mathewhe/aqua_rat huggingface dataset:
Question: In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.200 and B's share is Rs.130, what is C's capital?
(A) Rs.18800
(B) Rs.18700
(C) Rs.18600
(D) Rs.17500
(E) Rs.16400
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 8000
470 ---- ? => Rs.18800
ANSWER:A
Answer: (A) Rs.18800
Question: If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?
(A) Y2=XY
(B) X2=YZ
(C) Y2=XZ
(D) Z2=XZ
(E) Y2=XZ
Rationale: X = (Y*NR)/100 Y = (Z*NR)/100
X/Y = NR/100 Y/Z = NR/100
X/Y = Y/Z
Y2 = XZ
Answer:C
Answer: (C) Y2=XZ
Question: The average age of a group of n people is 14 years old. One more person aged 34 joins the group and the new average is 16 years old. What is the value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 14n + 34 = 16(n+1)
2n = 18
n = 9
The answer is C.
Answer: (C) 9
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 17 inches than that of a rectangular sheet of paper measuring 8.5 inches by 11 inches?
(A) 50%
(B) 87%
(C) 100%
(D) 187%
(E) 200%
Rationale: Area of sheet A = 11*17
Area of sheet B = 11*8.5
Difference in Area = 11*8.5
Required % = (11*8.5)*100/(11*8.5)% = 100%
ANSWER:C
Answer: (C) 100%
Question: An Olympic diver received the following scores: 4, 2, 5, 1. The standard deviation of her scores is in which of the following ranges?
(A) 2.01 to 2.99
(B) 4.01 to 4.99
(C) 1.01 to 1.99
(D) 3.01 to 3.99
(E) 5.01 to 5.99
Rationale: 4+2+5+1/4=3
∣4−3∣^2 =1^2 = 1
∣2−3∣^2 =1^2 = 1
∣5−3∣^2 =2^2 = 4
∣1−3∣^2 =2^2 = 4
sqrt 10/4 =1.58
Answer : C
Answer: (C) 1.01 to 1.99
Question: A train 140 m long running at 84 kmph crosses a platform in 16 sec. What is the length of the platform?
(A) 287
(B) 298
(C) 233
(D) 726
(E) 267
Rationale: D = 84 * 5/18 = 16
= 373 â€“ 140
= 233
Answer: C
Answer: (C) 233
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
(A) Rs 72
(B) Rs 88.20
(C) Rs 79.15
(D) Rs 93
(E) Rs 97
Rationale: C.P. = Rs.	(100/122.5)x 392	= Rs.	(1000/1225)x 392= Rs. 320
Profit = Rs. (392 - 320) = Rs. 72.
ANSWER :A
Answer: (A) Rs 72
Question: The average speed of a car is 1 3/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
(A) 400 km
(B) 320 km
(C) 360 km
(D) 550 km
(E) 600 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bike in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 8/5 * 50 = 80 km
So, the distance covered by car in 4 h is
80 × 4 = 320 km
Ans.(B)
Answer: (B) 320 km
Question: A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
(A) 50 %
(B) 40 %
(C) 35 %
(D) 32 %
(E) 20 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=20%.
Answer: E.
Answer: (E) 20 %
Question: How many integers E are prime numbers in the range 200 < E < 220?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: My friend, every single odd number greater than can be written either as 4E+1 or as 4E+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6E+1 or 6E-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.
Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:
{201, 203, 207, 209, 211, 213, 217, 219}
Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.
{203, 209, 211, 217}
Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that
210 - 7 = 203
210 + 7 = 217
Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with
{209, 211}.
We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that
220 - 11 = 209
is also a multiple of 11. We can eliminate this from the list also.
That leaves us with just 211. There's no zero option in the question, so this must be a prime number.
Answer = (A)
Answer: (A)  1
Question: The Price of 357 apples is Rs.2499. What will be the price of 49 dozens of such apples?
(A) Rs.3800
(B) Rs.2816
(C) Rs.4116
(D) Rs.3116
(E) None of these
Rationale: Expl : More apples, more cost(Direct)
357 *588 : : 2499 : x
x = (588*2499)/357 = 4116
Answer: C
Answer: (C) Rs.4116
Question: A cycle is bought for Rs.900 and sold for Rs.1100, find the gain percent?
(A) 11
(B) 22
(C) 99
(D) 77
(E) 18
Rationale: 900 ---- 200
100 ---- ? => 22%
Answer: B
Answer: (B) 22
Question: Sum of even numbers between 15 and 25 is
(A) 70
(B) 80
(C) 130
(D) 100
(E) 120
Rationale: Explanation: 16 + 18 + .......24.
Taking 2 common we get = 2 ( 8 + 9 + 10 +.....+ 12)
Sum of n natural numbers upto 12
8 + 9 + 10 +.....+ 12 = (1 + 2 + 3 + ......+ 12) - ( 1 + 2 + 3 + ....+ 7)
By applying the formula for the first n natural numbers sum n (n+1)/2we get, =50
So 16 + 18 + .......24 = 2 Ã— 50 = 100
ANSWER IS D
Answer: (D) 100
Question: A pair of prime numbers that can be expressed in the form E{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
(A)  11
(B)  13
(C)  17
(D)  19
(E)  23
Rationale: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that E for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Answer: (D)  19
Question: If g and h are positive integers, and 3 is not a factor of h, then h may be which of the following?
(A) (g−1)·g·(g+1)
(B) (g−3)·(g−1)·(g+1)
(C) (g−2)·g·(g+2)
(D) (g−1)·g·(g+2)
(E) (g−3)·(g+1)·(g+2)
Rationale: Plugged in values :
let g=5
A. (g−1)·g·(g+1) --> divisible by 3
B. (g−3)·(g−1)·(g+1) --> divisible by 3
C. (g−2)·g·(g+2) --> divisible by 3
D. (g−1)·g·(g+2) --> not divisible. Hence the answer.
Answer: (D) (g−1)·g·(g+2)
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 150
(B) 300
(C) 200
(D) 450
(E) 600
Rationale: Explanation:
d^2/2 = (20 * 20)/2 = 200
Answer: C
Answer: (C) 200
Question: When average age of 20 members are 0, how many members greater than 0?
(A) 17
(B) 19
(C) 21
(D) 24
(E) 25
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)
Answer is 19 (B)
Answer: (B) 19
Question: What is the remainder when 8^1 + 8^2 + 8^3 +...+ 8^9 is divided by 4?
(A) 4
(B) 3
(C) 2
(D) 5
(E) None of the above
Rationale: Notice that in the brackets we have the sum of 9 even multiples of 4, hence the sum in the brackets will be even multiple of 4 (the sum of 9 even numbers is even). which yields remainder of 0 upon division by 4.
Answer : E
Answer: (E) None of the above
Question: Evaluate
248+64−−√−−−−−−−−−√
(A) 14
(B) 26
(C) 16
(D) 36
(E) 46
Rationale: Explanation:
=248+64−−√−−−−−−−−−√
=248+8−−−−−−√
=256−−−√
=16
Answer: C
Answer: (C) 16
Question: The last day of a century cannot be
(A) Monday
(B) Wednesday
(C) Tuesday
(D) Friday
(E) Thursday
Rationale: Explanation:
We know that number of odd days in 100 years = 5
Hence last day of the first century is Friday
Number of odd days in 200 years = 5 x 2 = 10 = 3 (As we can reduce multiples of 7 from odd days which will not change anything)
Hence last day of the 2nd century is Wednesday
Number of odd days in 300 years = 5 x 3 = 15 = 1
Hence last day of the 3rd century is Monday
We know that number of odd days in 400 years = 0. (∵ 5 x 4 + 1 = 21 = 0)
Hence last day of the 4th century is Sunday
Now this cycle will be repeated. Hence last day of a century will not be Tuesday or Thursday or Saturday.
Answer: Option C
Answer: (C) Tuesday
Question: 325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 13
(D) 16
(E) 17
Rationale: 26 trees have 25 gaps between them,
Required distance (325/25) = 13
C
Answer: (C) 13
Question: The toll for crossing a certain bridge is $0.70 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
(A) 14
(B) 15
(C) 16
(D) 28
(E) 29
Rationale: Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: C
Answer: (C) 16
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 140 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 55
(B) 70
(C) 75
(D) 85
(E) 95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 140 + P
C + M = 140
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 140/2 = 70.
ANSWER:B
Answer: (B) 70
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 36 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
(A) 154.
(B) 172.
(C) 186.
(D) 198.
(E) 168.
Rationale: All of them catch fishes in relation to number 36....
2/3*36+2*36+2*1.5*36*2/3=168
Answer is E
Answer: (E) 168.
Question: 4y - 4x = xy and x ≠ 0. If x and y are integers, which of the following could equal y?
(A) 2
(B) 1
(C) 0
(D) 5
(E) 6
Rationale: Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> 8 - 4x = 4x >>> Holds true for x = 1, no need to check E. This is the answer.
Answer A
Answer: (A) 2
Question: An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 15%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
(A) $92.00
(B) $88.00
(C) $87.04
(D) $80.96
(E) $80.00
Rationale: Without any discount Sam should pay 10*10=$100. Now, the overall discount would be slightly less than 23%, thus he must pay slightly more than $77.
Answer: E.
Answer: (E) $80.00
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 33809
(B) 12000
(C) 26692
(D) 16689
(E) 27681
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
Answer: B
Answer: (B) 12000
Question: By selling a product with 20% profit, how much profit was earned?
I. The difference between cost and selling price is Rs. 40.
II. The selling price is 120 percent of the cost price.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answe
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
Gain = 20%
I. Profit = (S.P.) – (C.P.) = Rs. 40.
Thus, I give the answer. But, II does not give the answer.
answer is (A).
Answer: (A) I alone sufficient while II alone not sufficient to answer
Question: Nicky and Cristina are running a 400 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A) 40
(B) 25
(C) 35
(D) 30
(E) 50
Rationale: The distance traveled by both of them is the same at the time of overtaking.
3(t+12) = 5t
t=18.
Cristina will catch up Nicky in 18 seconds.
So in 18 seconds Cristina would cover = 18*5 = 90 meter.
Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.
D
Answer: (D) 30
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 50 percent were employees. What percent were stockholders, who were not employees?
(A) 52
(B) 50
(C) 54
(D) 55
(E) 56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
50% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 50% = 50%.
Answer: (B) 50
Question: Which of the following is a possible length for side AB of triangle ABC if AC = 5 and BC = 9?
I. 4
II. 9 √3
III. 13.5
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: (9-5) < AB < (9+5)
The answer is C.
Answer: (C) III only
Question: There is a vertical stack of books marked 1, 2, and 3 on Table-A, with 1 at the bottom and 3 on top. These are to be placed vertically on Table-B with 1 at the bottom and 2 on the top, by making a series of moves from one table to the other. During a move, the topmost book, or the topmost two books, or all the three, can be moved from one of the tables to the other. If there are any books on the other table, the stack being transferred should be placed on top of the existing books, without changing the order of books in the stack that is being moved in that move. If there are no books on the other table, the stack is simply placed on the other table without disturbing the order of books in it. What is the minimum number of moves in which the above task can be accomplished?
(A) One
(B) Two
(C) Three
(D) Four
(E) None
Rationale: Explanation :
1:2-3 moved to B
2:3 moved to A,
3:2 moved to A,
4: whole series shifted to B.
Hence, minimum number of moves is 4 .
Answer : D
Answer: (D) Four
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 4 miles per hour, then 5 miles per hour, then 6 miles per hour. If the test took 74 hours to complete, how many miles was the car driven during the entire test?
(A) 310
(B) 320
(C) 300
(D) 360
(E) 400
Rationale: x is the segment to be traveled
x/4+x/5+x/6 =74
or 74x/120 =74
x = 120 miles . total distance =3*120 = 360 miles
D
Answer: (D) 360
Question: A can complete a project in 30 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 5 days
(E) 12 days
Rationale: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).
(1/30)*(x-10) + (1/30)*(x) = 1
(x/30) + (x/30) - (10/30) = 1
2x/30 = 1/3
x =5
Therefore, the answer is D: 5.
Answer: (D) 5 days
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 160 = (180*4*R)/100
R = 5%.Answer: A
Answer: (A) 5
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
A)
Answer: (A) 2
Question: A and B started a business with initial investments in the ratio 2 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
(A) 6 months
(B) 8 months
(C) 9 months
(D) 5 months
(E) 7 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 2 : 3.
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(2 × 12) / (3 × a) = 8 / 7 => 24a = 168 or
a = 168 / 24 = 7 or 7 months
Option E
Answer: (E) 7 months
Question: A and B are two circles. The radius of A is 5 times as large as the radius of B. What is the ratio between the areas of the circles?
(A) 1:8.
(B) 1:2.
(C) 1:4.
(D) 1:25.
(E) 1:6.
Rationale: Given : The radius of A is 5 times as large as the radius of B. => R(a) = 5R(b). The radius are in ratio of 1:5 thus the area will be in the ratio of square of radius. 1:25. Hence D.
Answer: (D) 1:25.
Question: Arun has 13 boxes of chocolates with him, with an average of 17 chocolates per box. If each box has at least 11 chocolates and no two boxes have equal number of chocolates, then what can be the maximum possible number of chocolates in any box?
(A) 23
(B) 25
(C) 29
(D) Can't be determined
(E) None of these
Rationale: DETAILED SOLUTION
Total number of chocolates = 13 x 17 = 221
For one box to have maximum number of chocolates, the other boxes need to have minimum number of chocolates i.e. 11, 12, ………………….., 22
Total = 11 x 12 + (0+1+2+……………+11)
= 132 + 66 = 198
Therefore, maximum possible chocolates = 221 – 198 = 23
CORRECT ANSWER A.
Answer: (A) 23
Question: If X is the sum of first 20 positive even integers and Y is the sum of first 20 positive odd integers, what is the value of x-y?
Please try to explain your answers
(A) 0
(B) 20
(C) 50
(D) 75
(E) 100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 20 positive even integers minus the sum of first 20 positive odd integers will be 20.
Answer: B
Answer: (B) 20
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 186 ways
(B) 177 ways
(C) 188 ways
(D) 108 ways
(E) 189 ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Answer: (D) 108 ways
Question: A sock drawer contains eight socks, each one a different solid color. The colors of the socks are pink, red, orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 24
(B) 240
(C) 1,024
(D) 2,520
(E) 40320
Rationale: I see no condition for arrangement.
So 8! ways - IMO option E is correct answer..
Answer: (E) 40320
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x + 2y) is positive integer II. (xy)^2 is positive integer III. (y^2 - x) is positive integer
(A) I only
(B) II only
(C) II,III only
(D) III only
(E) none of these
Rationale: I. It is true if 3x < 2y
II. It is always positive
III. It is true
Answer : C
Answer: (C) II,III only
Question: Find the odd man out
1, 2, 5, 14, 41, 124
(A) 2
(B) 14
(C) 124
(D) 41
(E) 21
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:C
Answer: (C) 124
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability Q that both selected dogs are NOT littermates?
(A) 1/6
(B) 2/9
(C) 5/6
(D) 7/9
(E) 8/9
Rationale: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 Q= 1/12.
Again, we obtain 1 - (1/12 + 1/12) = 5/6.
Answer: C
Answer: (C) 5/6
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 15 years
(E) 16 years
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
A)
Answer: (A) 10 years
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 25 litres of tomato juice?
(A) 2.8 liters.
(B) 3.125 liters.
(C) 8.5 liters.
(D) 2.6 liters.
(E) 2.1 liters.
Rationale: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
â‡’â‡’ 10%(25) = 80%(x)
â‡’â‡’ x = 3.125 liters.
Answer:B
Answer: (B) 3.125 liters.
Question: By selling an umbrella for Rs. 300, a shop keeper gains 300%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 1000
(B) 1100
(C) 1150
(D) 1300
(E) 1200
Rationale: Marked price = Rs. 200
C.P. = 100/400 * 200 = Rs. 25
Sale price = 90% of Rs. 200 = Rs. 180
Required gain % = 300/25 * 100 = 1200%.
Answer:E
Answer: (E) 1200
Question: Which is the following is divisible by 11
(A) A)4305
(B) B)4825
(C) C)4805
(D) D)4905
(E) E)654
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 3(3 + 1)//2 = 3 x 2 = 6
Sum of first 99 natural numbers = 33(33 + 1)//2 = 33 x 20 =660
660- 6= 654
Answer: Option E
Answer: (E) E)654
Question: Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $700, how many sales has Matt made?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let, Average Commission = x
No. of items sold = y
Total Commission = xy
New Commission = xy+1000
New Average = (xy+1000) / (y+1) = 150+x
i.e. (xy+1000) = (y+1)* (150+x)
i.e. (xy+1000) = (xy+x+150y+150)
i.e. (850) = (x+150y)
New Commission = 700 = 150+x
i.e. x=550
i.e. y = 2
New Sales = y+1 = 3
Answer: option A
Answer: (A) 3