mathewhe/aqua_rat huggingface dataset:
Question: Two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?
(A) 85/852
(B) 45/69
(C) 18/456
(D) 13/102
(E) 23/125
Rationale: let S be the sample space then
n(S)=52C2=(52*51)/(2*1)=1326
let E be the event of getting 1 spade kings and 1 heart
let n(E)=number of ways of chossing 1 spade out of 13 and 1 heart out of 13=(13C1*13C1)=13*13=169
P(E)=n(E)/n(S)
=169/1326
=13/102 Answer(D)
Answer: (D) 13/102
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) x
(B) x/2
(C) 2x/3
(D) 3x/2
(E) 2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 10 = x/20 hours = 3x minutes
Jessica needs to wait 3x - x = 2x minutes.
The answer is E.
Answer: (E) 2x
Question: A fruit seller had some oranges. He sells 40% oranges and still has 540 oranges. How many oranges he had originally?
(A) 700
(B) 900
(C) 720
(D) 730
(E) 740
Rationale: 60% of oranges = 540
100% of oranges =(540×100)/6=900
total oranges = 900
ANSWER : B
Answer: (B) 900
Question: Count the two-digit whole numbers which yield a remainder of 5 when divided by 10 and also yield a remainder of 0 when divided by 3?
(A) Two
(B) Five
(C) Three
(D) One
(E) Six
Rationale: Answer = C) Three
Two digit Numbers giving remainder 5 when divided by 10 = 15, 25, 35, 45, 55, 65, 75, 85, 95
The numbers giving remainder 0 when divided by 3 = 15, 45, 75 = 3
Answer: (C) Three
Question: Find the amount on Rs.7000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5568
(B) 6369
(C) 5460
(D) 7644
(E) 6734
Rationale: 7000 * 104/100 * 105/100
=> 7644
Answer:D
Answer: (D) 7644
Question: A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
(A) 2,250 meters / minute
(B) 1,250 meters / minute
(C) 5,250 meters / minute
(D) 6,250 meters / minute
(E) 4,250 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 * 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer B
Answer: (B) 1,250 meters / minute
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 1067
(C) 1977
(D) 1056
(E) 1097
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: A
Answer: (A) 1000
Question: If two typists can type two pages in two minutes, how many typists will it take to type 49 pages in seven minutes?
(A) 3
(B) 4
(C) 6
(D) 12
(E) 14
Rationale: In 2 minutes 2 typists type 2 pages which means that in 7 minutes they will type 7 pages but to type 49 pages (7 times) we need 7 times more typists i.e. 2 x 7 = 14 typists.
E
Answer: (E) 14
Question: If a < 0, c > 0, and b > 5, which of the following is true?
I. a * b * c > 0
II. a * b * (-c) < 0
III. a^2 * b * c > 0
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: I. Not true, example: a = -1, b = 6, and c = 1, so a * b * c= -6
II. Not true, a and (-c) are both negative and b is positive so the product will be positive
III. True, a^2 is positive and so are b and c so the product is positive
C
Answer: (C) III only
Question: In a school with 632 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
(A) 150
(B) 200
(C) 250
(D) 158
(E) None
Rationale: Sol.
Let the number of grils be x.
Then, number of boys = (632 - x).
Then, (11 3/4 × 632)
⇔ 11x + 12(632 - x) ⇔ x = 7584 - 7426 ⇔ 158.
Answer D
Answer: (D) 158
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 10 cm, and the point of contact is 12 cm above the ground, what is the radius of the other ball (in centimeters)?
(A) 14
(B) 15
(C) 16
(D) 18
(E) 20
Rationale: A straight line will join the two centers and the point of contact, thus making similar triangles.
2/10 = (r-12)/r
2r = 10r - 120
r = 15
The answer is B.
Answer: (B) 15
Question: In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
(A) 28000
(B) 30000 candidates
(C) 32000
(D) 33000
(E) None of these
Rationale: Explanation :
Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)
Hence total eligible candidates = 95x/100
Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)
Hence Total eligible candidates belonged to other categories
= total eligible candidates × (15/100) = (95x/100) × (15/100)
= (95x × 15)/(100 × 100)
Given that Total eligible candidates belonged to other categories = 4275
⇒ (95x × 15)/(100 × 100) = 4275
⇒ (19x × 15)/(100 × 100) = 855
⇒ (19x × 3)/(100 × 100) = 171
⇒ (x × 3)/(100 × 100) = 9
⇒ x/(100 × 100) = 3
⇒ x = 3 × 100 × 100 = 30000
Answer : Option B
Answer: (B) 30000 candidates
Question: If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q?
(A) 35
(B) 42
(C) 45
(D) 49
(E) 54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × q
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x q
=> a^3 = 3^3 * 5^3 * 7 x q
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x q
q = 7^2 = 49
Answer D
Answer: (D) 49
Question: The number b yields a remainder p when divided by 15 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of b ?
(A) 45
(B) 52
(C) 66
(D) 80
(E) 96
Rationale: I solved this question in the following way:
Q<7 so Q can be from 0 to 6 and P<15 so P can be from 0 to 14, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 14.
b=15k + P or b= 15k + 7 to 14 and look at the answer as, place different values for k, B will give 52 which is 15*3 + 7, the other answers are out of the range
Answer: (B) 52
Question: A trader bought a car at 20% discount on its original price. He sold it at a 55% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 24%
(C) 12%
(D) 82%
(E) 16%
Rationale: Original price = 100
CP = 80
S = 80*(155/100) = 124
100 - 124 = 24%
Answer:B
Answer: (B) 24%
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 45 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
(A) 17
(B) 18
(C) 22
(D) 26
(E) 36
Rationale: The total sum of the numbers should be increased by 20.
Then the average will increase by 20/10 = 2.
The correct average is 18.
The answer is B.
Answer: (B) 18
Question: A fill pipe can fill 1/2 of cistern in 10 minutes. In how many minutes, it can fill 1/2 of the cistern?
(A) 1 min
(B) 4 min
(C) 6 min
(D) 10 min
(E) 25min
Rationale: Required time = 10*2*1/2 = 10 minutes
Answer is D
Answer: (D) 10 min
Question: 20 carrots on a scale weigh 3.64 kg. When 4 carrots are removed from the scale, the average weight of the 16 carrots is 180 grams. What is the average weight (in grams) of the 4 carrots which were removed?
(A) 160
(B) 170
(C) 180
(D) 190
(E) 200
Rationale: 16*180=2880.
The other 4 carrots weigh a total of 760 grams.
The average weight is 760/4 = 190 grams.
The answer is D.
Answer: (D) 190
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $5. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
(A) $24960
(B) $25920
(C) $28080
(D) $28350
(E) $29160
Rationale: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.
Therefore, the total revenue from ticket sales that day was 27*30*5+27*90*10=$28,350.
Answer: D.
Answer: (D) $28350
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
(A) 150
(B) 152
(C) 278
(D) 267
(E) 261
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer:A
Answer: (A) 150
Question: If a - b =4 and
a2+b2=52
, find the value of ab.
(A) 8
(B) 26
(C) 18
(D) 42
(E) 36
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2ab=52âˆ’16=36
=>ab=18
Option C
Answer: (C) 18
Question: The Simplistic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
(A) 9
(B) 12
(C) 36
(D) 72
(E) 108
Rationale: The nouns have fixed structure C-V-C-V-C. Now, each C can take 3 values (let's say X, Y or Z) and each V can take 2 values (let's say A or E), so there will be 3*2*3*2*3=108 nouns possible.
Answer: E.
Answer: (E) 108
Question: In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?
(A) 10
(B) 20
(C) 30 %
(D) 40
(E) 50
Rationale: Let the sample be 100.
Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.
60% = (x) + y
Given 30% = second year (x)
club both , we get y = 30%.
Answer: option C is correct answer.
Answer: (C) 30 %
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 7 times his original investment. What is the value of n?
(A) 50 years
(B) 25 years
(C) 12 years 6 months
(D) 37 years 6 months
(E) 75 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $700.
Therefore, the Simple Interest earned = 700 - 100 = $600.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 600 = (100 * n * 8) / 100
Or 8n = 600
Or n = 75 years.
correct choice is (E)
Answer: (E) 75 years
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 5 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
(A) 55
(B) 57
(C) 58
(D) 61
(E) 63
Rationale: 100%. There are total of 30+33-1=62 books and 2+5=7 books are removed, thus 62-7=55 books are left.
Answer: A.
Answer: (A) 55
Question: If a is the sum of u consecutive positive integers. b is the sum of v consecutive positive integers. For which of the following values of u and v is it impossible that a = b?
(A) u = 2; v = 6
(B) u = 3; v = 6
(C) u = 7; v = 9
(D) u = 10; v = 7
(E) u = 10; v = 4
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that a = b if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and D (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with E to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus E is the right answer.
Answer: (E) u = 10; v = 4
Question: X and Y are positive integers. If X is a prime factor of Y^2 , which of the following MUST be true?
(A) X is even
(B) X=Y^2
(C) Y/X is even
(D) X/Y is less than or equal to 1
(E) X+1 is also a prime factor of Y^2
Rationale: A. x is even --> not necessarily true: x=3=odd x=3=odd and y=3y=3;
B. x=y^2 --> never true, as x=primex=prime then it can not equal to square of another integer;
C. y/x is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd yx=1=odd;
D. x/y is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y^2 --> not necessarily true: if x=2x=2 and y=2y=2 then x+1=3x+1=3 and 3 is not a factor of y2=4y2=4.
Answer: D.
Answer: (D) X/Y is less than or equal to 1
Question: Which of the following is the product of two integers whose sum is 13?
(A)  -42
(B)  -28
(C)  12
(D)  26
(E)  32
Rationale: I solved this Question like this,
Let the two integers are x,y
x+y=13 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
C. 12
Do the factorization : (1,12)----> There sum is 13 Bingo!!!!
So, my answer is C...
As the answer is in C, it took me very less time to answer the question. but i think this method is be simple and efficient.
Answer: (C)  12
Question: A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 150 more than A :
(A) 2348
(B) 7250
(C) 4350
(D) 1998
(E) 2771
Rationale: Explanation:
A B C
investment 3x 4x 5x
Rate of return 6y% 5y% 4y%
Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100}
Total = (18+20+20) = \inline \frac{58xy}{100}
B's earnings - A's earnings = \inline \frac{2xy}{100} = 150
Total earning = \inline \frac{58xy}{100} = 4350
Answer: C) Rs.4350
Answer: (C) 4350
Question: If x and y are integers such that x^2= 2y and xy = 32, then x – y = ?
(A) -30
(B) -20
(C) -5
(D) -4
(E) 20
Rationale: here x and y are integers .
x^2=2y,xy =32.
substitute (x^2)/2=y in xy => x^3=32*2=>x^3=64.
here X3 is positive ,
X is also positive.
x=4 then y=8.
X-y=-4
so option D is correct
Answer: (D) -4
Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $15 more than that received by B, find the total amount shared by A, B and C.
(A) $250
(B) $340
(C) $640
(D) $440
(E) $540
Rationale: A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $15
A = 15+B
(1)===> C = 45+3B - B = 2B+45 ==> 2B-C = -45 ---(3)
(2)===> C = 3.5 B - B-15 = 2.5B-15==>2.5B-C = 15---(4)
from (4) and (3) 0.5B = 60
B = $120
A= $135
C =405-120=$285 Total amount = 135+120+285 = $540
Answer: E
Answer: (E) $540
Question: find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.
(A) 648
(B) 649
(C) 650
(D) 651
(E) 652
Rationale: when unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place.
=> 5*5p5 numbers
when unit place is 4, tenth place should be 2 or 6
=> 2*4p4 numbers
total = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648
ANSWER:A
Answer: (A) 648
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (2,2) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
(A) (-2,6)
(B) (0,4)
(C) (2,-6)
(D) (2,6)
(E) (4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,2) or (2,0), then the area is 1/2*2*2=2. Thus A must be at (4,0).
Answer: E.
Answer: (E) (4,0)
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 47%
(C) 57%
(D) 60%
(E) 62%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: In Orange County one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 60.
(B) 42.
(C) 85.
(D) 142.
(E) 112.
Rationale: The number must be an integer and multiple of both 8 and 7.
Only option E fulfill this condition and hence is the answer.
Answer: (E) 112.
Question: In how many ways can 6 apples (identical) be distributed among 3 children? (Some children may get no apples.)
(A) 32
(B) 34
(C) 36
(D) 28
(E) 30
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=6 r= 3
8C2 =28
Answer : D
Answer: (D) 28
Question: Two employees A and B are paid a total of Rs. 570 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
(A) s.130
(B) s.140
(C) s.150
(D) s.228
(E) s.282
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 570
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 570
⇒ y[15/10 + 1] = 570
⇒ 25y/10 = 570
⇒ 25y = 5700
⇒ y = 5700/25 = Rs.228
D)
Answer: (D) s.228
Question: If X, Y and Z are consecutive numbers (X>Y>Z). X +2Y +3Z = 5Y + 4. What is the value of Z?
(A) 6.
(B) 5.
(C) 4.
(D) 3.
(E) 2.
Rationale: Let the 3 consecutive integers be k-1 (Z), k (Y) and k+1 (X). Given : X +2Y +3Z = 5Y + 4.
k+1 + 2k + 3k - 3 = 5k+ 4 => k =6.
Thus Z = k-1 = 5.
ANSWER:B
Answer: (B) 5.
Question: Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?
(A) 50% lower
(B) 20% lower
(C) 5% lower
(D) 40% lower
(E) 30% lower
Rationale: In this word problem, the first key is to turn the story into equations:
Mandy scored 30% higher than Bertrand did: M = 0.30 + B
Tao scored 20% lower than Jackie did: T = J - 0.20
Jackie scored 40% higher than Mandy did: J = 0.40 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and T (how much higher did Bertrand score than Tao did?). This means that your goal is to get the equations in terms of B and T so that you can solve for the expression B - T.
Taking the first equation and solving for B, you have B = M - 0.30.
Taking the second equation and solving for T you have T = J - 0.20, and then with the third equation you can replace J with 0.40 + M so that both B and T are in terms of M: T = (0.40 + M) - 0.20.
So if B = M - 0.30 and T = M + 0.20, then:
B - T = (M - 0.30) - (M + 0.20)
B - T = M - 0.30 - M - 0.20 (remove the parentheses by distributing the multiplication)
B - T = -0.50, so the answer is A.
Answer: (A) 50% lower
Question: How many times digit 20 is used while writing numbers from 100 to 500?
(A) 20
(B) 30
(C) 15
(D) 25
(E) 20
Rationale: in 100 to 200 there are 5 20's
in 200 to 300 there are 5 20's
in 300 to 400 there are 5 20's
in 400 to 500 there are 5 20's
so, total 20 is 20's
CORRECT OPTION : A
Answer: (A) 20
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 321
(B) 276
(C) 342
(D) 265
(E) 162
Rationale: Explanation:
400*(90/100)*(95/100) = 342
Answer: C
Answer: (C) 342
Question: Find the middle one when The sum of three consecutive even numbers is 42?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 42.
Hence a = 14.
C
Answer: (C) 14
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 31%
(B) 38 1/3%
(C) 33 1/3%
(D) 33%
(E) 35%
Rationale: C
33 1/3%
The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: (C) 33 1/3%
Question: A train 100 meters long completely crosses a 300-meter long bridge in 40 seconds. What is the speed of the train in km/h?
(A) 28 km/h
(B) 32 km/h
(C) 36 km/h
(D) 40 km/h
(E) 44 km/h
Rationale: speed = distance / time = (100 + 300)/40 = 400/40 (m/s) * 3600/1000 = 36 km/h
The answer is C.
Answer: (C) 36 km/h
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
10 minutes more to walk to work than to ride his bicycle, then x equals
(A) 4
(B) 7
(C) 10
(D) 15
(E) 20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 10 mins or 10*60 secs in 10*60/40 =15 km
ANSWER:D
Answer: (D) 15
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many cubes are painted on only 2 faces?
(A) 12
(B) 8
(C) 6
(D) 10
(E) 16
Rationale: The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge.
There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube.
4 + 4 + 4 = 12.
Answer A
Answer: (A) 12
Question: Which of the following is equal to the value of 2^6 + 2^6 + 3^6 + 3^6 + 3^6 ?
(A) 2^7
(B) 2^7 + 3^7
(C) 3^7
(D) 2^8 + 3^8
(E) 2^7 + 3^8
Rationale: 2^6 + 2^6 + 3^6 + 3^6 + 3^6
= 2 (2^6) + 3 (3^6)
= 2^1 (2^6) + 3^1 (3^6)
= 2^(1+6) + 3^(1+6)
= 2^7 + 3^7
Ans: B
Answer: (B) 2^7 + 3^7
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 40?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 40
4n< 33
n < 8. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 8)
Combining the two
-1.5 < n<8.25
n = 1 to 8 (48 integers)
and n = -1 and 0
so 10 integers.
A
Answer: (A) 10
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 9 cm, what is CD, in centimeters?
(A)  1
(B)  8
(C)  3
(D)  4
(E)  5
Rationale: Putting a value to each point, lets use the following:
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 12 (BD = 9)
CD is 12-4 = 8.
Ans B
Answer: (B)  8
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 22 sec
(C) 27 sec
(D) 17 sec
(E) 37 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Answer: (A) 40 sec
Question: A and B enter into a partnership with capitals in the ratio 2 : 3. At the end of 9 months, A withdraws from the business. If their profits are in the ratio 1 : 2, how long did B invest his capital?
(A) 12 months
(B) 8 months
(C) 10 months
(D) 14 months
(E) None of these
Rationale: Explanation:
Let the initial investment of A and B be Rs. 2x and Rs. 3x respectively.
Let B invested for a period of y months.
Then, ratio of capitals of A and B
= (2x × 9) : (3x × y) = 1 : 2
=> 18x/(3x × y) = 1/2
=> 6/y = 1/2
=> y = 12
Hence, B's investment is for 12 months.
Answer: Option A
Answer: (A) 12 months
Question: Carol, Belle and Andrew are business partners. Carol's capital is Rs.12000. If his share of a profit of Rs.1000 is Rs.380 and Andrew's share is Rs.250, what is Belle's capital?
(A) 116847.21
(B) 14684.21
(C) 21684.21
(D) 11684.21
(E) 11685.21
Rationale: 380 + 250 = 630
1000 - 630 = 370
380 ---- 12000
370 ---- ? => 11684.21
ANSWER:D
Answer: (D) 11684.21