RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
A.1/6
B.7/216
C.1/36
D.9/216
Answer: C.1/36
Explanation: the total number of possible outcomes is, of course, 6^3.
Fortunately, there are only two combinations of three dice throws that will give you a sum of 16:
5, 5, 6
4, 6, 6
(I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large and difficult to map out.)
However, our denominator counts out the number of throwing sequences (permutations) and not just combinations, so we will need to do the same. Effectively there are three throwing sequences for either combination:
6, 5, 5
5, 6, 5
5, 5, 6
4, 6, 6
6, 4, 6
6, 6, 4
So 6 throwing sequences we want divided by 6^3 throwing sequences we could get gives us 1/(6^2) or 1/36.
ANSWER:C
Question: Two trains start from A & B and travel towards each other at
speed of 60kmph and 70kmph resp. At the time of the meeting the
second train has traveled 200km more than the first.the distance
between them.
A.2200 km
B.2400 km
C.2600 km
D.2800 km
Answer: C.2600 km
Explanation: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 200km
x/60 = x+200 / 70
x= 1200
so the distance between A & B is x + x + 200 = 2600 km
Answer is C.
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 6% of bananas were rotten. Find the percentage of fruits in good condition?
A.92.5%
B.88.6%
C.85.2%
D.96.8%
Answer: B.88.6%
Explanation: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 6% of 400
= 24
Therefore, total number of rotten fruits = 90 + 24= 114
Therefore Number of fruits in good condition = 1000 - 114 = 886
Therefore Percentage of fruits in good condition = (886/1000 × 100)%
= (88600/1000)%
= 88.6%
Answer:B
Question: The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
A.76 kg
B.77 kg
C.76.5 kg
D.Data inadequate
Answer: B.77 kg
Explanation: total weight increases = 8 × 1.5 = 12 kg
so the weight of new person = 65 + 12 = 77 kg
Answer B
Question: There are two numbers. If 10% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
A.3 : 2
B.2 : 7
C.8 : 5
D.5 : 2
Answer: D.5 : 2
Explanation: Let the two numbers be x and y.
(1/10) * x + y = (5/4) * y
(1/10) * x = (1/4) * y
x/y = 10/4 = 5/2
The answer is D.
Question: If two typists can type two pages in two minutes, how many typists will it take to type 72 pages in nine minutes?
A.3
B.4
C.6
D.16
Answer: D.16
Explanation: In 2 minutes 2 typists type 2 pages which means that in 9 minutes they will type 9 pages but to type 72 pages (8 times) we need 8 times more typists i.e. 2 x 8 = 16 typists.
D
Question: A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 9 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
A.1:4
B.1:5
C.3:2
D.1:2
Answer: C.3:2
Explanation: The cost price of a mango = 1/5 dollars.
The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/5 = 2/15 = 4/30 dollars.
The selling price of a mango from the second stack = 1/9 dollars --> the loss from one mango = 1/5 - 1/9 = 4/45 dollars.
The profit from one mango from the first stack is 4 times the loss from one mango from the second stack.
the ratio is 4/30*45/4 =3:2
C
Question: Find the odd man out.
2, 5, 10, 17, 26, 37, 50, 64
A.33
B.38
C.27
D.64
Answer: D.64
Explanation: Explanation:
(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1
But, 64 is out of pattern.
Answer: D) 64
Question: (35423+7164+41720)-(317x89)=?
A.28213
B.84307
C.50694
D.54094
Answer: D.54094
Explanation: =(84307)-317x89
=84307-(317x(90-1))
=84307-(317x90-317)
=84307-28213
=54094
Answer is D
Question: Jane and Ashley take 8 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
A.14 Days
B.15 Days
C.16 Days
D.18 Days
Answer: A.14 Days
Explanation: Let us assume that the work is laying 40 bricks.
Jane = 5 bricks per day
Ashley = 1 brick per day
Together = 6 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 20
Remaining bricks = 40 - 28= 12
So together, they would take 12/6 =2
Total no. of days = 8 + 4 + 2 = 14
Answer is A
Question: Today is Sunday. The day after 59 days will be
A.Monday
B.Wednesday
C.Saturday
D.Sunday
Answer: B.Wednesday
Explanation: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days)
= Wednesday. Answer : Option B
Question: A can finish a piece of work in 4 days. B can do it in 14 days. They work together for two days and then A goes away. In how many days will B finish the work?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: 2/4 + (2 + x)/14 = 1 => x = 5 days
Answer: B
Question: In how many words can be formed by using all letters of the word BHOPAL
A.420
B.520
C.620
D.720
Answer: D.720
Explanation: Explanation:
Required number
=6!=6∗5∗4∗3∗2∗1=720
Option D
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 7 * 8 =?
A.65
B.68
C.61
D.80
Answer: C.61
Explanation: (8 * 7) + 5 = 61
C
Question: What are the last two digits of (301*402*502*604*646*547*448*349)^2
A. 96
B. 76
C. 56
D. 36
Answer: C. 56
Explanation: ((301*402*502*604*646)*(547*448*349))^2
If you observe above digits, last digit are: 1,2,2,4,6,7,8,9; 3&5 are missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,02,04,46 and final three as 47*48*49.
Solving for only last two digits and multiplying them we get:( (04*04*46)(56*49))^2 = (36*44)^2=84^2=56
Hence answer is C
Question: If x and y are positive integers, and x^3*y^4 = 432, which of the following is the value of xy?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: 432 = 2^4*3^3
xy = 2*3 = 6
The answer is C.
Question: What is remainder of the division (1125*1127*1129)/12?
A.0
B.3
C.1
D.2
Answer: B.3
Explanation: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : B
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 10 years ago was 20 years. The present age of the husband is:
A.20 years
B.34 years
C.60 years
D.30 years
Answer: D.30 years
Explanation: D
30 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 10 x 2) years = 60 years.
Husband's present age = (90 - 60) years = 30 years.
Question: James Horner is having two coins in his hand. Out of the two coins, one is a real coin and the second one is a faulty one with Tales on both sides. He blind folds himself choose a random coin and tosses it in the air. The coin falls down with Tale facing upwards.
What is the probability that this is the faulty coin?
A.3/6
B.2/3
C.1/3
D.3/5
Answer: B.2/3
Explanation: B
2/3
While tossing the coins in this case only two cases are favorable:
1) A1 (H) A2 (H)
2) A2 (H) A1 (H)
3) B1 (H) B2 (T)
4) B2 (T) B1 (H)
Since the fourth case is not feasible, the probability is 2/3.
Question: Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly?
A.$645.56
B.$824.32
C.$954.26
D.$2472.96
Answer: D.$2472.96
Explanation: Principle = $10000
Rate = 2% half yearly = 4 half years
Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50
= $32472.96
C.I. = 32472.96-10000 = $2472.96
Answer is D
Question: An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
A.a profit of $5
B.a profit of $3
C.a loss of $3
D.a loss of $5
Answer: C.a loss of $3
Explanation: The cost of the first stock was 36/1.2=30, so the profit from it is 6.
The cost of the second stock was 36/0.8=45, so loss from it is 9.
Overall the loss is $3.
The answer is C.
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
A.a. 43
B.b. 53
C.c. 55
D.d. 68
Answer: B.b. 53
Explanation: 35 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (35 * 12.5 * 100) / (2.5 * 200)
thus, X = 87.5 that is approximately 88
Thus, more men needed to finish the task = 88-35=53
hence Answer is B
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
A.33
B.787
C.18
D.10
Answer: D.10
Explanation: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
Question: Find the value of (19 + 43/151) × 151
A.2924
B.2916
C.2614
D.2912
Answer: D.2912
Explanation: =(19 + 43/151) × 151
=(2869+ 43)/151× 151
=2912/151× 151
=2912
Answer is D.
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 3 men, 7 women, and 5 children contains exactly 1 woman?
A.56/195
B.77/832
C.11/77
D.308/1411
Answer: A.56/195
Explanation: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 7 women and 3 out of 8 (= 3 men + 5 children) = 7C1 * 8C3
Thus the required probability = 7C1*8C3 / 15C4 = 56/195. Thus A is the correct answer.
Question: What decimal fraction is 90 ml of a litre ?
A..9
B..009
C..09
D.0.09
Answer: C..09
Explanation: Answer
Required fraction = 90/1000
= 9/100
= .09
Correct Option: C
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 3737 feet, find out the area of the parking space in square feet?
A.126 sq. ft
B.64 sq. ft.
C.100 sq. ft.
D.102 sq. ft.
Answer: A.126 sq. ft
Explanation: Explanation:
length =9 feet
breadth =37−9/2=14feet
Area =9×14=126 square feet
Answer: Option A
Question: The graphs of the two equations y = a x 2 + b x + c and y = A x 2 + B x + C, such that a and A have different signs and that the quantities b 2 - 4 a c and B 2 - 4 A C are both negative,
A.intersect at two points
B.intersect at one point
C.do not intersect
D.none of the above
Answer: C.do not intersect
Explanation: Solution
Since a and A have different signs the graphs of the two equations are parabolas opening in diffent directions: If one opens up the other opens down. Also since b 2 - 4 a c and B 2 - 4 A C are both negative, none of the parabola cuts the x axis. This means that each one of these parabolas is either above the x axis or below the x axis and therefore do not intersect.
Answer C
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.
A.60
B.50
C.75
D.100
Answer: B.50
Explanation: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 3 = 50 meter
Answer:B
Question: A man can row downstream at 26 kmph and upstream at 22 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.24, 2
B.12, 6
C.15, 3
D.14, 4
Answer: A.24, 2
Explanation: Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 26 --- (1)
and x - y = 22 --- (2)
From (1) & (2) 2x = 48 => x = 24, y = 2.
Answer: Option A
Question: Two dogsled teams raced across a 400-mile course in Alaska. Team A finished the course in 4 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
A.12
B.15
C.18
D.20
Answer: D.20
Explanation: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 4 hours.
400/v - 400/(v+5)= 4
400v + 2000 - 400v = 4(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
A.1
B.2 digits
C.3
D.4
Answer: B.2 digits
Explanation: Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a =
2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
ANSWER:B
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.9 a.m
B.10 a.m
C.10.30 a.m
D.11 a.m
Answer: B.10 a.m
Explanation: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Question: A rower whose speed is 2.5 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km/hr. What is the rower's average speed (in km/hr) for the total journey?
A.2.2
B.2.3
C.2.4
D.2.5
Answer: C.2.4
Explanation: time upstream = d / 2
time downstream = d / 3
total time = d/2 + d/3 = 5d/6
average speed = 2d / (5d/6) = 2.4 km/hr
The answer is C.
Question: A train 150 m long crosses a platform 120 m long in 10 sec; find the speed of the train?
A.87 kmph
B.65 kmph
C.97 kmph
D.16 kmph
Answer: C.97 kmph
Explanation: D = 150 + 120 = 270
T = 10
S = 270/10 * 18/5 = 97 kmph
Answer:C
Question: Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A.ii only
B.iii only
C.i and ii only
D.i and iii only
Answer: D.i and iii only
Explanation: If n=2 then 2X3+1=7
if n=3 then 2*3*5=30+1=31 the answer will always be odd b/c 2 is a prime and the product will always be an even plus 1
If you try n=4 then you get 2*3*5*7=210 which is not a prime
ANSWER:D
Question: Find the value of 3+2.(8-3)
A.25
B.13
C.17
D.24
Answer: D.24
Explanation: 3+2.(8-3)
=3+2(5), =3+2*5, =3+10, =13 , Correct answer : (D)
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey?
A.20
B.30
C.43
D.24
Answer: D.24
Explanation: Ans.(D)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 4 x 6 = 24 ways
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 15 days before the project is completed, in how many days total will the project be completed?
A.12
B.14
C.16
D.18
Answer: D.18
Explanation: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 15 days, A can do 3/4 of the project.
Thus A and B must complete 1/4 of the project, which takes 3 days.
The total number of days is 3 + 15 = 18.
The answer is D.
Question: Of 30 applicants for a job, 10 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
A.14
B.13
C.9
D.7
Answer: C.9
Explanation: C. 9
30 - 3 = 27
27 - 10 - 18 = -9
Then 9 are in the intersection between 4 years experience and degree.
Answer C
Question: A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
A.104
B.190
C.109
D.278
Answer: C.109
Explanation: Explanation:
624/6 = 104 kmph
Answer:C
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A.160
B.175
C.180
D.195
Answer: B.175
Explanation: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
Therefore, 160 x 2.40 + x x 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER IS B
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
A.61.5
B.60.5
C.63.5
D.62.5
Answer: D.62.5
Explanation: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 2x/5
Hence, number of buckets needed = 25x/(2x/5)=(25×5)/2=62.5
Answer is D.
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
A.1000
B.1250
C.1300
D.1529.41
Answer: D.1529.41
Explanation: 300 gallons of water increases capacity by 30% that means
30% is 300 gallons, so 100% would be = 300*100/30= 1000 gallons
Now 1000 +300 gallons is 85% capacity of tank.
so 100% capacity would be= 1300 *100/85= 1529.41
D is the answer
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work?
A.5 days
B.15 days
C.28 days
D.4 days
Answer: D.4 days
Explanation: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
20 women’s 1 day’s work = 1/192 × 20 = 5/48
1 child’s 1 day’s work = 1/240
10 children’s 1 day’s work = 1/24
Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24
=1/4
The required No. of days = 4 days
Answer: Option D
Question: On increasing the price of T.V. sets by 30%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
A.4
B.5
C.56
D.2
Answer: A.4
Explanation: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(130 × 80) = Rs.10400
Increase% = 4001000040010000 × 100 = 4%
Answer: A
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 20%. What is the selling price of the cycle?
A.s. 1090
B.s. 1120
C.s. 1190
D.s. 1202
Answer: B.s. 1120
Explanation: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
20=(1400-s.p)/1400*100
so,after solving answer=1120.
ANSWER:B
Question: The average of 20, 40 and 180 is twice the average of 10, 30, and which of the following ?
A.1)10
B.2)30
C.3)60
D.4)80
Answer: D.4)80
Explanation: 20 40 180 = 180+60 = 240/3 = 80.
80/2 = 40
10 30 x = 40+x/3 should be smaller than 40
cross multiply 40*3-40 = 80
D
Question: A person covers a distance in 15 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
A.18 m/s
B.4 m/s
C.15 m/s
D.10 m/s
Answer: D.10 m/s
Explanation: Explanation:
T = 15 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
15 x (10/3) = 5x
x = 10 m/s
Answer: Option D
Question: How many diagonals does a 61-sided convex polygon have?
A.1182
B.1769
C.2456
D.3538
Answer: B.1769
Explanation: A 61-sided convex polygon has 61 vertices.
If we examine a single vertex, we can see that we can connect it with 58 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be (61)(58) = 3538
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3538 by 2 to get 1769.
The answer is B.
Question: if you toss a coin two times what is the probability that it will land either heads both times or tails both times?
A.A)1/8
B.B)1/6
C.C)1/4
D.D)1/2
Answer: D.D)1/2
Explanation: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get eithe r 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Question: Rs378 is divided among the three children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of Esha.how much the Rupee anusha get?
A.74
B.84
C.94
D.104
Answer: B.84
Explanation: If money with Anusha=a, Babu=b & Esha=e, then
a+b+e=378 ---(i) &
12a=8b=6e, so b=3a/2 & e=2a
Substituting these values of b & e in (i), a+(3a/2)+2a=378 , On solving, a=84
So, b=126, e=168
ANSWER:B
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 390 m long platform?
A.19
B.27
C.51
D.47
Answer: C.51
Explanation: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +390)/ 36 * 5/18
= 51 min.
Answer:C
Question: A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
A.100 Km
B.110 Km
C.120 Km
D.140 Km
Answer: C.120 Km
Explanation: Explanation :
In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.
x/6 = (30+x)/8
x = 90. So distance from start after which B will catch A = 90+30 =120km
Answer – C
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 4 less, he would have made a profit of 10%. The C.P. of the article was
A.344
B.600
C.200
D.800
Answer: D.800
Explanation: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 4
=> x = 800
Answer: D) Rs 800
Question: P = {105, 106, 107, 108, 109, x}
Set P above consists of 6 integers. For what value of x are the mode, the median and the average equal?
A.105
B.106
C.107
D.108
Answer: C.107
Explanation: Mode of a set is the number with max frequency.
Median for an even numbered set is the average of middle terms.
Average or mean is the sum of the set/No. of elements in the set.
Going from the answer choices, if we use 107 as the missing number.
The set becomes {105, 106, 107, 107, 108, 109}
Now the mode, median and mean are all same, 107
ANS (Option C)
Question: The sum of x, y coordinate values is 2490. if 6.5% of one coordinate is equal to 8.5% of the other, then the coordinate values are :
A.989,1501
B.1011,1479
C.1401,1089
D.1411,1079
Answer: D.1411,1079
Explanation: Explanation :
Solution: Let the coordinates be x and y. then, 6.5% of x = 8.5% of y
=> x = 85/65
y = 17/13 y
Now, x+y =249017y/13+y = 2490
=> 30y/13 = 2490
=> y = 2490*13/30 = 1079.
.'. One coordinate is = y= 1079, other coordinate = 17y/13 =1411
Answer : D