mathewhe/aqua_rat huggingface dataset:
Question: RAM and GOPAL invested in a business. They earned some profit which they divided in the ratio of 1:2. If RAM invested Rs.25, 000, the amount invested by GOPAL is:
(A) Rs. 65,000
(B) Rs. 50,000
(C) Rs. 80,000
(D) Rs. 90,000
(E) Rs. 60,000
Rationale: Invested by Gopal = 25000/1*2 = 50000
ANSWER : B
Answer: (B) Rs. 50,000
Question: A company has 15 managers and 75 associates. The 15 managers have an average salary of $90,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
(A) $35,000
(B) $40,000
(C) $55,000
(D) $65,000
(E) $75,000
Rationale: Another method is to get ratios
Say 30000=a and
We know the # of people are in 1:5 ratio
Average=(3a*1+a*5)/6= 8a/6=40000
Answer is B. $40,000
Answer: (B) $40,000
Question: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
(A) 1/7
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3
Rationale: Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 2Y
or 6X = Y
Total take-home salary= X+ 6X= 7X
hence, she saved 1/7-th portion of her take home salary
A
Answer: (A) 1/7
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 30 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 255$
(C) 420$
(D) 450$
(E) 480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 30 ) = 21 + 234 => 255
Hence answer will be (B)
Answer: (B) 255$
Question: A cycle is bought for Rs.1120 and sold for Rs.1200, find the gain percent?
(A) 7%
(B) 2%
(C) 6%
(D) 1%
(E) 8%
Rationale: Explanation:
1120---- 80
100 ---- ? => 7%
Answer: A
Answer: (A) 7%
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 80 meters apart,then at what speed is the train traveling?
(A) 100km/hr
(B) 110km/hr
(C) 240km/hr
(D) 150km/hr
(E) 200km/hr
Rationale: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*80 = 4000m = 4km
Speed = 60*4=240km/hr
Answer is C
Answer: (C) 240km/hr
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 165
(E) 252
Rationale: Ans: 252
7C1 * 9C2
Answer E)
Answer: (E) 252
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 9
(E) None of these
Rationale: by option
8*2=16(number is doubled)
add 9(16+9=25)
if 25 trebled it becomes 75
ANSWER:C
Answer: (C) 8
Question: A car covers a distance of 720 km in10 hrs. What is its speed in mps.
(A) 40 m/s
(B) 25 m/s
(C) 20 m/s
(D) 15 m/s
(E) 16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (720/10) = 72 kmph
Spees in mps = 72 x 5/18 = 4 x 5 = 20 mps.
Answer: Option C
Answer: (C) 20 m/s
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 20, 35, 45
(D) 20, 45, 55
(E) None of these
Rationale: Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4.
⇒ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer: B
Answer: (B) 16, 28, 36
Question: If x, y, and z are all factors of 35, which of the following must be true?
(A) The product xyz > 35
(B) Either x = y, y = z, or x = z
(C) x – y – z = even
(D) The product xyz is odd
(E) yz/x is an integer
Rationale: All the factors of 35 are odd numbers.
The product of odd numbers is odd.
The answer is D.
Answer: (D) The product xyz is odd
Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged?
(A) 230
(B) 240
(C) 260
(D) 280
(E) 360
Rationale: Number of ways = 61/21 6X5X4X3X2X1 - 360
E
Answer: (E) 360
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Explanation:
Let the Cost Price of one article = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
⇒(SP−CP /CP)=25/ 100=1/4
⇒(20−x)/x=1/4
⇒80−4x=x
⇒5x=80
Option D
⇒x=805=16
Answer: (D) 16
Question: What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”?
(A) 5
(B) 7
(C) 49
(D) 20
(E) 25
Rationale: The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum).
C
Answer: (C) 49
Question: If an item that originally sold for r dollars was marked up by p percent and then discounted by q percent, which of the following expressions represents the final price of the item?
(A) (10,000r + 100r(p – q) – pqr)/10,000
(B) (10,000r + 100r(q – p) – pqr)/10,000
(C) (100r(p – q) – pqr)/10000
(D) (100r(q – p) – pqr)/10000
(E) 10000 /(p – q)
Rationale: Assume r=100, p=10, q=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Answer: (A) (10,000r + 100r(p – q) – pqr)/10,000
Question: The product of n consecutive positive integers is always divisible by?
(A) n^2 -1
(B) (n+1)!
(C) 2n +1
(D) n!
(E) n^2 + 1
Rationale: Plug in some vlues and check -
Product of first 2 number is 2*1
Product of first 3 number is 3*2*1
Product of first 4 number is 4*3*2*1
Product of first 5 number is 5*4*3*2*1
So, The product of first n natural numbers is always divisible by n! , answer will be (D)
Answer: (D) n!
Question: A bag marked at $240 is sold for $120. The rate of discount is?
(A) 10%
(B) 25%
(C) 20%
(D) 50%
(E) 45%
Rationale: Rate of discount = 120/240 * 100 = 50%
Answer is D
Answer: (D) 50%
Question: What is the sum of odd integers from 20 to 80, inclusive?
(A) 1,550
(B) 1,500
(C) 1,240
(D) 1,120
(E) 1,100
Rationale: Number of odd integers = (80-20)/2 + 1
= 60/2 + 1
= 31
Sum of odd integers = (20+80)/2 * 31
= 50 * 31
= 1550
Answer A
Answer: (A) 1,550
Question: A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
(A) 85
(B) 66
(C) 27
(D) 19
(E) 17
Rationale: Explanation:
Total balls in a box = 2W + 3B + 5R = 10 balls.
Therefore total number of ways of drawing 3 balls from 10 balls is 10C3 = 120 ways ........(1)
This includes all types of color combinations of white, black and red.
Now total balls in a box of white and red color = 2W + 5R = 7 balls.
Therefore total number of ways of drawing 3 balls from 7 balls is 7C3 = 35 ways ........(2)
This includes all types of color combinations of white and red only.
Therefore from (1) and (2), we get the total number of ways of drawing 3 balls, which includes at least one black ball = 120 – 35 = 85 ways.
ANSWER: A
Answer: (A) 85
Question: Adam, Bryan, Chris, and David are all basketball players. An unknown habit of Adam's is to score 7 more than half as many points as Bryan. Bryan is their star player and will always score at least 50 points plus Chris' score. Chris is a consistent player in that he will score twice as many points as David. Write a general equation that shows the total score of these four players in a game in terms of David, D
(A) 82 +6D
(B) 82 +4D
(C) 82 +8D
(D) 8D
(E) 50+4D
Rationale: A = B/2+7
B = 50+C
C = 2D
D = D
Now compile new equations
A+B+C+D = (B/2+7) +(50+C) +(2D) +(D)
= (B/2+7) +(50+C) +3D, look back at original equations
=(B/2+7) +(50+2D) +3D
=(B/2+7) +50+5D
= (50+2D)/2+7 +50 +5D
= 25 +D +7+50+5D
=82 +6D
Answer: A
Answer: (A) 82 +6D
Question: A mixture of 70 lts. Of wine and water contains 10% of water. How much water must be added to make 37% of the resulting mixture?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: Its given that currently water is 10% of the mixture.
=> (10/100)(70) = 7lts
lets say x litres of water is added.
=> 7+x = (37/100)(70+x)
=> x = 30 liters
ANSWER:A
Answer: (A) 30
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8. If the shop carries 330 dogs and bunnies total in stock, how many dogs are there?
(A) 42
(B) 66
(C) 98
(D) 112
(E) 154
Rationale: Let us assume the number of dogs, cats and bunnies to be 7x, 7x and 8x
Total dogs and bunnies = 15x.
And we are given that 15x = 330.
Hence x = 22.
Dogs = 7x = 7*22 = 154 (Option E)
Answer: (E) 154
Question: During a sale, the price of a pair of shoes is marked down 14% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
(A) 9%
(B) 10%
(C) 11%
(D) 16%
(E) 90%
Rationale: Assume the price = 100
Price during sale = 86
Price after sale = 100
Percent increase = 14/86*100 = 16% approx.
Correct Option: D
Answer: (D) 16%
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.85 less, he could have gained 25%. What is the cost price?
(A) 372
(B) 375
(C) 278
(D) 425
(E) 288
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
85 ----- ? => 425
Answer:D
Answer: (D) 425
Question: A car covers a distance of 600 km in 6 hours. Find its speed?
(A) 104
(B) 100
(C) 266
(D) 288
(E) 121
Rationale: 600/6 = 100 kmph
Answer:B
Answer: (B) 100
Question: If two sides of a triangle have lengths 10 and 8, which of the following could be the perimeter of the triangle? I. 29 II. 26 III. 30
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(10-8) < {third side} < (8+10).
2 < {third side} < 18.
Perimeter = {third side} + 8 + 10 = {third side} + 18.
20 < {perimeter} < 36.
answer E
Answer: (E) I, II, and III
Question: The function f is defined for all the positive integers n by the following rule: f(a) is the number of positive integers each of which is less than a and has no positive factor in common with a other than 1 . if p is a prime number then f(p)?
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The moment you put a prime number in the function f(a), notice that all the numbers lesser than a have no divisor clashing with divisor of a since a is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: (A) p-1
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 71.5
(B) 72
(C) 72.5
(D) 73
(E) 94.7
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 100 kilometers per hour is 1/100 hours = 3,600/100 seconds = 36 seconds;
Time to cover this distance at regular speed is 36+2=38 seconds = 38/3,600 hours = 4/379 hours;
So, we get that to cover 1 kilometer 1/(4/379) hours is needed --> regular speed 94.7 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: E.
Answer: (E) 94.7
Question: A rectangular circuit board is designed to have width w inches, perimeter p inches, and area x square inches. Which of the following equations must be true?
(A) w^2 + pw + x = 0
(B) w^2 - pw + 2x = 0
(C) 2w^2 + pw + 2x = 0
(D) 2w^2 - pw - 2x = 0
(E) 2w^2 - pw + 2x = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Width =w = 1 inchand length = 1 inch;
Perimeter =p = 4 inches;
Area =x = 1 square inches.
Plug the values of w, p, and x into the answer choices: only for E 2w^2 - pw + 2x = 2 - 4 + 2 = 0.
Answer: E.
Answer: (E) 2w^2 - pw + 2x = 0
Question: All of the students of the Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 98 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
(A) 36
(B) 39
(C) 42
(D) 45
(E) 48
Rationale: 50% of students are in the band only, so 30% of students are in the orchestra only.
Since 20% of students are in both, then 70% of students are in the band which is 98 students.
The number of students in the orchestra is (30/70)*98 = 42.
The answer is C.
Answer: (C) 42
Question: In a group of 80 children and 17 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1140
(B) 1160
(C) 1180
(D) 1300
(E) 1210
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 17 youngsters got = 17 * 20 = 340.
Total number of sweets = 960 + 340 = 1300.
D)
Answer: (D) 1300
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km?
(A) 3
(B) 5
(C) 8
(D) 9
(E) 6
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 10
T = 10/2 = 5
Answer:B
Answer: (B) 5
Question: A librarian has a set of seven books, including four different books about Abraham Lincoln. The librarian wants to put the seven books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other three books. How many different arrangements of the seven books are possible?
(A) (7!)/(4!)
(B) (4!)(3!)
(C) (4!)(4!)
(D) (4!)(7!)
(E) (4!)(3!)(7!)
Rationale: You can club the four Lincoln books as one, which leaves us with three other books plus this one to think about. So, these four items can be arranged in 4! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 4!*4!, which is C.
Answer: (C) (4!)(4!)
Question: A committee of 3 people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 30
(E) 32
Rationale: Each couple can send only one "representative" to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 4 to send only one "representatives" to the committee: 4C3=4.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: E.
Answer: (E) 32
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 100 m
(B) 350 m
(C) 25 m
(D) 30 m
(E) 35 m
Rationale: Explanation:
Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: (B) 350 m
Question: Can you find the missing number in the sequence given below?
11 14 17 12 15 ? 13 16 19 14 17 20
(A) 20
(B) 21
(C) 18
(D) 23
(E) 24
Rationale: Solution:
18
Explanation :
The sequence is given in the puzzle is :
11 14 17 12 15 ? 13 16 19 14 17 20
Let's break the given series as below:
11 14 17
12 15 ?
13 16 19
14 17 20
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 18.
Answer C
Answer: (C) 18
Question: In a drawer there is a number of pair of socks, out of which 1/5 are white pairs, 1/10 are black pairs, and the remaining 7 pairs are red. How many white socks are in the drawer?
(A) 10
(B) 2
(C) 1
(D) 7
(E) 4
Rationale: Let x be the total number of pairs of socks.
x(1/5+1/10)=3x/10 the number of pairs white and black.
x-3x/10=7x/10 is the number of red pairs of socks
7x/10=7 implies x=10.
There are 10 pairs of socks out of which 1/5 are white, that is, 1/5*10=2.
Thus, the total number of white socks is 2*2 =4.
Answer E 4.
Answer: (E) 4
Question: How many of the following numbers are divisible by 3 but not by 9.
4320, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Taking the sum of the digits, we have :
S1 = 9, S2 = 12, S3 = 18, S4 = 9, S5 = 21, S6 = 12, S7 = 18, S8 = 21, S9 = 15, S10 = 24.
Clearly, S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9.
So, the number of required numbers = 6.
ANSWER:B
Answer: (B) 6
Question: Find the sum of first 16 natural numbers
(A) 136
(B) 468
(C) 465
(D) 463
(E) 485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=16(16+1)/2=16(17)/2=136
Answer: Option A
Answer: (A) 136
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 3 men and 2 women from the given committee?
(A) 150
(B) 200
(C) 250
(D) 300
(E) 350
Rationale: The number of ways to select three men and two women = 5C3 * 6C2 = 10 * 15 = 150
The answer is A.
Answer: (A) 150
Question: After decreasing 24% in the price of an article costs Rs.836. Find the actual cost of an article?
(A) 1218
(B) 2777
(C) 1100
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 836
CP= 11 * 100 => CP = 1100
Answer: C
Answer: (C) 1100
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg. How much amount did he pay to the shopkeeper?
(A) A)1235
(B) B)1055
(C) C)1065
(D) D)1075
(E) E)1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 75 × 9 = 675.
Total cost he has to pay = 560 + 675 = 1235.
A)
Answer: (A) A)1235
Question: A Winson's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A)  1:2
(B)  4:5
(C)  1:1
(D)  3:2
(E)  5:3
Rationale: A Winson's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y
1997- x1---- y1-- x1+y1
x1= a*x .....(P)
y1= 1.07*y...(Q)
x1+y1/x+y = 1.01
solve using P and Q and find x/y
Answer: (A)  1:2
Question: Find the average of all the numbers between 6 and 36 which are divisible by 5.
(A) 18
(B) 20
(C) 24
(D) 30
(E) 22.5
Rationale: Solution
Average	= (10+15+20+25+30+35)/6)
= 135 / 6
= 22.5
Answer E
Answer: (E) 22.5
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8091 for a computer table, then what was the cost price of the computer table?
(A) 7297
(B) 2977
(C) 2871
(D) 6725
(E) 6525
Rationale: Explanation:
CP = SP * (100/(100 + profit%))
= 8091(100/124) = Rs. 6525.
Answer: E
Answer: (E) 6525
Question: One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 10 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(B) 20
(C) 12
(D) 8
(E) 4
Rationale: N - Not rented trucks; R - Rented trucks
N + R = 20
N + R/2 = 10
R = 20
B
Answer: (B) 20
Question: 2x + y = 20
|y| <= 20
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 25
Rationale: Hi - The questions says |y| <=20 so the values of y will range from 0 to 20. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. So 21 (d) is the answer. remember sign doesn't matter for y as y will always be positive.D
Answer: (D) 21
Question: 998 x 998 = ?
(A) 996000
(B) 1000000
(C) 996004
(D) 4000
(E) 996008
Rationale: 998 x 998= (998)2
= (1000 - 2)2
= (1000)2 + (2)2 - (2 x 1000 x 2)
= 1000000+ 4 - 4000
= 1000004 - 4000
= 996004.
C)
Answer: (C) 996004
Question: Solve for x: 2x – y = (3/4)x + 6.
(A) (y + 6)/5
(B) 4(y + 6)/5
(C) (y + 6)
(D) 4(y - 6)/5
(E) 2(y - 6)/5
Rationale: Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
Answer: (B).
Answer: (B) 4(y + 6)/5
Question: If 0 < x < 1 < y, which of the following must be true?
(A) 1 < 1/x < 1/y
(B) 1/x < 1 < 1/y
(C) 1/x < 1/y < 1
(D) 1/y < 1 < 1/x
(E) 1/y < 1/x < 1
Rationale: Soln:
0<x<1<y. Let x=1/2 and y =2
Substituting values:
A. 1<2<1/2 --- Wrong
B. 2<1< 1/2 --- Wrong
C. 2<1/2<1 --- Wrong
D. 1/2<1<2 --- Correct
E. 1/2<2<1 --- Wrong
Hence answer is D
Answer: (D) 1/y < 1 < 1/x
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
(A) Rs.201
(B) Rs.220
(C) Rs.228
(D) Rs.205
(E) Rs.202
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer: D
Answer: (D) Rs.205
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
(A) 150
(B) 140
(C) 130
(D) 120
(E) 110
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
ANSWER:A
Answer: (A) 150
Question: Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window?
(A) a 100
(B) b 112
(C) c 90
(D) d 120
(E) e 30
Rationale: D
David's position is fixed. Now we need to arrange all others around David.
There are 5x4x3x2x1= 120 ways to arrange five people.
Answer: (D) d 120
Question: If m / p is an integer, which of the following statements must be true?
(A) m / p is an integer
(B) p is an integer
(C) both m and p are integers
(D) either m or p is negative
(E) m = np where n is an integer
Rationale: Let m = 1/4; p = 1/8 -->m/p = 2
m= np where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: E
Answer: (E) m = np where n is an integer
Question: A box contain 12 chocolates and 10 biscuit packets .What is the probability that one chocolate is selected is:
(A) 12/22
(B) 10/22
(C) 21
(D) 5/22
(E) 6/11
Rationale: Total number of chocolates and biscuit packets = 12+10= 22
no.of chocolates in a box = 12
probability of one chocolate is selected = 12/22= 6/11
Answer is E
Answer: (E) 6/11
Question: Look at this series: 2.2, 2.5, 2.8, 3.1, ... What number should come next?
(A) 3.2
(B) 3.3
(C) 3.4
(D) 3.5
(E) 3.6
Rationale: C
3.4
In this simple addition series, each number increases by 0.3.
Answer: (C) 3.4
Question: For a positive integer n, let Pn denote the product of the digits of nn and Sn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n
(A) 2
(B) 3
(C) 9
(D) 12
(E) None
Rationale: Explanation:
Let the two digit number be 'ab'
Given, a × b + a + b = 10a + b
a × b = 9a
b = 9
Therefore, for b = 9, the above condition satisfies. So all the two digit numbers for which units digit is 9 are our solutions. They range from 19 to 99. Total 9 numbers.
Correct option: c
Answer: (C) 9