mathewhe/aqua_rat huggingface dataset:
Question: Three friends (Sam, Jerry and Guy) are employees of a company. Their respective salaries are in the ratio of 2 : 5 : 7. Jerry and Guy's salaries together is Rs. 6600. By what percent is Guy's salary than that of Sam?
(A) 250%
(B) 200%
(C) 150%
(D) 350%
(E) 110%
Rationale: Explanation:
Let the salaries of A, B, C be 2x, 5x and 7x respectively.
Then,5x + 7x = 6600 => x = 550.
Sam's salary = Rs. 1100, , Jerry's salary = Rs. 2750, and Guy's salary Rs. 3850.
Excess of Guy's salary over Sam's=[ (2750 /1100) x 100] = 250%.
Answer: A
Answer: (A) 250%
Question: Solve the equation:
A) 16x + 10 – 32 = 35 – 10x - 5,
B) y + 3/2y + 25 = 1/2y + 3/4y – 5/2y + y + 37,
C) 7u – 9 – 3u + 5 = 11u – 6 – 4u
(A) 2, 48/11, 2/3
(B) 3, 48/11, 2/3
(C) 2, 48/11, 2/4
(D) 4, 48/11, 2/3
(E) None
Rationale: Solution:
A)We do some of the makred actions and we get
16x – 22 = 30 – 10x
After using rule 2 we find 16x + 10x = 30 + 22
After doing the addition 26x = 52
We find unknown multiplier by dividing the product by the other multiplier.
That is why x = 52/26
Therefore x = 2
B) By analogy with A) we find:
y(1 + 3/2) + 25 = y(1/2 + 3/4 – 5/2 + 1) + 37 <=>
5/2y + 25 = -1/4y + 37 <=> 5/2y + 1/4y = 37 - 25 <=>
11/4y = 12 <=> y = 12.4/11 <=> y = 48/11
C) 4u – 4 = 7u – 6 <=> 6 – 4 = 7u – 4u <=> 2 = 3u <=> u = 2/3
Answer A
Answer: (A) 2, 48/11, 2/3
Question: A person walks from one end to the other of a 80-meter long moving walkway at a constant rate in 40 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
(A) 56
(B) 60
(C) 64
(D) 68
(E) 72
Rationale: Let v be the speed of the person and let x be the speed of the walkway.
40(v+x)=80 then 120(v+x)=240
120(v-x)=80
When we add the two equations:
240v=320
v=4/3
time = 80 / (4/3) = 60 seconds
The answer is B.
Answer: (B) 60
Question: A group consists of 8 men, 8 women and 4 children. In how many ways can 2 men , 2 women and 1 child selected from the given group?
(A) 3236
(B) 3336
(C) 3436
(D) 3136
(E) 6436
Rationale: Two men, two women and one child can be selected in 8C₂ * 8C2 * 4C₁ ways
8*7/2*1*8*7/2*1*4
=3136 ways
Answer : D
Answer: (D) 3136
Question: A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 3
(B) 2.5
(C) 2.25
(D) 1.5
(E) 4
Rationale: M = 7.5
S = x
DS = 7.5 + x
US = 7.5 - x
7.5 + x = (7.5 - x)2
7.5 + x = 15 -2x
3x = 7.5
x = 2.5
ANSWER:B
Answer: (B) 2.5
Question: The inverse ratio of 3: 5: 1 is?
(A) 2:3:7
(B) 5:3:15
(C) 2:3:2
(D) 2:3:6
(E) 2:3:1
Rationale: 1/3: 1/5: 1/1 = 5:3:15
Answer:B
Answer: (B) 5:3:15
Question: If a and b are positive numbers, and a^3 + b^3 = 100, then the greatest possible value of a is between:
(A) 0 and 3
(B) 3 and 4
(C) 4 and 5
(D) 5 and 7
(E) 7 and 9
Rationale: If a = 4.5 and b is a bit more than 2, then a^3 + b^3 can equal 100.
If a > 5, then a^3 + b^3 > 100.
The answer is C.
Answer: (C) 4 and 5
Question: a and b can do a piece of work in 28 days. with the help of c, they can finish it in 21 days .how long will c take to finish it
(A) 84 days
(B) 74 days
(C) 64 days
(D) 82 days
(E) 86 days
Rationale: A + B 's 1 day work = 1/28
A + B + C 's 1 day work = 1/21
1/28 + C= 1/21
C = 1/21 - 1/28
C = 1/84
So C ll finish the work alone in 84 days
ANSWER:A
Answer: (A) 84 days
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) Rs.4086.40
(B) Rs.4882.40
(C) Rs.4089.40
(D) Rs.4082.40
(E) Rs.3082.40
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6
= Rs.4082.40
Answer:D
Answer: (D) Rs.4082.40
Question: A machine puts d caps on bottles in m minutes. How many hours will it take to put caps on b bottles?
(A) 60bm/d
(B) b/60dm
(C) bd/60m
(D) 60b/dm
(E) bm/60d
Rationale: A machine puts d caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/d minutes
In order to calculate the no. of hours taken , divide the product by 60.
So, our answer is bm/60d
Answer : E
Answer: (E) bm/60d
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 35 limes are used, how many oranges are needed?
(A) 2
(B) 5
(C) 10
(D) 40
(E) 50
Rationale: 70%= 35 fruit
100%=50 fruit
10% of 50 fruit=5 fruit
5 oranges
ANSWER:B
Answer: (B) 5
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-9)(x+8)(2X+5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: x = -1
Prob = 1/12
Answer - A
Answer: (A) 1/12
Question: 193,194,207,.....?
(A) 340
(B) 341
(C) 342
(D) 343
(E) 344
Rationale: first increment is by 1 which is the first odd number second increment is by 13 in this 2nd term is 3 which is second odd number the next increment should be by 135 in this the third term is 5 which is third odd number .Thus 342 is the answer.
ANSWER:C
Answer: (C) 342
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
(A) 228
(B) 217
(C) 100
(D) 288
(E) 772
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer: C
Answer: (C) 100
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of
21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 121 KM
(B) 242 KM
(C) 224 KM
(D) 112 KM
(E) 120 KM
Rationale: AVERAGE SPEED = 2*21*24/21+24 = 22.4 KM/HR
TOTAL DIST = 22.4 * 10 =224 KM
DIST = SPEED * TIME
LET TIME TO TRAVEL THE FIRST HALF = X HR
THEN TIME = (10-X) HR
DIST COVERED IN FIRST HALF = 21X
DISTANCE COVERED IN SECOND HALF = 24(10-X)
BUT DISTANCE COVERED BOTH EQUAL
21X = 24(10-X)
X=16/3
HENCE 21X = 21 * 16/3 = 7 * 16 = 112 KM TOTAL DIST = 2 * 112 = 224 KM
ANSWER B
Answer: (B) 242 KM
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?
(A) 7:15 am
(B) 7:30 am
(C) 7: 42 am
(D) 7:50 am
(E) 7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 7:30 + 12 mins = 7:42
Option C
Answer: (C) 7: 42 am
Question: Pipes A and B can fill a tank in 6 and 8 hours. Pipe C can empty it in 4 hours. If all pipes are opened together, then the tank will be filled in?
(A) 3/2hr
(B) 24hr
(C) 22hr
(D) 20hr
(E) 5/3hr
Rationale: Net part filled in 1 hour = 1/6 + 1/8 - 1/4 = 1/24
The tank will be full in 24 hr
Answer is B
Answer: (B) 24hr
Question: John purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
(A) Rs. 100
(B) Rs. 130
(C) Rs. 200
(D) Rs. 230
(E) Rs. 250
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: (C) Rs. 200
Question: The area of a triangle is with base 2m and height 5m?
(A) 11
(B) 10
(C) 787
(D) 122
(E) 5
Rationale: 1/2 * 2 * 5 = 5 m2
Answer: E
Answer: (E) 5
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.25 %
(B) 56.25 %
(C) 56.85 %
(D) 52.25 %
(E) 56.55 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer:B
Answer: (B) 56.25 %
Question: (X)+3612+16125-6149=90189. Calculate the value of X
(A) 76601
(B) 76600
(C) 76655
(D) 76313
(E) 76723
Rationale: x+3612+16125-6149=90189
=x+3612+16125=90189+6149
=x+19737=96338
=x=96338-19737
=76601
Answer is A
Answer: (A) 76601
Question: There are 10 magazines lying on a table; 5 are fashion magazines and the other 5 are sports magzines. If 4 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?
(A) 60/61
(B) 40/42
(C) 41/42
(D) 45/46
(E) 54/55
Rationale: 1- (5c4/10c4) = 1-1/42 = 41/42
Answer : C
Answer: (C) 41/42
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 60. What is the total number of students in the school?
(A) 72
(B) 80
(C) 125
(D) 150
(E) 100
Rationale: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 60 + 2/3 of 60
80/100x = 100
x = 125.
Answer: Option C
Answer: (C) 125
Question: On an order of 9 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Clearly, the retailer gets 1 dozen out of 10 dozens free.
Equivalent discount = 1/10 * 100 = 10%.
Answer A) 10%
Answer: (A) 10%
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
(E) None of these
Rationale: Solution
Time =(100*81/450*4.5) years =4 years
Answer B
Answer: (B) 4 years
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 100?
(A) 30
(B) 28
(C) 27
(D) 25
(E) 26
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 100
4n< 93
n < 23. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 23)
Combining the two
-1.5 < n<23.25
n = 1 to 23 (23 integers)
and n = -1 and 0
so 25 integers.
D is the answer
Answer: (D) 25
Question: A cricket player whose bowling average was 22.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?
(A) 64
(B) 72
(C) 121
(D) 984
(E) 108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 22.5w + 52
Total wickets after last match = w + 5
(22.5w + 52) / (w + 5) = 22.5 - 0.5 = 22
w = 116
so total wickets aftr last match = w+5 = 121
ANSWER:C
Answer: (C) 121
Question: There has been a successive increase of 25% and 20% in the price of petrol from the previous month. By how much %age a man should reduce his consumption so that his expenditure does not change?
(A) 33.33%
(B) 50%
(C) 66.66%
(D) 15%
(E) 75%
Rationale: Earlier price of petrol = x
Current price of petrol = (5/4) * (6/5) * x = 1.5x
Let earlier Consumption = 100 gallons
Earlier: x dollars --> 100 gallons
Now: 1.5x dollars --> 100 gallons --> x dollars --> 100*2/3 = 66.66 gallons
Therefore the person should reduce his consumption by 100 - 66.66 = 33.33 gallons if his expenditure has to remain same.
Answer: A
Answer: (A) 33.33%
Question: In an office, totally there are 5200 employees and 45% of the total employees are males. 50% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 1040
(B) 1170
(C) 1150
(D) 4160
(E) None of these
Rationale: Number of male employees = 5200* 45/100 = 2340
Required number of male employees who are less than 50 years old = 4160 * (100 - 50)%
= 2340* 50/100 = 1170.
ANSWER:B
Answer: (B) 1170
Question: In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?
(A) 1242
(B) 1728
(C) 1484
(D) 1734
(E) 1726
Rationale: Soln:
= 3! * 4! * 2! * 3!
= 1728
Ans is B
Answer: (B) 1728
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 405 tiles in the floor, how many tiles does the leftmost row contain?
(A) 53
(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 405 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 405 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 405/9 = 45. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 45 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
45 +2 +2 +2 +2 = 53.
Final Answer:
A
Answer: (A) 53
Question: A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train?
(A) 270 m
(B) 200 m
(C) 400 m
(D) 340 m
(E) 150 m
Rationale: speed = 72 * 5/18 = 20 m/s
length of the train - x m
distance covered = 250 + x
time = 26 s
250+x/26=20
250+x=26*20=520
x=520-250=270
ANSWER A
Answer: (A) 270 m
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
(A) 20
(B) 24
(C) 26
(D) 28
(E) 32
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
B
Answer: (B) 24
Question: Speed of a boat in standing water is 8kmph and speed of the stream is 0.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?
(A) 27.35hours
(B) 26.35hours
(C) 25.35hours
(D) 24.35hours
(E) 23.35hours
Rationale: Speed upstream = 7.5kmph
Speed downstream = 8.5kmph
Total time taken = 105/7.5 + 105/8.5 = 26.35 hours
Answer is B
Answer: (B) 26.35hours
Question: A teacher will pick a group of 4 students from a group of 8 students that includes Lisa. If one of all the possible four-student groups is picked at random, what is the probability of picking a group that includes Lisa?
(A) 1/7
(B) 3/14
(C) 1/2
(D) 1/3
(E) 3/7
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 4 out of 8 = 8C4 = 8! / (4! * 4!) = 70
Favorable Outcomes= Total No. of ways of Picking Group of 4 out of 8 such that L is always in the group (i.e. we only have to pick remaining 3 out of remaining 7 as L must be there in group) = 7C3 = 35
Hence,Probability=35/70=1/2
Answer: Option C
Answer: (C) 1/2
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ?
(A) 3 hours
(B) 2.4 hours
(C) 1.4 hours
(D) 1 hour
(E) None of these
Rationale: Explanation:
Let the duration of the flight be x hours.
Then
600/x−600 /x+1/2=200
600/x−1200 /2x+1=200
x(2x+1)=3
2x2+x−3=0
=>(2x+3)(x−1)=0
Neglecting the negative value for x we get x = 1
Option D
Answer: (D) 1 hour
Question: The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income ofQ is:
(A) 1100
(B) 2100
(C) 1200
(D) 3100
(E) 1300
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (2050 x 2) = 4100 .... (i)
Q + R = (5250 x 2) = 10500 .... (ii)
P + R = (6200 x 2) = 12400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)
Subtracting (iii) from (iv), we get P = 1100.
P's monthly income = Rs. 1100.
Answer: A
Answer: (A) 1100
Question: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed
(A) 52 kmph
(B) 56 kmph
(C) 58 kmph
(D) 62 kmph
(E) 72 kmph
Rationale: Explanation:
Relative speed = 280/9 m / sec = ((280/9)×(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph
Answer: Option D
Answer: (D) 62 kmph
Question: If 2994 Ã· 14.5 = 177, then 29.94 Ã· 1.45 = ?
(A) 17.1
(B) 17.3
(C) 17.5
(D) 17.7
(E) 17.2
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 177 in the place of 2994/14.5 ]
= 177/10
= 17.7
Answer is D.
Answer: (D) 17.7
Question: In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
(A) 221/250
(B) 199/250
(C) 33/50
(D) 8/25
(E) 209/260
Rationale: The number of people younger than 70 years old is 2600-800 = 1800
The number of females older than 70 years old is 0.6*850 = 510
Then the number of males older than 70 years old is 800 - 510 = 290.
The number of people who are either male or younger than 70 is 1800+290 = 2090.
P(a person is younger than 70 or male) = 2090/2600 = 209/260
The answer is E.
Answer: (E) 209/260
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
Rationale: otal time for travelling 80 miles @ 60 mph = 80/60 = 4/3 hour = 80 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 80 minutes it will use = 2 gallons. Thus, full tank = 2+8 = 10 gallons ---> 2/10 = 20% of the fuel used. B is the correct answer.
Answer: (B) 20%
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have C=2*3*5*7 = 840
Thus, answer B
Answer: (B) 3
Question: The area of a triangle will be when a = 1m, b = 4m, c = 5m, a, b, c being lengths of respective sides?
(A) 2
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: S = (1 + 4 + 5)/2
= 5
Answer: C
Answer: (C) 5
Question: Five pieces of wood have an average length of 120cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
(A) a) 90
(B) b) 100
(C) c) 110
(D) d) 130
(E) e) 140
Rationale: A. 90
sum of all lengths of all 5 pieces of wood = 124 * 5 = 600
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 600 - 420 = 180
each of these 2 will have length 180/2 = 90
Answer A
Answer: (A) a) 90
Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
(A) 10 am
(B) 11 am
(C) 12 pm
(D) 1 pm
(E) 2 pm
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m.
then
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
So, 60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
Option B
Answer: (B) 11 am
Question: A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 14 per metre of cloth. What is the cost price of one metre of cloth?
(A) Rs. 80
(B) Rs. 86
(C) Rs. 90
(D) Rs. 95
(E) None of these
Rationale: SP of 1m of cloth = 4500/45= Rs. 100
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 14 = Rs. 86.
ANSWER:B
Answer: (B) Rs. 86
Question: A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1?
(A) 5 kg
(B) 6.5 kg
(C) 7.5 kg
(D) 8 kg
(E) 9 kg
Rationale: Milk in 85 kg of mix = 85* (27/34) = 135/2 kg.
Water in it = 85-135/2 = 35/2 kg.
Let x kg of water be added to it.
Then, (135/2)/(35/2 + x) = 3/1; 135/(35 +2x) = 3/1;
105 + 6x = 135 ; 6x = 30; x = 5
The quantity of water to be added = 5 kg
ANSWER:A
Answer: (A) 5 kg
Question: In a room of length 24mts, breadth 18mts, height 16 mts. what is the length of longest rod that can be placed in the room?
(A) 24 mtres.
(B) 34 mtres.
(C) 44 mtres.
(D) 54 mtres.
(E) 64 mtres.
Rationale: diagonal = 30m
now hypo of (floor)
diag and height will be =34 mtres.
ANSWER:B
Answer: (B) 34 mtres.
Question: From a total of 3 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
(A) 18
(B) 24
(C) 60
(D) 120
(E) 240
Rationale: Answer=C=18
No of 4 person committees that can be formed=3C2*4C2=18
Answer A
Answer: (A) 18
Question: A tourist purchased a total of $1,300 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $1,310
(C) $1,290
(D) $1,070
(E) $1,150
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1300 - 230 = 1070 hence answer is D
Answer: (D) $1,070
Question: A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
(A) 5 minutes
(B) 6 minutes
(C) 8 minutes
(D) 9 minutes
(E) 10 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 18 minutes a bus overtakes cyclist: \frac{d}{b-c}=18, d=18b-18c;
Every 6 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=6, d=6b+6c;
d=18b-18c=6b+6c, --> b=2c, --> d=18b-9b=9b.
Interval=\frac{d}{b}=\frac{9b}{b}=9
Answer: D (9 minutes).
Answer: (D) 9 minutes
Question: If −2≤a≤0 and n > 19, which of the following CANNOT be the value of an?
(A) -48
(B) -38
(C) -20
(D) 0
(E) 19
Rationale: value of an not equal to -19=E....Rest all are achievable
Answer: (E) 19