mathewhe/aqua_rat huggingface dataset:
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 240 m long?
(A) 40
(B) 99
(C) 48
(D) 77
(E) 21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 240 = 600 m
Required time = 600 * 2/25 = 48 sec
Answer:C
Answer: (C) 48
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 29
(B) 27
(C) 27
(D) 80
(E) 26
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: (D) 80
Question: Elena purchased Brand X pens for $5.00 apiece and brand Y for $2.80 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: C.
Answer: (C) 6
Question: A reduction of 40% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 80
(B) 72
(C) 64
(D) 56
(E) 48
Rationale: 800*(40/100) = 320 ---- 5
? ---- 1 => Rs.64
Answer: C
Answer: (C) 64
Question: How many figures are required to number the pages the pages of a book containing 365 pages?
(A) 987
(B) 656
(C) 286
(D) 126
(E) 181
Rationale: Explanation:
1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
-----------
987
Answer: A
Answer: (A) 987
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 126 kmph. In how much time will the trains cross each other?
(A) 87/7 sec
(B) 80/7 sec
(C) 80/9 sec
(D) 80/5 sec
(E) 20/3 sec
Rationale: Relative speed = (90 + 126)* 5/18 = 12 * 5 = 60 mps.
The time required = d/s = (100 + 100 + 200)/60
= 400/60 = 20/3 sec.
Answer: E
Answer: (E) 20/3 sec
Question: The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 72 on the exam is in what percentile of the school?
Choices
(A) 63rd percentile
(B) 68th percentile
(C) 84th percentile
(D) 96th percentile
(E) 98th percentile
Rationale: (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 68th percentile
B
Answer: (B) 68th percentile
Question: Two trains 140 m and 170 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) 10.9 sec
(B) 10.1 sec
(C) 10.6 sec
(D) 10.8 sec
(E) 11.16 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 170 = 310 m.
Required time = 310 * 9/250=11.16 sec.
Answer:E
Answer: (E) 11.16 sec
Question: Question: What is the remainder when T=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
(A)  0
(B)  25
(C)  49
(D)  81
(E)  100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when T=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: (D)  81
Question: Billy lives in a town in which 75% of pets are dogs. Of the non-dog pets, 50% are cats. If there are 50 pets in town that are not cats or dogs, how many pets are there in town?
(A) 250
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: Let x be the number of pets in town.Then N is the number of non-dog pets given byN = x - 75%xAnd P is the number of pets that aren't cats or dogs, given byP = N - 50%Nfor P = 50, solve for x50 = (x - 75%x) - 50%(x - 75%x)x = 400, correct answer C
Answer: (C) 400
Question: What is the dividend? The divisor is 800, the Quotient is 594, and the Remainder is -968.
(A) 6623
(B) 43036
(C) 51515
(D) 474232
(E) 2025
Rationale: Dividend=?
?=D * Q + R
?= 800 * 594 + -968
?= 475,200 + -968
?= 474,232
Answer: (D) 474232
Question: A reduction of 24% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) s.2.8
(B) s.2.4
(C) s.2.5
(D) s.2.2
(E) s.3.16
Rationale: 100*(24/100) = 24 --- 10
? --- 1 => Rs.2.4
100 --- 76
? --- 2.4 => Rs.3.16
Answer:E
Answer: (E) s.3.16
Question: A certain sum of money at simple interest amounted Rs.800 in 12 years at 3% per annum, find the sum?
(A) 337
(B) 268
(C) 198
(D) 588
(E) 168
Rationale: 800 = P [1 + (12*3)/100]
P = 588'
Answer:D
Answer: (D) 588
Question: Priya takes a trip and drives 5 hours from Town X to Town Z at a rate of 50 miles per hour. On her way back, Priya drives 60 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?
(A) 3.0
(B) 2.25
(C) 2.08
(D) 1.75
(E) 2.0
Rationale: distance from X to Z =5 hr* 50 mph= 250 miles
hence distance from Y to Z= 1/2*250=125
time=125/60=2.08 hrs
IMO: C
Answer: (C) 2.08
Question: Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 7, when a # b = 100?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 7 = 10/2 + 7 =12.
The correct answer is D.
Answer: (D) 12
Question: A number when divided by a divisor leaves a remainder of 27. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 12
(B) 13
(C) 35
(D) 40
(E) 59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+27
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 40
as D is also integer and 40 is a prime number, the D should be 40 to satisfy the above equation.
Hence answer is 'D'
Answer: (D) 40
Question: Find the L.C.M of 6, 15, 24 and 20.
(A) 140
(B) 160
(C) 120
(D) 150
(E) 250
Rationale: Explanation:
2 x 3 x 5 x 2 x 2 = 120
Answer: Option C
Answer: (C) 120
Question: Solve the equation for time, "t" : 9(t + m) + 1 = 9(-t + m) + 19
(A) 1
(B) -1
(C) 2
(D) -2
(E) 3
Rationale: A
1
9(t + m) + 1 = 9(-t + m) + 19
9t + 9m +1 = -9t + 9m + 19
18t = 18
t = 1
Answer: (A) 1
Question: Of the 4 numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is?
(A) 36
(B) 40
(C) 48
(D) 52
(E) 56
Rationale: Let the first number be x
sum of the 4 numbers = x+4x = 5x
5x/4 = 60
x = 60*4/5 = 48
Answer is C
Answer: (C) 48
Question: Set X consists of 10 integers and has median of 30 and a range of 30. What is the value of the greatest possible integer that can be present in the set?
(A) 32
(B) 37
(C) C.40
(D) 43
(E) 50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 40, 50
This is possible. Hence it is the greatest such number.
Answer (E)
Answer: (E) 50
Question: If 0 < x ≤ 5, then which one of the following is the maximum value of (x – 1)^2 + x ?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 21
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 5 is when x=5 --> (x – 1)^2 + x = 21
Answer E
Answer: (E) 21
Question: A train covers a distance of 16 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: Speed = (16/10 * 60) km/hr
= (96 * 5/18) m/sec = 80/3 m/sec.
Length of the train = 80/3 * 6
= 160 m.
Answer:C
Answer: (C) m
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 1267
(B) 1201
(C) 1200
(D) 1209
(E) 1216
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C
Answer: (C) 1200
Question: The salaries of A and B together amount to $3000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
(A) $1000
(B) $1250
(C) $2500
(D) $2250
(E) $1200
Rationale: Let A's salary is x
B's salary = 3000-x
(100-95)% of x = (100-85)% of (3000-x)
x = $2250
Answer is D
Answer: (D) $2250
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 50 Kmph
(C) 52 Kmph
(D) 56 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
E
Answer: (E) 60 Kmph
Question: If an object travels at 9 feet per second, how many feet does it travel in one hour?
(A) 32400
(B) 30000
(C) 32000
(D) 1800
(E) 22000
Rationale: If an object travels at 5 feet per second it covers 9x60 feet in one minute, and 9x60x60 feet in one hour.
Answer = 32400 Answer:A
Answer: (A) 32400
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 90kmph, find the rate at which the train B runs.
(A) 40
(B) 60
(C) 120
(D) 80
(E) 135
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 90 kmph, speed of B must be 90*(3/2) = 135 kmph
Answer E
Answer: (E) 135
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 140 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 $300, how many of the books sold were paperbacks?
(A) 100
(B) 110
(C) 120
(D) 130
(E) 140
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 140 books were paperbacks, the dealer would earn a profit of $280.
Since the actual profit was $300, the dealer must have sold 20 hardbacks.
Then the number of paperbacks sold was 140-20 = 120.
The answer is C.
Answer: (C) 120
Question: A certain taxi company charges $3.00 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
(A) 15.6
(B) 16.0
(C) 17.5
(D) 18.6
(E) 19.1
Rationale: A certain taxi company charges $3.00 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $3.00 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $3.0 + $15.6 = $18.6.
Answer: D.
Answer: (D) 18.6
Question: Ten persons in an organization including A and B were to be divided in two groups of 5 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed?
(A) 1/4
(B) 1/189
(C) 3/14
(D) 1/10
(E) 28/189
Rationale: The fraction is nothing but the probability..
Number to choose 5 out of 10= 10C5
Number to choose A and B and 2 from remaining 8=8C2..
prob of A and B choosen=8C2/10C5=28/189
Answer :E
Answer: (E) 28/189
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 11 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2/1
(B) 4/1
(C) 2/3
(D) 9/5
(E) 3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+11) = 36/20 = 9/5.
Answer: D.
Answer: (D) 9/5
Question: The ratio 5:20 expressed as percent equals to
(A) 50 %
(B) 125 %
(C) 25 %
(D) 75 %
(E) None of above
Rationale: Explanation:
Actually it means 5 is what percent of 20, which can be calculated as,
(5/20)*100 = 5 * 5 = 25
Answer: Option C
Answer: (C) 25 %
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability E that Kate has more than $10 but less than $15?
(A) 5/16
(B) 1/2
(C) 12/30
(D) E=15/32
(E) E=3/8
Rationale: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32=D
Answer: (D) E=15/32
Question: A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can be make out of this cloth?
(A) 300
(B) 360
(C) 400
(D) None of these
(E) cannot be determined
Rationale: Solution
Length of each pieces	= (1 / 8) m
= 0.125 m
Required number of pieces(37.5/0.125)	= (375×100 / 125)
= 300.
Answer A
Answer: (A) 300
Question: Find 96 ×× 97
(A) 91/198
(B) 91/12
(C) 91/13
(D) 91/10
(E) 91/11
Rationale: Here both numbers are less than 100. So they are deficient of - 4 and - 3 compared with 100. So
Answer:	B
Answer: (B) 91/12
Question: The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 40, what is the greatest possible value that one of the other 2 integers can have?
(A) 55
(B) 65
(C) 119
(D) 109
(E) 115
Rationale: a + b + c + d = 200
a + b = 80
c + d = 120
Greatest possible = 119 (Just less than 1)
Answer = C
Answer: (C) 119
Question: If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab?
(A) 10
(B) 25
(C) 36
(D) 61
(E) 87
Rationale: Explanation:
a2 + b2 + ab = a2 + b2 + 2ab - ab
i.e., (a + b)2 - ab
from x2 - 9x + 20 = 0, we have
a + b = 9 and ab = 20. Hence the value of required expression (9)2 - 20 = 61.
Answer D
Answer: (D) 61
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 29
(B) 27
(C) 25
(D) 11
(E) 65
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer:C
Answer: (C) 25
Question: The ratio of the age of a man and his women is 4:3. At the time of first meet theratio was 5:3 and After 4 years this ratio will become 9:7. How many yrs ago were they met?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 20
Rationale: Let the present age of the man and his wife be 4x and 3x respectively.
After 4 years this ratio will become 9:7
⇒(4x+4):(3x+4)=9:7⇒7(4x+4)=9(3x+4)⇒28x+28=27x+36⇒x=8
Present age of the man =4x=4×8=32
Present age of his wife =3x=3×8=24
Assume that they got married before t years. Then,
(32−t):(24−t)=5:3⇒3(32−t)=5(24−t)⇒96−3t=120−5t⇒2t=24⇒t=242=12
B
Answer: (B) 12
Question: When a 80 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ?
(A) 52
(B) 68
(C) 25
(D) 67
(E) 69
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 80/3.2
= 25
Option: C
Answer: (C) 25
Question: Find the average of first 30 natural numbers.
(A) 15.5
(B) 15.9
(C) 15.2
(D) 15.8
(E) 65.2
Rationale: Explanation:
Sum of first n natural numbers = n(n+1)/2
Hence, sum of first 30 natural numbers = (30 x 31)/2 = 465
Therefore, required average of = 465/30 = 15.5
ANSWER: A
Answer: (A) 15.5
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
(A) 12
(B) 61
(C) 15
(D) 72
(E) 30
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.
Answer:E
Answer: (E) 30
Question: How many four letter combinations can be formed using the letters of the word HEART?
(A) 15
(B) 25
(C) 60
(D) 120
(E) 200
Rationale: The number of letters in the given word is five.
The number of four letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 = 120.
Answer: D
Answer: (D) 120
Question: Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do
the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works
independently, how many hours will it take Ann to complete the remainder of the jobs?
(A) 2/3
(B) 3/4
(C) 1
(D) 2
(E) 3
Rationale: Work done by Tina in 1 hr=1/12
Work done by Tina in 8 hr=1/12*8 which is 2/3
Now,the remaining work is 1/3 which is completed by Ann in 1/3*9 which is 3hr
ANSWER:E
Answer: (E) 3
Question: Dhoni weighs twice as much as Nameetha. Nameetha's weight is 75% of Bima's weight. Dravid weighs 20% of Leela's weight. Leela weighs 40% of Dhoni's weight. Who among these 5 persons weighs the least?
(A) Bima
(B) Leela
(C) Dravid
(D) Nameetha
(E) Dhoni
Rationale: if
Bima weight = x
we get
Nameetha's weight = 0.75x
Dhoni's weight = 1.5x
Leela's weight = 0.6x
and Dravid's weight = 0.12x
Answer : C
Answer: (C) Dravid
Question: Number of prime numbers between 10 and 20 is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: total 4=1, 13, 17, 19
ANSWER:A
Answer: (A) 4
Question: The line Q represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
(A) y = 2x^2+5x+1
(B) y = x^2+5x+2
(C) y = 3x^2+5x+2
(D) y = 3x^2+7x+2
(E) y = x^2+7x+1
Rationale: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.
So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line Q which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C
Answer: (C) y = 3x^2+5x+2
Question: What is the sum of all even integers between 99 and 301?
(A) 40000
(B) 20000
(C) 40400
(D) 20200
(E) 20400
Rationale: Even integers between 99 and 301 are 100,102,104,....,300
To find total even numbers n , 300=100+(n-1)2, n=101
Sum of all numbers=(101/2)[2*100+ (101-1)2]
=10100+10100 =20200
ANSWER:D
Answer: (D) 20200
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 8 km in stationary water?
(A) 2 hours
(B) 1 hour
(C) 1 hour 15 min
(D) 1 hour 30 min
(E) 1 hour 10 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(10/60)= 6 kmhr
speed in still water = 1/2 (2+6) = 4 kmhr
time taken in stationary = 8/4 = 2 hrs
ANSWER:A
Answer: (A) 2 hours
Question: A man sells a car to his friend at 15% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
(A) Rs.22941.18
(B) Rs.32941.18
(C) Rs.52941.18
(D) Rs.62941.18
(E) None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 15%.
Now S.P = Rs.45000 and loss = 15%
C.P. Rs.[100/85Ã—45000]= Rs.52941.18
Correct Option : C
Answer: (C) Rs.52941.18
Question: If (4x + y)/(x + 4y) = 2/3, then find the value of (x + 4y)/(4x + y).
(A) 3/8
(B) 3/4
(C) 3/2
(D) 3/6
(E) 3/8
Rationale: Explanation:
Given, (4x + y)/(x + 4y) = 2/3
=> 3(4x + y) = 2(x + 4y)
=> 2x = y
.: (x + 4y)/(4x + y) = x + 4(2x)/(4x + 2x) = 9x/6x = 3/2
Answer: Option C
Answer: (C) 3/2
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 3 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
(A) 1/60
(B) 1/45
(C) 2/45
(D) 3/22
(E) 5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/45)*(2), which indeed is 2/45.
C
Answer: (C) 2/45
Question: If the President and Vice President must sit next to each other in a row with 6 other members of the Board, how many different seating arrangements are possible?
(A) 12010
(B) 10080
(C) 10228
(D) 11080
(E) 72000
Rationale: We need to take President and VP as one unit. Therefore we have 7 people to arrange=7! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=7!*2!=10080 ways
Answer B
Answer: (B) 10080
Question: 0.35 represents what percent of 0.005?
(A) 0.05%
(B) 0.5%
(C) 5%
(D) 500%
(E) 7000%
Rationale: One more method
0.35 represents what percent of 0.005?
Adjusting the decimal
350 represents what percent of 5?
Divide by 5
70 represents what percent of 1?
Answer = 70*100 = 7000% = E
Answer: (E) 7000%
Question: A train passes a station platform in 60 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 615 m
(B) 420 m
(C) 168 m
(D) 197 m
(E) 691 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x
= 420 m
Answer: B
Answer: (B) 420 m
Question: An empty pool being filled with water at a constant rate takes 8hours to fill to 3/7 of its capacity.how much more time will it take to finish filling the pool?
(A) 5hr 30min
(B) 5hr 20min
(C) 4hr 48min
(D) 3 hr 12min
(E) 2hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 4 hours 48 minutes.
Answer: C.
Answer: (C) 4hr 48min
Question: There are 12 slate rocks, 16 pumice rocks, and 8 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
(A) 3/32
(B) 7/64
(C) 11/105
(D) 15/127
(E) 19/134
Rationale: 12/36*11/35 = 11/105
The answer is C.
Answer: (C) 11/105