mathewhe/aqua_rat huggingface dataset:
Question: In Net's hair salon 54% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
(A) 5%
(B) 9%
(C) 12%
(D) 15%
(E) 21%
Rationale: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 54 % = 54
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 54+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures = 21%
E
Answer: (E) 21%
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 27
(C) 40
(D) 99
(E) 12
Rationale: Relative speed = 60 + 30 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000/25 = 40 sec.
Answer: C
Answer: (C) 40
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
(A) 3/7
(B) 4/9
(C) 1/3
(D) 3/5
(E) 2/7
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: C
Answer: (C) 1/3
Question: Find a sum for first 8 prime number'ss?
(A) 25
(B) 28
(C) 77
(D) 60
(E) 32
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) = 77
Note: 1 is not a prime number
Option C
Answer: (C) 77
Question: There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation :
GIVEN:
RED + GREEN + BLUE = 20
GREEN = 7
SOLUTION:
R + G < 13
THEREFORE R + 7 < 13
SO r < 6
ANS: AT most 5 red balls
B. 5
Hence (B) is correct.
Answer : B
Answer: (B) 5
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 15% impurities to the product. Find the net profit percentage of the dealer?
(A) 46.85%
(B) 43.75%
(C) 50%
(D) 56.25%
(E) 36%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 20% impurities to the product.
It means that he is selling $5 worth of product for $5.75.
So his profit is $5.75-$4 = $1.75
and his profit percent is
(1.75/4)*100 = 43.75%
Answer:- B
Answer: (B) 43.75%
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
(A) 65 sec
(B) 89 sec
(C) 100 sec
(D) 150 sec
(E) 120 sec
Rationale: Speed =	240/24 m/sec = 10 m/sec.
Required time = (240 + 650)/10	sec = 89 sec.
Answer: Option B
Answer: (B) 89 sec
Question: (4300231)-?=2535618
(A) 1865113
(B) 1775123
(C) 1764613
(D) 1675123
(E) None of them
Rationale: Let 4300231-x=2535618
then x=4300231-2535618
=1764613
Answer is C
Answer: (C) 1764613
Question: A train 605 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 81
(B) 16
(C) 33
(D) 54
(E) 12
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 605 * 3/55 = 33 sec.
Answer: C
Answer: (C) 33
Question: From the top of a 9 metres high building AB, the angle of elevation of the top of a tower CD is 30º and the angle of depression of the foot of the tower is 60º. What is the height of the tower?
(A) 11
(B) 12
(C) 88
(D) 27
(E) 10
Rationale: We have to find the value of CD. We use Sine rule to find the answer easily. Sine rule is aSinA=bSinB=cSinCaSinA=bSinB=cSinC
In triangle BDE, 9Sin60=xSin309Sin60=xSin30
So 93–√2=x12⇒x=93–√932=x12⇒x=93
In triangle BCD, CDSin30=93–√Sin60CDSin30=93Sin60
CD12=93–√3–√2⇒CD=3CD12=9332⇒CD=3
So height of the tower = 9 + 3 = 12
Answer:B
Answer: (B) 12
Question: If one person completes a journey in 10 hrs. He travels 1st half of the journey at the rate of 21 km/hr and 2nd half at therate of 24 km/hr. Find the total journey in km.
(A) 189 km
(B) 210 km
(C) 224 km
(D) 256 km
(E) 274 km
Rationale: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
C
Answer: (C) 224 km
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train?
(A) 27 7/6
(B) 27 7/5
(C) 277/2
(D) 300/9
(E) 27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 6 = 300/9
= 300/9 m.
Answer:D
Answer: (D) 300/9
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $626,500 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
(A)  $1,568,000
(B)  $448,000
(C)  $406,000
(D)  $313,600
(E)  $116,000
Rationale: My take is C.
(626500*4 + 112000*3)/7 = 406000
Answer: (C)  $406,000
Question: A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 40 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 260
(B) 280
(C) 325
(D) 340
(E) 355
Rationale: Let total capacity be x
we know 200 = 0.40x
x = 200/0.40 = 500
Prior to storm, we had 160 bn gallons
500-160 = 340
Answer : D
Answer: (D) 340
Question: The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 76 kg
(B) 76.5 kg
(C) 85 kg
(D) Data inadequate
(E) None of these
Rationale: EXPLANATION
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer C
Answer: (C) 85 kg
Question: Each week the forensics teams at Roslyn High School and Manchester High School debate each other. Each team has several members, and each week three are selected to debate. Whenever Aviva debates for Roslyn, Roslyn wins; and whenever Zachary debates for Roslyn, Roslyn wins. Whenever Josh debates for Roslyn, Manchester wins.
(A) 287
(B) 268
(C) 26
(D) 17
(E) 191
Rationale: Explanation:
It is clear that if Josh debates for Rosln, Manchester wins. So Option A is correct.
Answer: A
Answer: (A) 287
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 12 II. 3 III. 6
(A) I only
(B) II only
(C) III only
(D) I and III
(E) I, II, and III
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 7,8,9,10,11 and 12, then the sum = 57.
57 is divisible by 3
57 is NOT divisible by 6
57 is NOT divisible by 12
There's only one answer that 'fits' with these facts, so Answer : B
Answer: (B) II only
Question: if x:y = 1:2, then find the value of
(7x+3y):(2x+y)
(A) 13:4
(B) 15:5
(C) 16:5
(D) 17:5
(E) None of these
Rationale: Explanation:
let x = 1k and y = 2k, so
=7(k)+3(2k)/ 2(k)+1(2k)
=13k/4k
=13:4
Option A
Answer: (A) 13:4
Question: A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Explanation: When you read the math problem, you probably saw that the bat and the ball cost a dollar and ten cents in total and when you processed the new information that the bat is a dollar more than the ball, your brain jumped to the conclusion that the ball was ten cents without actually doing the math. But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.
The ball costs 5 cents.
correct answer is C)5
Answer: (C) 5
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 267
(B) 2667
(C) 200
(D) 269
(E) 265
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50
= 200 km away from Mumbai.
Answer:C
Answer: (C) 200
Question: Four persons enter the lift of a four storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 81
(B) 129
(C) 154
(D) 182
(E) 250
Rationale: Each person out of 4 has 3 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 3*3*3*3=3^4=81.
Answer: A.
Answer: (A) 81
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If r of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A)  y/R
(B)  y/(R-x)
(C)  xy/(R-x)
(D)  ry/(R(R-r))
(E)  y/(R(R-x))
Rationale: y/(R-r)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: (D)  ry/(R(R-r))
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 22,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got five times as many votes as the other candidate, how many people have voted in each round?
(A) 15,000
(B) 66,000
(C) 40,000
(D) 50,000
(E) 60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+22000 = 5(x-22000) => x = 33000
2x = 66000
IMO option B.
Answer: (B) 66,000
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 8%
(D) 10%
(E) None of these
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/1600x100% = 5%.
Answer: Option B
Answer: (B) 5%
Question: Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
(A) 2345
(B) 2445
(C) 2653
(D) 3334
(E) 3456
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: (D) 3334
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 3?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: Salary grade of 5 is p(5)=9.50+0.25(5–1)=9.50+0.25*4;
Salary grade of 3 is p(3)=9.50 + 0.25(3–1)=9.50+0.25*2;
p(5)-p(3)=9.50+0.25*4-9.50-0.25*2=0.5.
Answer: A.
Answer: (A) $0.50
Question: Rain is falling at a rate of 10 centimeters per hour all over North Carolina. Somewhere downtown in North Carolina a group of people are waiting for the rain to stop. If the rain filled a round puddle the with a base area of 300 square centimeters and a depth of 30 centimeters, how long did the people wait for the rain to stop?
(A) 4 hours
(B) 11 hours
(C) 7 hours 15 minutes
(D) 3 hours
(E) 14 hours
Rationale: Answer is : D, 3 hours
The volume of the puddle is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only 30 / 10 = 3 hours of rain to fill the puddle
Answer: (D) 3 hours
Question: C and D start a business with Rs.25000 and Rs.35000 respectively. Hoe should they share their profits at the end of one year?
(A) 5:7
(B) 7:5
(C) 4:7
(D) 7:4
(E) 3:7
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by C and D =
25000 : 35000 => 5:7
Answer:A
Answer: (A) 5:7
Question: Two trains 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 12.6 sec
(B) 10.1 sec
(C) 10.6 sec
(D) 10.8 sec
(E) 10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 210 = 350 m.
Required time = 350 * 9/250
= 12.6 sec.
Answer:A
Answer: (A) 12.6 sec
Question: The fourth proportional to 7, 9, 14 is:
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the fourth proportional to 7, 9, 14 be x.
Then, 7 : 9 : 14 : x
7x = (9 x 14)
x =	(9 x 14)/7
x=126/7 =18
Answer: Option C
Answer: (C) 14
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
(A) 10%
(B) 11%
(C) 12.5%
(D) 13%
(E) 15%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
C)
Answer: (C) 12.5%
Question: The shopkeeper sale, all of the prices of the items sold were different. If the price of a radio sold at the shopkeeper sale was both the 9th highest price and the 14th lowest price among the prices of the items sold, how many items were sold at the shopkeeper sale?
(A) 23
(B) 22
(C) 32
(D) 26
(E) 17
Rationale: 8+13+1= 22
Answer: B
Answer: (B) 22
Question: What is the minimum percentage increase in the mean of set F {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A)  25%
(B)  50%
(C)  75%
(D)  100%
(E)  200%
Rationale: Mean of F is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of F, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: (D)  100%
Question: Judges will select 6 finalists from the 8 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
(A) 10
(B) 21
(C) 210
(D) 420
(E) 560
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
8C6*6C3 =28 * 20 = 560
ANS:E
Answer: (E) 560
Question: If a^5 ≤ a, which of the following must be true?
I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1
(A) None of the above
(B) I only
(C) II only
(D) III only
(E) I and III only
Rationale: The trick here is more on the answer choices.
Look at I II and III. all are right (pick out some numbers).
Therefore I was totally confused because non of the answers had the right answer (I II and III)
I finally chose D, but hesitate between A and D quite a long time...
This is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers.
Therefore it is A.
Answer: (A) None of the above
Question: How many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph?
(A) 54 sec
(B) 65 sec
(C) 25 sec
(D) 22 sec
(E) 24 sec
Rationale: D = 100 + 120 = 220
S = 36 * 5/18 = 10 mps
T = 220/10 = 22 sec
Answer:D
Answer: (D) 22 sec
Question: A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 288
(B) 350
(C) 400
(D) 276
(E) 234
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
3x + 900 = 2100 => x = 400 m.
Answer:C
Answer: (C) 400
Question: How many times digit 6 is used while writing numbers from 150 to 1000?
(A) 648
(B) 300
(C) 252
(D) 225
(E) 26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 252. Hence C.
Answer: (C) 252
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 42. No two digits of h are identical. How many different numbers are possible values of h?
(A) 12
(B) 36
(C) 24
(D) 42
(E) 54
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 42
a,b,c,d can be 1,2,3,7
Number of ways = 4*3*2 = 24
Answer: (C) 24
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 94m & 54m respectively?
(A) s. 6420
(B) s. 3563
(C) s. 2400
(D) s. 5480
(E) s. 5076
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 94 * 54 = 5076m.
Total cost of levelling = Rs.5076
E
Answer: (E) s. 5076
Question: If 'a' and 'b' are non-zero numbers such that their sum is eight times the product, what is the value of 1/a + 1/b?
(A) 2
(B) 4
(C) 8
(D) 12
(E) 16
Rationale: a+b = 8ab
1/a + 1/b = (b + a)/(ab) = 8.
The answer is C.
Answer: (C) 8
Question: If [x] is the greatest integer less than or equal to x, what is the value of [1.6]+[-3.4]+[10.7]?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  7
Rationale: You are asked what the closest lesser integer value to [x] is.
[1.6] = 1.0
[-3.4] = -4.0
[10.7] = 10.0
Therefore , answer is: 1.0 -4.0 + 10.0 = 7.0
Option E.
Answer: (E)  7
Question: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
(A) 70
(B) 72
(C) 66
(D) 74
(E) 71
Rationale: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72.
Answer is B.
Answer: (B) 72
Question: Tim and Élan are 30 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
(A) 20 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.
Rationale: Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.
Plugging in the answer choice Only Answer Choice A meet the 2:1(Tim:Elan=20:10) ratio of maintaining total distance traveled 30 miles
So Correct answer A
Answer: (A) 20 miles.
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 160 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 160 books were paperbacks, the dealer would earn a profit of $320.
Since the actual profit was $400, the dealer must have sold 80 hardbacks.
Then the number of paperbacks sold was 160-80 = 80.
The answer is B.
Answer: (B) 80
Question: Cost of 1 chair is Rs. 214 and cost of one table is Rs. 937, then what is the approximate cost of 6 dozen chairs and 4 dozen table ?
(A) Rs. 60000
(B) Rs. 58000
(C) Rs. 55000
(D) Rs. 62000
(E) None
Rationale: Answer
∵ Cost of 6 dozen chairs = 6 x 12 x214 = Rs. 15408
And cost of 4 dozen tables = 4 x 12 x 937 = Rs. 44976
∴ Total cost =15408 + 44976
= Rs. 60384
= Rs. 60000 (Approximately)
Option: A
Answer: (A) Rs. 60000
Question: Three hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(300) / 500 = 30%
The answer is C.
Answer: (C) 30%
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 300
(B) 320
(C) 350
(D) 345
(E) 568
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350
Answer: Option C
Answer: (C) 350
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 16 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) 477
(B) 444
(C) 279
(D) 276
(E) 291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444.Answer: B
Answer: (B) 444
Question: A hotel has 10 storeys.Which floor is above the floor below the floor, below the floor above the floor, below the floor above the fifth.
(A) 5 th Floor
(B) 4 th Floor
(C) 6 th Floor
(D) 1 st Floor
(E) None of these
Rationale: Explanation :
Just start from last
below the floor above the 5th is again -- 5th only [since above d 5th is 6th nd below the 6th is 5th]
below the floor above the floor means -- 5th only [above the 5th is 6th nd below the 6th is 5th]
above the floor below the floor means -- again 5th only [below the 5th is 4th nd above the 4th is 5th]
Hence (A) is correct answer.
Answer : A
Answer: (A) 5 th Floor
Question: In an election between 2 candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election?
(A) 16800
(B) 15268
(C) 14800
(D) 15620
(E) 16850
Rationale: Let the total number of votes enrolled be x.
Then, number of votes cast = 75% of x.
Valid votes = 98% of (75% of x)
75% of (98% of (75% of x)) = 9261
(75/100)*(98/100)*(75/100)x = 9261
x = 16800
Answer is A
Answer: (A) 16800