mathewhe/aqua_rat huggingface dataset:
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is?
(A) 2267
(B) 1162
(C) 2276
(D) 1250
(E) 1262
Rationale: Explanation:
speed = (5x5/18)m/sec
= 25/18 m/sec.
Distance covered in 15 minutes = (25/18 x 15 x 60)m
= 1250 m.
Answer: D
Answer: (D) 1250
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
(A) 4/29
(B) 4/20
(C) 4/23
(D) 4/13
(E) 4/92
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
=4/13
Answer: D
Answer: (D) 4/13
Question: If the probability R of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4
Rationale: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
R= 5/16
Answer - C
Answer: (C) 5/16
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 2:1 be mixed with another Mixture Q of milk and water in the ratio 1:5 so that the resultant mixture contains equal quantities of milk and water?
(A) 3:2
(B) 2:1
(C) 4:3
(D) 3:5
(E) 3:1
Rationale: (2/3)*P +(1/6)*Q = (1/3)*P+(5/6)*Q
2P=4Q
P/Q = 2/1
The answer is B.
Answer: (B) 2:1
Question: What is the simple interest on Rs 7000 at 10% per annum for the period from 16th January 2017 to 8th April 2017.
(A) Rs.77.8
(B) Rs.95.8
(C) Rs.47.8
(D) Rs.97.8
(E) Rs.90.8
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which
money is withdrawn is counted.
So lets calculate the number of days now,
Time = (15+28+8) days = 51/365 years
P = 7000
R = 10%
S.I. = =7000Ã—10Ã—51/(365*100)=97.8
Answer: D
Answer: (D) Rs.97.8
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
(A) 7/88
(B) 7/78
(C) 7/11
(D) 7/12
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂
= 7/15
Answer: E
Answer: (E) 7/15
Question: Calculate the percentage gain if a trader bought a bicycle for Rs.550 and sold it for Rs.650?
(A) 11.18%
(B) 13.18%
(C) 18.18%
(D) 19.18%
(E) 12.18%
Rationale: C.P. = 500
S.P. = 650
Gain = 650-550 ---- 100
% Gain => 100/550*100 => 18.18%
Answer:C
Answer: (C) 18.18%
Question: If a certain sample of data has a mean of 30.0 and a standard deviation of 3.5, which of the following values is more than 2.5 standard deviations from the mean?
(A)  12.0
(B)  13.5
(C)  17.0
(D)  23.5
(E)  26.5
Rationale: The standard deviation is 3.5. 2.5 standard deviations, which is just 2.5 x 3.5 is 8.75. The only answer more than 8.75 away from the mean is A.
Answer: (A)  12.0
Question: In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is married?
(A) 2/7
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/7
Rationale: let assume there are 100 students of which 70 are male and 30 are females
if 30 are married then 70 will be single.
now its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married
if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married.
total females = 30
married females = 10
then single females = 30-10 = 20
we need to find the fraction of female students who are single i.e single female students / total female student
= 10/30 = 1/3 [B]
Answer: (B) 1/3
Question: One fourth of a solution that was 8% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 40%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 8% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-24% = 40%
ans A it is.
Answer: (A) 40%
Question: If you cut a 22ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece?
(A) 4ft
(B) 6ft
(C) 8ft
(D) 10ft
(E) 9ft
Rationale: Total length is 22ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).
(x)+ (x+4)=22
x+x+4-4=22-4
2x=18
2x/2=18/2
x=9
The piece is E) 9ft.
Answer: (E) 9ft
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7
(B) 4
(C) 3
(D) 2
(E) 9
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4
Question: L2Q,L6S,P12U,R20W,T30U,?
(A) V42Y
(B) U47Y
(C) V47Z
(D) V47Y
(E) V46X
Rationale: L - Q = 2
L - S = 6
P - U = 12
R - W = 20
T - W = 30
1^2 + 1 , 2^2 + 2 , 3^2 + 3 , 4^2 + 4 , 5^2 + 5 ---> As per number sequence
=> next number = 6^2 + 6 = 42
V - Y = 42 => V42Y
ANSWER:A
Answer: (A) V42Y
Question: If two sides of a triangle have lengths 5 and 7, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
Rationale: Let x be the length of the third side.
7-5 < x < 7+5
2 < x < 12
14 < perimeter < 24
The answer is D.
Answer: (D) II and III only
Question: If TIER is written as 7163 and BRAIN is written as 23415, how is RENT coded ?
(A) 3653
(B) 3657
(C) 2977
(D) 2790
(E) 2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 6 3 2 4 5
Thus, the code for RENT is 3657.
ANSWER:B
Answer: (B) 3657
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg, what is his percent?
(A) 28%
(B) 25%
(C) 55%
(D) 28%
(E) 28.2%
Rationale: 780 --- 220
100 --- ? => 28.2%
Answer: E
Answer: (E) 28.2%
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 40 grades are D's. What is the number of students in the course?
(A)  80
(B)  110
(C)  160
(D)  800
(E)  400
Rationale: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 40 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 40 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 800 = 20T
19T + 800 = 20T
800 = T
There are a total of 800 students in the math class.
Answer is D.
Answer: (D)  800
Question: What percent of 16 is 16 percent of 1?
(A)  0.001
(B)  1
(C)  0.1
(D)  100
(E)  101.
Rationale: 16 % of 1 = (16/100) * 1 = 16/100
To determine what percentage of 16 this is :
[16][/100*16] *100 = 1%
Ans : B
Answer: (B)  1
Question: If “&” implies “Add”, “@” implies “multiply”, “#” implies “subtract”, “$” implies “division”,
12 & 3 @ 2 # 32 $ 4 = ?
(A) 10
(B) 99
(C) 27
(D) 29
(E) 16
Rationale: Explanation:
Given:
12 & 3 @ 2 # 32 $ 4 = ?
By substituting appropriate mathematical symbols, we get,
12 + 3 * 2 – 32/4 = ?
12 + 3 * 2 – 8 = ?
12 + 6 – 8 = ?
18 – 8 = 10
ANSWER:A
Answer: (A) 10
Question: In how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
(A) 4 years
(B) 6 years
(C) 8 years
(D) 9 years
(E) 10 years
Rationale: Explanation:
Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years
(150×6×n)/100 = (800 × (9/2) × 2)/100
(150 × 6 × n) = (800 × (9/2) × 2
150 × 6 × n = 800 ×9
3 × 6 × n = 16 × 9
6 × n = 16 × 3
2 × n = 16
n = 8 years
Answer: Option C
Answer: (C) 8 years
Question: A certain team has 10 members, including Joey. A three-member relay team will be selected as follows: one of the 10 members is to be chosen at random to run first, one of the remaining 9 members is to be chosen at random to run second, and one of the remaining 8 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/5
(B) 3/10
(C) 4/15
(D) 3/20
(E) 6/25
Rationale: Each member has an equal probability to run second (1/10) or third (1/10).
The probability that Joey runs second or third is 1/10 + 1/10 = 1/5
The answer is A.
Answer: (A) 1/5
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 14 m wide at the top and 4 m wide at the bottom and the area of cross-section is 380 sq m, the depth of cannel is?
(A) 39
(B) 28
(C) 27
(D) 42
(E) 71
Rationale: 1/2 * d (14 + 4) = 380
d = 42
Answer: D
Answer: (D) 42
Question: A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare, the jackal takes 7 leaps. Find the ratio of the speed of the hare to the speed of the jackal.
(A) 64:25
(B) 8:7
(C) 5:8
(D) 25:64
(E) 6:7
Rationale: The hare takes 6 leaps and the jackal takes 7 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 6 leaps = 6*(4/3) = 8 jackal leaps.
The ratio of their speeds is 8:7.
The answer is B.
Answer: (B) 8:7
Question: A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member?
(A) 10%
(B) 20%
(C) 25%
(D) 40%
(E) 50%
Rationale: Committee #1: 50% chance that David will be a member, leaving 2 possible spots the other 5 people. Michael's chances of being one of those 2 is 2/5 or 40%. Chances of David and Michael being on this committee is
50%x40%=20%.
Committee #2: Same.
20% + 20% = 40%.
ANSWER:D
Answer: (D) 40%
Question: 50 liters of a mixture contains milk and water in the ratio 3:2. If 5 liters of this mixture be replaced by 5 liters of milk, the ratio of milk to water in the new mixture would be?
(A) 6:5
(B) 6:2
(C) 6:4
(D) 7:4
(E) 7:2
Rationale: Quantity of milk in 50 liters if mix = 50*3/5 =30 liters
Quantity of milk in 55 liters of new mix = 30+5 = 35 liters
Quantity of water in it = 55-35 = 20 liters
Ratio of milk and water in new mix = 35:20 = 7:4
Answer is D
Answer: (D) 7:4
Question: If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
Answer: (C) 50%
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
(A) 349
(B) 339
(C) 400
(D) 500
(E) 600
Rationale: x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p
17
The least value of p for which q =	2 + 13p	=> p = 26
17
x = (13 x 26 + 11)
= (338 + 11)
= 349
ANSWER A
Answer: (A) 349
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 15% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 10%
(C) 15%
(D) 25%
(E) 30%
Rationale: The formula is
n(AUBUC) = n(A)+n(B)+n(C)-B+A-N
where B is both (it will sum of (AB), (BC), (CA)).
and A is All
and N is neither
so plugging in we get
100 = 60+50+15+10-B-0
B = 35.
exactly two = 35 - 3(10) = 5
subtracting 10% three times as this value is including in all the (AB), (BC), (CA).
Answer A
Answer: (A) 5%
Question: The function f is defined for all positive integers w by the following rule. f(w) is the number of positive integers each of which is less than w and has no positive factor in common with w other than 1. If p is any prime, number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
For example: if p=4 how many numbers are less than 4 having no common factors with 4: 1, 2, 3, --> 4-1=3.
Answer: A.
Answer: (A) p-1
Question: Abhijit started a business investing 2000. Anuja joined him after 8 months with an amount of 6000 and Sunil joined them with 60,000 after another 4 months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?
(A) 6 : 13 : 90
(B) 5 : 12 : 90
(C) 5 : 11 : 80
(D) 6 : 11 : 90
(E) 12 : 6 : 90
Rationale: Ratio of their investments
= 2 × 36 : 6 × 22 : 60 × 18 = 6 : 11 : 90
Answer D
Answer: (D) 6 : 11 : 90
Question: If p and q are prime numbers, how many divisors does the product p^6 * q^7 have?
(A) 40
(B) 56
(C) 60
(D) 62
(E) 70
Rationale: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is B. 7*8=56
Answer: (B) 56
Question: If 9^y = 3^12, what is y?
(A) 2
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: (E) 6
Question: A fruit drink is made of orange, watermelon, and grape juice, where 15 percent of the drink is orange juice and 60 percent is watermelon juice. If the drink is made with 35 ounces of grape juice, how many ounces is the drink total?
(A) 120
(B) 140
(C) 160
(D) 180
(E) 200
Rationale: Let the total number of ounces in the drink be x.
% of orange = 15%
% of watermelon = 60%
% of grape = 100% - 75% = 25%
0.25x = 35
x = 140
Therefore there are a total of 140 ounces in the drink.
The answer is B.
Answer: (B) 140
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 1000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
(A) 250
(B) 1,600/3
(C) 1,000
(D) 1,500
(E) 2,500
Rationale: X13: (t, d, s)
Y14: (t, 3d, s+1000mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+1000)*t ===> 3d = ts+1000t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 1000t
-2d = -2st + 1000t
2d = 2st - 1000t
d = st -500t
x13: d = s*t
st - 500t = s*t
s - 500 = s
-250 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 1000 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 1000
2 = 500
d=s*t
d=500*(1/2)
d=250
ANSWER: A
Answer: (A) 250
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What
percentage of the total votes did the winning candidate got
(A) 55%
(B) 56%
(C) 57%
(D) 58%
(E) None of these
Rationale: Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
Answer: Option C
Answer: (C) 57%
Question: A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by 53 m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop.
(A) 206
(B) 216
(C) 226
(D) 256
(E) 246
Rationale: First let us determine the speed of the train after the stop. The speed was increased by 53 m/sec =5⋅60⋅6031000 km/hr = 6 km/hr. Therefore, the new speed is 48+6=54 km/hr. If it took x hours to cover the first half of the distance, then it took x−1560=x−0.25 hr to cover the second part.
So the equation is: 48⋅x=54⋅(x−0.25)
48⋅x=54⋅x−54⋅0.25
48⋅x−54⋅x=−13.5
−6x=−13.5
x=2.25 h.
The whole distance is
2×48×2.25=216 km.
Answer is B.
Answer: (B) 216
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 77 seconds
(B) 66 seconds
(C) 40 seconds
(D) 55 seconds
(E) 43 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40 seconds
Question: The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides
does the polygon have?
(A) 4 sides
(B) 5 sides
(C) 6 sides
(D) 7 sides
(E) 8 sides
Rationale: Sum of Interior angles of Polygon=180(n-2)
Sum of Exterior angles of Polygon=360
so 180(n-2)=2*360
by solving we get ans=6 sides
ANSWER:C
Answer: (C) 6 sides
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 16,000 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) 25,000
(C) 40,000
(D) 48,000
(E) 60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+16000 = 5(x-16000) => x = 24000
2x = 48000
IMO option D.
Answer: (D) 48,000
Question: Working together, John, David, and Roger require 2 1/4 hours to complete a certain task, if each of them works at his respective constant rate. If John alone can complete the task in 4 1/2 hours and David alone can complete the task in 9 hours, how many hours would it take Roger to complete the task, working alone?
(A) 2 1/3
(B) 4 1/2
(C) 6 3/4
(D) 9
(E) 12
Rationale: (J+D+R)(9/4)=1
J+D+R= 4/9
(2/9 + 1/9 + R) = 4/9
R=1/9
9 hours
Answer: D
Answer: (D) 9
Question: Jimmy drove the first half of a 50-mile trip in x hours and the second half in y hours. Which of the following is equal to Jimmy’s average speed, in miles per hour, for the entire trip?
(A) 50/(x + y)
(B) 100/(x + y)
(C) 25/x + 25/y
(D) 50/x + 50/y
(E) 100/x + 100/y
Rationale: Time taken by Jimmy to cover first half i.e 25 miles of a 50 mile trip = x
time taken by Jimmy to cover the second half i.e 25 miles of a 50 mile trip = y
Total time taken by Jimmy = x+y
Jimmy's average speed for the entire trip =total distance /total time
=50/(x+y)
Answer: A
Answer: (A) 50/(x + y)
Question: The greatest number that exactly divided 105, 1001 and 2436 is :
(A) 3
(B) 7
(C) 11
(D) 21
(E) 24
Rationale: Solution
H.C.F. of 2436 and 1001 is 7. also, H.C.F. of 105 and 7 is 7.
∴ H.C.F. of 105, 1001 and 2436 is 7. Answer B
Answer: (B) 7
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8091 for a computer table, then what was the cost price of the computer table?
(A) 6727
(B) 6887
(C) 6728
(D) 6725
(E) 6525
Rationale: :
CP = SP * (100/(100 + profit%))
= 8091(100/124) = Rs. 6525.
Answer: E
Answer: (E) 6525
Question: In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father?
(A) 27
(B) 36
(C) 28 years
(D) 46 years
(E) 91
Rationale: Raj present age = 32 - 8 = 24.
After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2 = 56, and his present age is 52.
Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46
Answer:C
Answer: (C) 28 years
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 4 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 76 km/hr
(B) 66 km/hr
(C) 60 km/hr
(D) 67 km/hr
(E) 120 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/4 = 3x => x = 50/3
So, speed of the faster train = 100/3 = 100/3 * 18/5 = 120 km/hr.
Answer:E
Answer: (E) 120 km/hr
Question: The ratio of two numbers is 2 : 3 and their H.C.F. is 4. Their L.C.M. is
(A) 48
(B) 24
(C) 56
(D) 27
(E) 35
Rationale: Explanation:
Let the numbers be 2x and 3x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 8 and 12.
L.C.M. of 8 and 12 = 24.
Answer: Option B
Answer: (B) 24
Question: A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
(A) 7%
(B) 8%
(C) 8.5%
(D) 10%
(E) 11%
Rationale: Cost of kit = $57.50
If filters are purchased individually - $10.45*2 + $12.05*2 + $17.50 = $62.50
Amount saved = $62.50 - $57.50 = $5
Required %age = ($5/$62.50)*100 = 8%
So, the correct answer is B.
Answer: (B) 8%
Question: The sector of a circle has radius of 14 cm and its perimeter 50 cm. Find its central angel?
(A) 180o
(B) 225o
(C) 270o
(D) 150o
(E) 90o
Rationale: Lte central angle = x
Perimeter of the sector = length of the arc + 2(radius)
50= (x/360 * 2 * 22/7 * 14) + 2(14)
50 = 88x/360 + 28
88x/360 = 22
88x = 7920
x = 90
Answer: E
Answer: (E) 90o
Question: Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings
(A) 50
(B) 100
(C) 20
(D) 25
(E) 40
Rationale: Let the original income=Rs.100 . Then , expenditure=Rs.75 and savings =Rs.25
New income =Rs.120 , New expenditure =
Rs.((110/100)*75)=Rs.165/2
New savings = Rs.(120-(165/2)) = Rs.75/2
Increase in savings = Rs.((75/2)-25)=Rs.25/2
Increase %= ((25/2)*(1/25)*100)% = 50%.
ANSWER A
Answer: (A) 50
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 4?
(A) 1/4
(B) 1/12
(C) 2/11
(D) 3/13
(E) 1/5
Rationale: n(S) = 6*6 = 36
E = {(1,3),(3,1),(2,2)}
Probability = 3/36 = 1/12
Answer is B
Answer: (B) 1/12
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) 23277
(B) 23922
(C) 22877
(D) 15000
(E) 28322
Rationale: Explanation:
The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
Answer: D
Answer: (D) 15000