
(C) 88
(D) 76
(E) 12
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer:A
Answer: (A) 50
Question: January 1, 2004 was a Thursday, what day of the week lies on January 1 2005.
(A) Saturday
(B) Monday
(C) Saturday
(D) Tuesday
(E) Wednesday
Rationale: Explanation:
Given that January 1, 2004 was Thursday.
Odd days in 2004 = 2 (because 2004 is a leap year)
(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)
Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday
Answer: Option C
Answer: (C) Saturday
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
(A) 125
(B) 144
(C) 516
(D) 143
(E) 142
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer:B
Answer: (B) 144
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 5.09%
(B) 5.9%
(C) 5.6%
(D) 3.6%
(E) 78.6%
Rationale: C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer:C
Answer: (C) 5.6%
Question: If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 9 inclusive?
(A) 3/16
(B) 5/16
(C) 7/32
(D) 11/32
(E) 17/64
Rationale: One possible case is: rainy-rainy-rainy-not rainy-not rainy-not rainy.
The probability of this case is (1/2)^6 = 1/64
The number of possible cases is 6C3 = 20.
P(exactly 3 rainy days) = 20*1/64 = 5/16
The answer is B.
Answer: (B) 5/16
Question: What least number must be subtracted from 427398 so that remaining no.is divisible by 12
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
On dividing 427398 by 12 we get the remainder 6, so 6 should be subtracted
Answer: Option C
Answer: (C) 6
Question: By selling 18 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%?
(A) 8
(B) 9
(C) 10
(D) 89
(E) 81
Rationale: 85% --- 18
115% --- ?
85/115 * 18 = 13
Answer: B
Answer: (B) 9
Question: Which of the following are/is prime?
I. 143
II. 147
III. 149
(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III
Rationale: Which of the following are/is prime?
I. 143:
- sum of digits multiple of 3? NO
- divisible by 7? NO
- divisible by 11? YES, 13x11=143 --> Not prime
II. 147
- sum of digits multiple of 3? YES, 1+4+7=12 --> Not prime
III. 149
- sum of digits multiple of 3? NO
- divisible by 7? NO
- divisible by 11? NO
- divisible by 13? NO
B is the only possible solution
Answer: (B) III only
Question: John is driving A Royal Enfield motor cycle at 66 km per hour when his rest duration is not considered. He takes small breaks each of 1 minute for every 10 minute of his drive. How much distance will the motor cycle cover in 90 minutes?
(A) 89.9Km
(B) 89.1Km
(C) 89.2Km
(D) 89.3Km
(E) 89.8Km
Rationale: he take break each of 1 minute for every 10 minutes so he drives 81 minutes
66/60*81=89.1km
ANSWER:B
Answer: (B) 89.1Km
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
(A) 50
(B) 58
(C) 60
(D) 65
(E) 70
Rationale: (x+x1+...x14)/15 = 40
50
Option A
Answer: (A) 50
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?
(A) 15
(B) 17
(C) 19
(D) 18
(E) 16
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 57/3 = 19 kmph.
Answer:C
Answer: (C) 19
Question: If 5% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
(A) 2:5
(B) 20:3
(C) 3:7
(D) 6:11
(E) 2:3
Rationale: Let 5% of A = 1/3 B
then 5A/100 = 1B/3
A/20 = B/3
A/B = 20/3
A:B = 20:3
Answer is B
Answer: (B) 20:3
Question: If a farmer sells 5 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 10 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 12
(B) 24
(C) 20
(D) 55
(E) 60
Rationale: Say farmer has n chicken and he is good for d days.:-
We have 3 equations given in question:-
(n-5) * d+4 =(n+10) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
10d-3n=30
4n-5d =20
=> n=20
Ans C it is!
Answer: (C) 20
Question: If a·b·c·d=450, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: prime factorize : 450 = 2*3*5*15
Hence a = 2 and d = 15 .
Hence answer is 15 - 2 = 13
Answer D
Answer: (D) 13
Question: A crate measures 3 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
(A) 27
(B) 3
(C) 6
(D) 8
(E) 12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=3 for the surface 8*12 face.
Volume = 27pi
Answer B
Answer: (B) 3
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 2 ½ kmph
(B) 6 2 ½ kmph
(C) 5 2 ½ kmph
(D) 2 8 ½ kmph
(E) 6 5 ½ kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer:A
Answer: (A) 2 2 ½ kmph
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 18 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
(A) A)11
(B) B)18
(C) C)24
(D) D)29
(E) D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 13..
so total who won N = 11+18 = 29..
D
Answer: (D) D)29
Question: A person walks from one end to the other of a 90-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Let v be the speed of the person and let x be the speed of the walkway.
30(v+x)=90 then 120(v+x)=360
120(v-x)=90
When we add the two equations:
240v=450
v=15/8
time = 90 / (15/8) = 48 seconds
The answer is C.
Answer: (C) 48
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
(A) 30, 40
(B) 30, 47
(C) 30, 46
(D) 30, 498
(E) 30, 41
Rationale: Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Answer: A
Answer: (A) 30, 40
Question: A and b make a business together, and make a profit of Rs 84000. If A get Rs 48000, what was the ratio of investment between them?
(A) 4 : 3
(B) 3 : 2
(C) 5 : 2
(D) 4 : 5
(E) 6 : 5
Rationale: A get 48000
Then B get = (84000-48000) = 36000
Ratio between A and B is = 48000 : 36000 = 4 : 3
Answer : Option A
Answer: (A) 4 : 3
Question: Solve the following quadratic equation by factoring.
u2+15u=-50
(A) -5,-10
(B) 5,10
(C) 4,3
(D) -4,3
(E) 2,5
Rationale: u+5=0=>u=-5
u+10=0=>u=-10
ANSWER A
Answer: (A) -5,-10
Question: A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs.900in the same period of 2 years, What must be the rate of interest?
(A) 25%
(B) 10%
(C) 15%
(D) 20%
(E) 30%
Rationale: Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (900 – 800) = S.I. on Rs. 400 for 1 year
100 = (400 * R * 1) / 100
R = 25% p.a.
ANSWER: A
Answer: (A) 25%