mathewhe/aqua_rat huggingface dataset:
Question: Two sets A and B consists only of positive integers such that mean of set A is 70 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>
(A) [A] 65
(B) [B] 60
(C) [C] 70
(D) [D] 55
(E) [E] cannot be determined
Rationale: For this question, we have zero information about the size of two sets, sets AB. These two sets may have the same size or may be wildly different. Thus, the answer is (E), the mathematical answer cannot be determined. This is a very weak math question. As someone who writes GMAT practice questions, I would give this a grade of anD-as a question.
Answer E
Answer: (E) [E] cannot be determined
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 8 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
(A) 13
(B) 15.5
(C) 14
(D) 14.5
(E) 15
Rationale: Ans is B
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/8)+(x/18)) = 15.5 (formula avg speed = total distance/ total time)
Answer: (B) 15.5
Question: The Fisherman sale, all of the prices of the fishes sold were different. If the price of a radio sold at the fisherman sale was both the 4th highest price and the 13th lowest price among the prices of the fishes sold, how many fishes were sold at the fisherman sale?
(A) 13
(B) 14
(C) 15
(D) 41
(E) 16
Rationale: 3+12+1= 16
Answer: E
Answer: (E) 16
Question: Each of the following equations has at least one solution EXCEPT A. Is it true?
(A) -3*a = -3-a
(B) 2*a = (–2)*-a
(C) 2* -a = (–2)*a
(D) (–2)-a = –2-a
(E) -2*-a = 2a
Rationale: If we put a=1 then
B. 2
C. -2
D. -3
E. 2
A. -3=-4 not true.
Answer: (A) -3*a = -3-a
Question: A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
(A) 67/90
(B) 29/60
(C) 17/30
(D) 19/30
(E) 11/15
Rationale: I think A - 67/90 is the correct answer.
Here goes:
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 7x
So old = x, New = 6x
Now 1/3 of x are occupied and 1/5 of 6x are occupied which simplifies to (6/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 6/5 of x occupied in the new ward. Add them up to get 23/15 of x
There are 6x beds in New Tower so ratio is:
(23/15)x / 6x = 23/90 of x
Subtract that from 90/90 of x and you get the number of un-occupied beds to total capacity of New Tower = 67/90.
A
Answer: (A) 67/90
Question: 5+3
(A) 8
(B) 13
(C) 28
(D) 6
(E) 2
Rationale: A
Answer: (A) 8
Question: A boy can reach a certain place in 15 hours. If he reduces his speed by 1/30th, he goes 4 km less in that time. Find his speed.
(A) 4 km/hr.
(B) 6 km/hr
(C) 8 km/hr
(D) 14 km/hr
(E) None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
15x - (15 * 29x/30) = 4
=> 30x-29x = 4*2
=> x = 8 km/hr.
Answer : C
Answer: (C) 8 km/hr
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
(A) 33
(B) 50
(C) 99
(D) 87
(E) 71
Rationale: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: B
Answer: (B) 50
Question: If A=x% of y and B=y% of x, then which of the following is true?
(A) A is smaller than B.
(B) A is greater than B.
(C) Relationship between A and B cannot be determined.
(D) If x is smaller than y, then A is greater than B.
(E) None of these
Rationale: Explanation :
Given,
A=x% of y=(x/100)×y.
And, B=(y/100)×x
Hence, A = B.
Answer : E
Answer: (E) None of these
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 504. Find the sum?
(A) 7000
(B) 7029
(C) 2778
(D) 4200
(E) 2791
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 504 => 36x/100 - 24x/100 = 504
=> 12x/100 = 840 => x = 4200.Answer:D
Answer: (D) 4200
Question: Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
Solving we get X= -2/3 or -2
Y= 3/4 or 4
C)
Answer: (C) If x<y
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 5?
(A) 0.1
(B) 10
(C) π/10
(D) 8
(E) π
Rationale: Maximum distance straight line is diameter
d = 2r = 10..
ANS option B.
Answer: (B) 10
Question: Find the simple interest on Rs.850 for 10 months at 7 paisa per month?
(A) s.768
(B) s.329
(C) s.595
(D) s.600
(E) s.725
Rationale: Explanation:
I = (850*10*7)/100 = 595
Answer: Option C
Answer: (C) s.595
Question: What is the next number of the following sequence
1,3,4,5,6,7,8,9,1,9,16,25,36,49,64...
(A) 14
(B) 15
(C) 81
(D) 17
(E) 18
Rationale: (1, 3 ,4, 5, 6, 7, 8, 9) (1, 9,16, 25, 36, 49, 64, x)
square of 1st group gives 2nd group
1^2 = 1
3^2 = 9
4^2 = 16
5^2 =25
6^2 =36
7^2 = 49
8^2=64
9^2=81
ANSWER:C
Answer: (C) 81
Question: If x and y are integer, which of the following must also be an integer?
I. x/y
II. y/x
III. x
(A) I alone
(B) II alone
(C) III alone
(D) I and III
(E) None of the above
Rationale: Let's take X = 4and Y = 3
Then X/Y = 4/3 Not an integer.
Y/X = 3/4 Not an integer.
X alone is 4 which is an integer.
Hence C.
Answer: (C) III alone
Question: A number increased by 20% gives 480. The number is?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 480 (120 × 4 = 480)
100 % -------> 400 (100 × 4 = 400)
Option 'C'
Answer: (C) 400
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 26 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 288
(B) 564
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 26 + 21 = 47
T = 12
D = 47 * 12 = 564
Answer: B
Answer: (B) 564
Question: 1/2 + [(2/3 * 3/2)/4] - 9/16 =
(A)  1/16
(B)  3/16
(C)  15/16
(D)  9/13
(E)  0
Rationale: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is B.
Answer: (B)  3/16
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 70% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 30% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
(A) 16 2/3%
(B) 23.53 %
(C) 50%
(D) 60%
(E) 66 2/3 %
Rationale: Assumption
Miles/Gallon
T = 100
P = 170 ( 70% more)
$/gallon
T = 100
P = 130 (30% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 76.47
Hence 100 - 76.47 = 23.53%
Ans B
Answer: (B) 23.53 %
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 10
(B) 40
(C) 48
(D) 56
(E) 34
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: Option C
Answer: (C) 48
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
(A) 3 2/5 Km
(B) 3 3/5 Km
(C) 4 1/5 Km
(D) 5 1/5 Km
(E) None
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 18/6
= 24/2 * 18/60
= 18/5 = 3 3/5 Km
B
Answer: (B) 3 3/5 Km
Question: If Tim had lunch at $50.50 and he gave 30% tip, how much did he spend?
(A) A)$57.45
(B) B)$35.42
(C) C)$65.65
(D) D)$21.56
(E) E)$78.45
Rationale: The tip is 30% of what he paid for lunch.
tip = 30% of 50.50 = (30/100)*50.50 = $15.15
Total spent
50.50 + 15.15 = $65.65
correct answer is C)$65.65
Answer: (C) C)$65.65
Question: Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
(A) Square
(B) Rectangle but not a square
(C) Rhombus
(D) Parallelogram but not a rhombus
(E) Kite
Rationale: Explanatory Answer
The lengths of the four sides, AB, BC, CD and DA are all equal to 41−−√41. (Computation given in the last paragraph)
Hence, the given quadrilateral is either a Rhombus or a Square.
How to determine whether the quadrilateral is a square or a rhombus?
The diagonals of a square are equal. The diagonals of a rhombus are unequal.
Compute the lengths of the two diagonals AC and BD.
The length of AC is √162 and the length of BD is 2–√2.
As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.
Choice C
Answer: (C) Rhombus
Question: The events A and B are independent. The probability that event A occurs is m and the probability that event B occurs is n. Which of the following is equal to the probability that exactly one of the events A and B occurs?
(A) m − 2mn
(B) n − mn
(C) m + n − 2mn
(D) m + n − mn
(E) m + n
Rationale: Probability of A occuring = m , Probability of A NOT occuring = 1-m
Probability of B occuring =n , Probability of B not occurring = 1-n
Probability of atleast of one of A and B occuring = 1-(1-m)(1-n) =m+n -mn
D
Answer: (D) m + n − mn
Question: Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
(A) 17
(B) 88
(C) 21
(D) 26
(E) 18
Rationale: Relative speed = 5.5 - 5 = .5 kmph (because they walk in the same direction)
distance = 8.5 km
time = distancespeed=8.5.5=17 hr
Answer :A
Answer: (A) 17
Question: A starts a business with a capital of Rs. 8500. B joins in the business with Rs.17000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 2 months
(B) 6 months
(C) 7 months
(D) 8 months
(E) None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 8500*12 : x* 17000 = 3 : 1
=> 85*12 : 170x= 3 : 1
=> 85*12/ 170x = 3/1 = 3
=> 85*4 /170x = 1
=> 2/x = 1
=> x = 2. Answer : Option A
Answer: (A) 2 months
Question: If the wheel is 19 cm then the number of revolutions to cover a distance of 1156 cm is?
(A) 11
(B) 14
(C) 18
(D) 10
(E) 19
Rationale: 2 * 22/7 * 19 * x = 1156 => x = 9.7
Answer: D
Answer: (D) 10
Question: A photo-mat shop charges $0.40 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos?
(A) 2 films and 26 photos
(B) 5 films and 6 photos
(C) 5 films and 14 photos
(D) 6 films and 4 photos
(E) 6 films and 28 photos
Rationale: 1st photo = 0.4
Subsequent = 0.4*0.6=0.24
Price of 1 full film=0.4+0.24*35=8.8
Price of 2 full film = 8.8*2=17.6
24-17.6=6.4
6.4=0.4+0.24x
x=25
24--->2 full films and 1+25=26 photos
Answer: A
Answer: (A) 2 films and 26 photos
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average W(arithmetic mean) annual increase in the index over this period?
(A)  (x + 100)/18
(B)  x/18
(C)  (100 − x)/18
(D)  (x − 100)/18
(E)  100x/18
Rationale: CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI W= (x-100)/18
Answer D
Answer: (D)  (x − 100)/18
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 9:00 a.m. and drives north on the same highway at an average speed of 75 km per hour. Mr. Dinkle will
(A) overtake Mr. Smitherly at 9:30 am
(B) overtake Mr. Smitherly at 10:30 am
(C) overtake Mr. Smitherly at 11:00 am
(D) be 30 miles behind at 9:35 am
(E) never overtake Mr. Smitherly
Rationale: After one hour, Mr. Smitherly is ahead by 50 km.
Mr. Dinkle gains on Mr. Smitherly 25 km each hour.
2 hours after 9:00 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: (C) overtake Mr. Smitherly at 11:00 am
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?
(A) 22
(B) 12
(C) 66
(D) 88
(E) 55
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.
Answer: B
Answer: (B) 12
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
(A) 1
(B) 2
(C) 34
(D) 12
(E) 13
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: (A) 1
Question: 60% of the population of a village is 23040. The total population of the village is ?
(A) 38400
(B) 24000
(C) 24936
(D) 25640
(E) None
Rationale: Answer
∵ 60% of P = 23040
∴ P = (23040 x 100) / 60 = 38400
Correct Option: A
Answer: (A) 38400
Question: B is 8km East of A. C is 6km North of B. D is 12km East of C. E is 16km North of D. What is the distance b/w A and E.
(A) 20km
(B) 22km
(C) 18km
(D) 30km
(E) 33km
Rationale: it will make two rightangle triangles
1. 1st triangle ABC AB=8km & BC=6km.So AC=Squareroot(64+36)=10km.
2. 2nd triangle CDE CD=12km & DE=16km.So CE=Squareroot(144+256)=20km.
So, AC+CE = AE = 30km.
ANSWER:D
Answer: (D) 30km
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 18, Find x and y ?
(A) x=4,y=8
(B) x=4,y=9
(C) x=4,y=27
(D) x=4,y=9
(E) x=5,y=8
Rationale: 4+27=31
when reversed 13
31-13=18
x=4,y=27
ANSWER:C
Answer: (C) x=4,y=27
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 360 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 287
(C) 197
(D) 287
(E) 720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 360) = 2 + 2(extra)
=> 2x - 720 = x => x = 720.
Answer: E
Answer: (E) 720
Question: The length R of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
Rationale: Let the length R of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: (D) Increases by 19%
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) 128228
(B) 12800
(C) 12819
(D) 12818
(E) 12812
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: (B) 12800
Question: Use distributive property to solve the problem below:
Maria bought 15 notebooks and 6 pens costing 2 dollars each.How much did Maria pay?
(A) 30 dollars
(B) 40 dollars
(C) 50 dollars
(D) 42 dollars
(E) 70 dollars
Rationale: Solution
2 × (15 + 6) = 2 × 15 + 2 × 6 = 30 + 12 = 42 dollars
Answer D
Answer: (D) 42 dollars
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) 729
(B) 144
(C) 627
(D) 255
(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: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 450 km from the starting point ?
(A) 8 hrs 29 min
(B) 4 hrs 50 min
(C) 2 hrs 28 min
(D) 6 hrs 28 min
(E) 1 hrs 28 min
Rationale: Explanation:
Time taken to cover 450 km = 450/100 = 4 hrs 30 mins
Number of stoppages = 450/75 - 1 = 5
Total time of stoppages = 4 x 5 = 20 min
Hence, total time taken = 4 hrs 50 min.
Answer: B
Answer: (B) 4 hrs 50 min
Question: The average age of man, women and their child 3 years ago was 27 years and that of women and the child 5 years ago was 20 years. The presentage of the man is?
(A) 35
(B) 37
(C) 40
(D) 41
(E) 56
Rationale: Sum of the present ages of man, women and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of women and child = (20 x 2 + 5 x 2) years = 50 years.
man's present age = (90 - 50) years = 40 years.
C
Answer: (C) 40
Question: Pointing to a person, a man said to a woman, "His mother is the only daughter of your father." How was the woman related to the person ?
(A) Aunt
(B) DAUGHTER
(C) father
(D) mother
(E) sister
Rationale: Explanation:
Daughter of your father — Your sister. So, the person's mother is woman's sister or the woman is person's aunt.
Answer: A) Aunt
Answer: (A) Aunt
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 20% but the selling price
remains constant, approximately what percentage of the selling price is the profit
(A) 71%
(B) 81%
(C) 90%
(D) 100%
(E) None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 120% of Rs. 100 = Rs. 120
New S.P. = Rs. 420.
Profit = Rs. (420 - 120) = Rs. 300
Required percentage = (300/420) * 100
= 71.40%(approx) =71%
Answer: A
Answer: (A) 71%
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set E, which cannot be the range of the set E?
(A) 8
(B) B.11
(C) C.14
(D) D.17
(E) E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set E becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: (B) B.11
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
(A) 400
(B) 365
(C) 385
(D) 315
(E) 325
Rationale: Explanation:
Average of the two areas =7002=350
one-fifth of the average of the two areas=3505=70
⇒ Difference of the two areas =70
Let area of the smaller part =x hectares.
Then, area of the larger part =x+70 hectares.
x+(x+70)=700
⇒2x=630
⇒x=315
Answer: Option D
Answer: (D) 315
Question: If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 101 * n^2 <=8100
n^2 <=8100/101 which will be less than 81 since 8100/100 = 81 which is the square of 9
Next closest value of n where n^2<=81 is 8
Ans B
Answer: (B) 8
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) 20%
(B) 28%
(C) 33 1/3 %
(D) 35 2/7 %
(E) 25%
Rationale: 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
Answer: (C) 33 1/3 %
Question: How many terms are there in 2,4,8,16……1024?
(A) 10
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2 =2.
Let the number of terms be n . Then
2 x 2n-1 =1024 or 2n-1 =512 = 29.
n-1=9 or n=10.
ANSWER A 10
Answer: (A) 10
Question: What is the smallest integer k for which 64^k > 4^20?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 64^k > 4^20
4^(3k) > 4^20
3k > 20
k = 7
The answer is D.
Answer: (D) 7
Question: Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 14 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
(A) A)1/12
(B) B)9/100
(C) C)1/8
(D) D)4/5
(E) E)9/10
Rationale: Total letters 14,out of which the first letter is anything of 10 but N or X...
So there are 12possible letters for first place..
And only one of them is correct..
So 1/12
Answer: A
Answer: (A) A)1/12
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/5 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
(A) 10
(B) 12
(C) 15
(D) 25
(E) 30
Rationale: Machine K works at a rate of 1/15 of the units per hour.
The rate of K + M together is 4/5 * 1/6 = 2/15 of the units per hour.
The rate of machine M is 2/15 - 1/15 = 1/15.
It would have taken machine M a total time of 15 hours.
The answer is C.
Answer: (C) 15
Question: Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/7, 1/2, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?
(A) 1/21n
(B) (n-1)/14n
(C) 1/7n
(D) (n+2)/72n
(E) (3n-2)/2n
Rationale: 1/7 * 1/2 * (1-1/n)
= 1/14 * (n-1)/n
= (n-1)/14n
Answer - B
Answer: (B) (n-1)/14n
Question: A and B complete a work in 8 days. A alone can do it in 12 days. If both together can do the work in how many days?
(A) 4.8 days
(B) 3.8 days
(C) 3.65 days
(D) 3.77 days
(E) 5.75 days
Rationale: 1/8 + 1/12 = 5/24
24/5 = 4.8 days
Answer:A
Answer: (A) 4.8 days
Question: Aishwarya’s mom was 36 years of age at the time of her birth, while her mom was 30 years old when her 4 years younger sister was born. The variance between the parents ages is :
(A) 6 years
(B) 11 years
(C) 10 years
(D) 9 years
(E) 4 years
Rationale: C
10 years
Mom’s age when Aishwarya’s sister was born = 30 years.
Dad’s age when Aishwarya’s sister was born = (36 + 4) years = 40 years.
Needed Variance = (40 – 30) years = 10 years.
Answer is C
Answer: (C) 10 years