mathewhe/aqua_rat huggingface dataset:
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many Q miles will Tom drive before Karen wins the bet?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him : T*(t+4/60) = 45 (7/15+4/60) Q= 24 miles. D is the correct answer.
Answer: (D) 24
Question: In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
(A) 67 kg
(B) 68 kg
(C) 69 kg
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Let Arun's weight by X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average = 66 + 67 + 68/ 3 = 201	/ 3	= 67 kg.
ANSWER IS A
Answer: (A) 67 kg
Question: There are 27 different three-digit integers that can be formed using only the digits 1, 3, and 4. If all 27 of the integers were listed, what would their sum be?
(A) 7592
(B) 7692
(C) 7792
(D) 7892
(E) 7992
Rationale: There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 3's and 4's. Then the sum is:
9(111+333+444)=9*(888)=7992.
The answer is E.
Answer: (E) 7992
Question: Mary's income is 500 dollars per week. How much does she makes every year?
(A) 1000 dollars
(B) 12000 dollars
(C) 4000 dollars
(D) 5000 dollars
(E) 26000 dollars
Rationale: Solution:
1 year = 52 weeks.
Mary's one week's income = 500 dollars
Thus, 500 Ã— 52 = 26,000 dollars
Option E
Answer: (E) 26000 dollars
Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
(A) 23
(B) 28
(C) 25
(D) 19
(E) 11
Rationale: Explanation:
Given
R – Q = Q – T and R + T = 50 which gives Q = 25
As the difference between R & Q and Q & T is same
So Answer is 25 years
Answer: C
Answer: (C) 25
Question: In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 360 tiles in the floor, how many tiles does the leftmost row contain?
(A) 48
(B) 56
(C) 60
(D) 64
(E) 68
Rationale: This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 360 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 360 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 360/9 = 48. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 48 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
40 +2 +2 +2 +2 = 48.
Final Answer:
A
Answer: (A) 48
Question: When Q is divided by W, the quotient is R and the remainder is X. Which of the following expressions is equal to X?
(A) RW + Q
(B) RW - Q
(C) Q/R
(D) QW - R
(E) Q - RW
Rationale: Q/W = R + X/W
Q -RW = X
Amswer: E
Answer: (E) Q - RW
Question: A and B invests Rs.3000 and Rs.4500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 6:8
(B) 9:8
(C) 7:9
(D) 9:5
(E) 1:1
Rationale: (3*6 + 6*6): (4.5*12)
54:54 => 1:1
Answer: E
Answer: (E) 1:1
Question: Mr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.jones have initially?
(A) 100000
(B) 12000
(C) 15000
(D) 13000
(E) 65000
Rationale: Let the initial amount with Mr.Jones be Rs.x
Then, (1/2)[100-(3*20)]% of x=12000
 (1/2)*(40/100)*(60/100)*x=12000
x=((12000*25)/3)=100000
ANSWER A
Answer: (A) 100000
Question: On a schoolâ€™s Annual day sweets were to be equally distributed amongst 112 children. But on that particular day, 32 children were absent. Thus the remaining children got 6 extra sweets. How many sweets was each child originally supposed to get ?
(A) 28
(B) 27
(C) 11
(D) 15
(E) 19
Rationale: Explanation:
Let 'K' be the total number of sweets.
Given total number of students = 112
If sweets are distributed among 112 children,
Let number of sweets each student gets = 'L'
=> K/112 = L ....(1)
But on that day students absent = 32 => remaining = 112 - 32 = 80
Then, each student gets '6' sweets extra.
=> K/80 = L + 6 ....(2)
from (1) K = 112L substitute in (2), we get
112L = 80L + 480
32L = 480
L = 15
Therefore, 15 sweets were each student originally supposed to get.
Answer: D
Answer: (D) 15
Question: A group of boy scouts and girls scouts is going on a rafting trip. 60% of the scouts arrived with signed permission slips. If 45% of the scouts were boy scouts and 50% of the boy scouts arrived with signed permission slips, then what percentage of the girl scouts arrived with signed permission slips? Round to the nearest percent.
(A) 64
(B) 68
(C) 72
(D) 76
(E) 80
Rationale: 45% were boy scouts so 55% (100-45=55) were girl scouts.
# of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed
(50% of 45% of the total going) + (?% of 55% of the total going) = 60% of the total going
We can let the "total going" = 1,000 arbitrarily since we only care about the percent (of girl scouts w/ permission signed)
.50*.45*1,000 + x*.55*1,000 = .60*1,000
225 + x*550 = 600
550x=375
x=375/550
x=.6818181818 which converts to a percent of 68.18181818% which rounds to 68%
B
Answer: (B) 68
Question: 5,9,18,31,52,__
(A) 79
(B) 80
(C) 86
(D) 82
(E) 83
Rationale: (9+5) +4 = 18
(16+9) +6 = 31
(28+16)+8 = 52
(48+28)+10 = 86
ANSWER:C
Answer: (C) 86
Question: An investment compounds annually at an interest rate of 10% What is the smallest investment period by which time the investment will more than triple in value?
(A) n =log 3/log 1.1
(B) 11/10 ^n
(C) (11/10)^n
(D) 1.1^n
(E) 1.2^n
Rationale: Assume initial amount is x
Annual Interest is 10% so after 1 year the amount will become x * (100+10)/100 => x*11/10
now we need to find n for x * (11/10)^n = 3x
or in other words or 3 =(11/10)^n or 3= (1.1^n)
log 3 =nlog 1.1 then n = log 3/log1.1
A
Answer: (A) n =log 3/log 1.1
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 22
(B) 56
(C) 44
(D) 55
(E) 81
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
Answer: B
Answer: (B) 56
Question: A certain no. when divided by 140 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 7
(D) 8
(E) 11
Rationale: Explanation:
140 + 25 = 165/15 = 11 (Remainder)
E
Answer: (E) 11
Question: In how many different ways can the letters of the word VALUE be arranged in such a way that the vowels occupy only the odd positions?
(A) 10
(B) 12
(C) 18
(D) 24
(E) 32
Rationale: The 3 vowels can be arranged in three odd places in 3! ways.
The 2 consonants can be arranged in two even places in 2! ways.
The total number of arrangements in which vowels occupy odd positions = 3! Ã— 2! = 6 Ã— 2 = 12
The answer is B.
Answer: (B) 12
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 2/9%
(C) 2 2/3%
(D) 6 5/3%
(E) 5 2/3%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%.Answer:A
Answer: (A) 6 2/3%
Question: A cylinder of height h is 2/3 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 90%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 2/3
New cylinder 3/5
So 3/5/2/3 = 3/5*3/2 = 0.90 or 90%.
Answer E
Answer: (E) 90%
Question: Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 3 feet were added to each fence, which of the following must be true?
I) Y is 3 feet shorter than X.
II) Y is 2 feet shorter than Z.
III) X is shorter than Z.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: If X= 6
Y= 3
Z= 5
Then, after adding 3 feet to each:
X= 9
Y=6
Z=8
And the answer would be D, which is wrong.
Answer: (D) I and II
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 250
(B) 375
(C) 300
(D) 540
(E) 560
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER B
Answer: (B) 375
Question: Food grains are to be sent to city from go down. Owner wants to reach the food grains at 11 O' Clock in the city. If a truck travels at a speed of 30km/hr then he will reach the city one hour earlier. If the truck travels at a speed of 20km/h then he will reach the city one hour late. Find the distance between the go down to city. Also with which speed the truck should travel in order to reach at exactly 11 'O clock.
(A) 24 kmph
(B) 25 kmph
(C) 26 kmph
(D) 27 kmph
(E) 28 kmph
Rationale: Let distance be x km and original time be t hr, when he travels at constant speed, say s kmph.
Clearly, x = st.
Now, x=30(t-1) and x=20(t+1). Solving these to simultaneous linear eqns, we get x=120 km and t=5 hr. So, distance between city and go-down=120km. To reach exactly at 11 o'clock, he must travel at speed s=x/t = 120/5 = 24 kmph
ANSWER:A
Answer: (A) 24 kmph
Question: The contents of a certain box consist of 14 apples and 20 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 3
(B) 6
(C) 14
(D) 17
(E) 20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 20 oranges, so to get to 6 oranges, we should remove 20 - 6 = 14 oranges.
Answer C
Answer: (C) 14
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 3451
(B) 3467
(C) 3891
(D) 4601
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 20/67
(B) 20/63
(C) 20/19
(D) 20/18
(E) 20/28
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer: B
Answer: (B) 20/63
Question: Dhoni spent 40 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?
(A) 30%
(B) 28%
(C) 32%
(D) 33%
(E) 34%
Rationale: Say Dhoni's earning last month was $100.
Dhoni spent 40 percent of his earning last month on rent --> $40 on rent;
20 percent less than what he spent on rent to purchase a new dishwasher --> $40*0.8=$32 on the dishwasher.
Left over amount 100 - (40 + 32) = $28
Answer: B
Answer: (B) 28%
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.65 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 42
(B) 77
(C) 48
(D) 99
(E) 11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.65 = 1.75 km = 1750 m.
Required time = 1750 * 3/125 = 42 sec.
Answer: A
Answer: (A) 42
Question: x is a positive integer less than 500. When x is divided by 5, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: the nubmer which when divided by 5 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=500
n=24.42
or n= 24
Answer:- D
Answer: (D) 24
Question: If 0 < a < b and k = (3a + 5b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k > 3
(D) k > 9
(E) k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
~~~~
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 since a < b, you get k = (3+10)/2 = 6.5, thus leaving the option B as the correct answer..
Answer: (B) k < 7
Question: If an investor puts $600 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
(A) $661.50
(B) $663.50
(C) $665.50
(D) $667.50
(E) $669.50
Rationale: 1.05*1.05*600=$661.50
The answer is A.
Answer: (A) $661.50
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,44,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
(A) 0.23255
(B) 0.14544
(C) 0.25632
(D) 0.35466
(E) 0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 344000x
\therefore Required percentage = \inline \frac{800x}{344000}\times 100 = 0.23255
A
Answer: (A) 0.23255
Question: By selling an article at $600, a profit of 25% is made. Find its cost price?
(A) $580
(B) $400
(C) $480
(D) $570
(E) $330
Rationale: C
$480
SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = $480
Answer: (C) $480
Question: The average of the marks of 12 students in a class is 50. If the marks of each student are doubled, find the new average?
(A) 160
(B) 120
(C) 100
(D) 150
(E) 170
Rationale: Sum of the marks for the 12 students
= 12 * 50 = 600. The marks of each student are doubled, the sum also will be doubled.
The new sum =600 * 2 = 1200. So, the new average
= 1200/12 = 100.
Answer:C
Answer: (C) 100
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Thursday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Wednesday, Sunday
(B) Thursday, Monday
(C) Sunday, Thursday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on thursday -i.e. 3 days earlier
so actual day to return home is sunday.
Rohit returned after days so thursday
ANSWER:C
Answer: (C) Sunday, Thursday
Question: For numbers x, y, z, and w, if x is 50% greater than y, and z is 20% greater than w, is what percent greater or less than ?
(A) 20 % greater
(B) 20 % less
(C) 25 % greater
(D) 25 % less
(E) 50 % greater
Rationale: x = 1.5y
z = 1.2w
=> x/y = 1.5
z/w = 1.2
so x/y is greater by 0.3/1.2 * 100 = 25%
Answer - C
Answer: (C) 25 % greater
Question: If a + b - c = 2d, and if a - b + c =-4e, then a =
(A) 2(d + e)
(B) d – e
(C) (d + e)/2
(D) d-2e
(E) e-d
Rationale: Add both equations:
a + b - c = 2d
a - b + c =--4e
a+b-c+a-b+c=2d-e
2a=2d-4e
a=d-2e
Ans:D
Answer: (D) d-2e
Question: There are 12 pieces of radioactive metal A that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: (B) 3
Question: 10/21 of 3/5 of a number is greater than 4/7 of 1/5 of the same number by 36. What is half of that number?
(A) 105
(B) 180
(C) 210
(D) 240
(E) 315
Rationale: Let no. be x
10/21*3/5*x - 4/7*1/5*x =8
by further solving
30x/105- 4x/35=36
18x/105=36
x=210
we have to find x/2
=210/2=105
ANSWER:A
Answer: (A) 105
Question: How many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 28 sec
(B) 23 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
Rationale: D = 110 + 150 = 260
S = 36 * 5/18 = 10 mps
T = 260/10 = 26 sec
E
Answer: (E) 26 sec
Question: United Telephone charges a base rate of $9.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?
(A) 2 minutes
(B) 10 minutes
(C) 20 minutes
(D) 40 minutes
(E) 60 minutes
Rationale: Lets take number of minutesx.
Given that, 9+0.25x=12+0.2x ->0.05x=2 -> x=60minutes
ANS E
Answer: (E) 60 minutes
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/8 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/8
(E) 1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/8.
The number of non-upgraded sensors on the whole satellite is 24(x/8) = 3x.
The fraction of sensors which have been upgraded is x / (x+3x) = x/4x = 1/4
The answer is A.
Answer: (A) 1/4
Question: If 10 typists can type 20 letters in 20 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?
(A) 220
(B) 210
(C) 200
(D) 240
(E) 260
Rationale: No. of letters typing by 10 typists in 20 minutes = 20
No. of letters typing by 10 typists in 60 minutes = 20*3 = 60
No. of letters typing by 40 typists in 60 minutes = 60/10*40 = 240
Answer : D
Answer: (D) 240
Question: There are two cars. One is 90 miles north of the other. Simultaneously, the car to the north is driven westward at 25 miles per hour and the other car is driven eastward at 35 miles per hour. How many miles apart are the cars after 2 hours?
(A) 120
(B) 130
(C) 140
(D) 150
(E) 160
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 90 and a height of 120. The hidden pattern here is a 3/4/5 right triangle (the 90 lines up with the '3' and the 120 lines up with the '4'). In this way, you can deduce that each side is '30 times' bigger than it's corresponding side:
3/4/5 becomes
90/120/150
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer: D
Answer: (D) 150
Question: Recipe requires 15mins to cook. you have 7 mins hourglass and a 11 mins hourglass with you. how will you measure 15 mins using them?
(A) 15 mins
(B) 12 mins
(C) 13 mins
(D) 17 mins
(E) 20 mins
Rationale: Correct Answer : A
Put up both hour glasses. time starts when 7 min hourglass turns empty. and 11 min hourglass will run for 4 min. now flip 11 min hour glass upside down as soon as it runs empty. it will be empty in another 11 mins. and time is up. so 4+11= 15 mins
Answer: (A) 15 mins
Question: At what rate percent per annum will a sum of money double in 2 years.
(A) 34%
(B) 50%
(C) 11.5%
(D) 20%
(E) 21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 2)]% = 50% per annum. Answer: B
Answer: (B) 50%
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 20
(B) 22
(C) 27
(D) 28
(E) 30
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
A
Answer: (A) 20
Question: Positive integer y is 50 percent of 25 percent of positive integer x, and y percent of x equals 100. What is the value of y?
(A)  50
(B)  125
(C)  200
(D)  1,000
(E)  2,000
Rationale: y = 50% of 25 % 0f x
= x/8
and
y/100 of x = 100
y /100 *8y =100
y = 125
Answer - B
Answer: (B)  125
Question: Three balls are to be tossed in a row. How many different sequences are possible if red and blue always follow one-another in each toss ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Consider red and blue as one. But, in this arrangement they can be tossed in two different combinations.
Red first and Blue second or blue first and red second. Total we have (R and B) and third color = 2 arrangements to do. Total arrangements= 2*2= 4
B is the answer
Answer: (B) 4
Question: A train 210 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) 50 sec
(C) 44 sec
(D) 49 sec
(E) 28 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 210 + 140 = 350 m
Required time = 350 * 2/25 = 28 sec
Answer:E
Answer: (E) 28 sec