RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 170. If the ratio of his marks in English and Maths is 1:4, find his marks in Science?
A.17
B.77
C.66
D.55
Answer: A.17
Explanation: S:E = 1:3
E:M = 1:4
------------
S:E:M = 1:4:12
1/17 * 170 = 17
Answer: A
Question: Two trains are moving in the same direction at 90 kmph and 36 kmph. The faster train crosses a man in the slower train in 29 seconds. Find the length of the faster train?
A.425
B.435
C.445
D.455
Answer: B.435
Explanation: Relative speed = (90 - 36) * 5/18 = 3 * 5
= 15 mps.
Distance covered in 29 sec
= 29 * 15
= 435 m.
The length of the faster train
= 435 m.
Answer:B
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.
A.150 m
B.50 m
C.75 m
D.135 m
Answer: B.50 m
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: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
A.3977
B.2887
C.3972
D.26990
Answer: C.3972
Explanation: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: C
Question: A man can row downstream at 16 kmph and upstream at 12 kmph. Find the speed of the man in still water .
A.14
B.13
C.12
D.16
Answer: A.14
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 16 --- (1)
and x - y = 12 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 2.
Answer:A
Question: The price of a TV was increased by 30 percent. The new price was then increased by 20 percent. A single increase of what percent is equivalent to these two successive increases?
A.50%
B.60%
C.65%
D.56%
Answer: D.56%
Explanation: consider base price - $100
25% increase = 1.30*100 = $130
another 20% increase on new price = 1.2* 130 = $156
so final price of radio - $156
therefore a 56% increase
correct option - D
Question: If a = (1/2)b and c = 3a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
A.2a
B.3a
C.4a
D.5a
Answer: A.2a
Explanation: a = (1/2)b --> b=2a.
The mean = (a + b + c)/3 = (a + 2a + 3a)/3 = 2a.
Answer is A
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
A.36
B.39
C.42
D.45
Answer: B.39
Explanation: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 87 = 17x or x = (87 – 48) = 39.
Answer B
Question: Two persons C & D started traveling from A and B which are 300 km apart, towards B and A
respectively at 1.00 p.m. C travels at a constant speed of 30 kmph whereas D doubles his speed every
hour. If D reaches A in 4 5/8 hours, at what time did C and D meet each other ?
A.4:30 p.m.
B.4:40 p.m
C.5:00 p.m
D.5:10 p.m.
Answer: C.5:00 p.m
Explanation: Let speed of D in first hour = x
D’s speed = x+ 2x+ 4x+ 8x+ 16x*(5/8) = 25x
Given 25x=300 :. X = 12
At the end of four hours C traveled 120 (30 *4) kmph and D traveled 12 + 24+ 48 +96 = 180kmph
:. They meet each other after 4 hours ie at 5: p.m.
Answer : C
Question: The ration of the number of boys and girls in a college is 7:8. If the percentage is increase in the number of boys and girls be 20% and 10% respectively. What will be the new ration?
A.5:7
B.15:21
C.21:22
D.13:17
Answer: C.21:22
Explanation: Let the number of boys and girls be 7x and 8x
their increased number is 120% of 7x and 110% of 8x
7x*120/100 and 8x*110/100
42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer is C
Question: In a contest, a bowl contains 14 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
A.1/14
B.1/7
C.13/140
D.2/21
Answer: B.1/7
Explanation: P(not winning) = 13/14*12/13 = 6/7
P(winning) = 1 - 6/7 = 1/7
The answer is B.
Question: 12,?,68,129,220,347,516
A.129
B.220
C.347
D.31
Answer: D.31
Explanation: 2*2*2 + 4 = 12
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
3*3*3 +4 = 31
ANSWER : D
Question: If 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
A.55
B.42
C.43
D.44
Answer: A.55
Explanation: n(n-1)/2 =11*10/2
=55
ANSWER:A
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is:
A.647
B.738
C.654
D.847
Answer: B.738
Explanation: S.I. for 1 year = Rs. (854 - 825) = Rs. 29.
S.I. for 3 years = Rs.(29 x 3) = Rs. 87.
Principal = Rs. (825 - 87) = Rs. 738
Answer:B
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
A.3:6
B.3:4
C.3:7
D.3:9
Answer: B.3:4
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer: B
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
A.90days
B.60days
C.67days
D.70days
Answer: B.60days
Explanation: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = 7x/30 kg.
Quantity consumed by 70 men in x days = (7x/30)(70)kg
(7x/30)(70) = 980
x = (980 * 30)/490 => x = 60 days
Answer & Answer: B
Question: A box contains 3 red balls and 3 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
A.1/4
B.1/2
C.1/2
D.2
Answer: D.2
Explanation: My complicated version of your simple approach
Let the 3 black balls be BBB and 3 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (6!)/ (3!x3!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 5 slots and 2 Black (BB) and 3 Red (RRR)
They can be arranged in (5!)/ (2!x3!)
Hence required probability = [(6!)/ (3!x3!)]/[(5!)/ (2!x3!)]
=2
D
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team T. If team A's average speed was 5 mph greater than team T's, what was team T's average mph?
A.12
B.15
C.18
D.20
Answer: D.20
Explanation: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team T's speed was s. Then Team T's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team T. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team T is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
A.15
B.20
C.25
D.30
Answer: D.30
Explanation: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 6) = 3 (x-16-6)
=> x � 6 = 3x � 66
=> 2x = 60
=> x = 60/2 = 30
Answer: Option D
Question: What is the greatest positive integer n such that 3^n is a factor of 36^50?
A.100
B.200
C.300
D.600
Answer: A.100
Explanation: 36 = 3^2 * 2^2.
36^50 = 3^100 * 2^100
The answer is A.
Question: At a monthly meeting, 3/5 of the attendees were males and 4/5 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
A.6/25
B.11/50
C.14/75
D.23/100
Answer: C.14/75
Explanation: Males who did not arrive on time are 1/5*3/5 = 3/25 of the attendees.
Females who did not arrive on time are 1/6*2/5 = 1/15 of the attendees.
The fraction of all attendees who did not arrive on time is 3/25 + 1/15 = 14/75
The answer is C.
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
A.1/8
B.1/2
C.1/6
D.1/1
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E)
= 1 - 1/2 = 1/2.
Answer: B
Question: Which of the following integers is a divisor of(15!+14)?
A.15
B.14
C.13
D.7
Answer: B.14
Explanation: When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 14) = 14 (1*2*3*4*5*...*12*13*15 + 1) We obtain this by taking 14 common.
Hence 14 is definitely a divisor of (15! + 14).
B
Question: The faces of storage box are to be painted by 6 different colors. In how many ways can be this be done?
A.A.720
B.B.256
C.C.1
D.D.12
Answer: A.A.720
Explanation: If I have to paint 6 sides with 6 different colour...
First face can have 6c1 options,
2nd would have 5c1, and subsequent ones would have 4c1, 3c1, 2c1 and 1 options respectively.
Total options = 6c1 X 5c1 x 4c1 x 3c1 x 2c1 x 1 = 720 distinct ways
Correct answer - A
Question: Tom can hit a target 3times in 6shots, Karan can hit the target 2times in 6 shots & Ashwini can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?
A.2/5
B.3/7
C.2/3
D.2/5
Answer: C.2/3
Explanation: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Question: If h and g are distinct prime numbers less than 10, which of the following cannot be the product of h and g?
A.6
B.9
C.10
D.14
Answer: B.9
Explanation: If h and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Question: Express of the following as a fraction:
36%
A.14/25
B.13/25
C.9/25
D.17/25
Answer: C.9/25
Explanation: 36% = 36/100= 9/25.
Answer is C.
Question: Milk is poured from a full rectangular container with dimensions 4 inches by 9 inches by 10 inches into a cylindrical container with a diameter of 6 inches. If the milk does not overflow, how many inches high will the milk reach?
A.60/π
B.24
C.40/π
D.10
Answer: C.40/π
Explanation: Let the height of level of milk in the cylinder = h
Since , volume of milk is constant .
Therefore
4*9*10 = ππ* 3^2 * h
=> π * h = 40
=> h = 40/ (π )
Answer C
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
A.6 days
B.8 days
C.8 ½ days
D.7 ½ days
Answer: A.6 days
Explanation: Explanation:
4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
Answer: A
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A.1789
B.19799
C.29918
D.13500
Answer: D.13500
Explanation: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer:D
Question: A recipe for a large batch of fruit juice at a factory calls for 25% oranges, 25% lemons, and 50% limes. if 200 lemons are used, how many limes are needed?
A.100
B.125
C.400
D.600
Answer: C.400
Explanation: 25%= 200 fruit
100%=800 fruit
50% of 800 fruit=400 fruit
400 limes
ANSWER:C
Question: What are the two main types of access control lists (ACLs)?
A.1 and 3
B.1 and 2
C.2 and 1
D.1 and 5
Answer: A.1 and 3
Explanation: Explanation:
Standard and extended access control lists (ACLs) are used to configure security on a router.
Answer: Option A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
A.2/9
B.3/2
C.2/1
D.2/7
Answer: B.3/2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer:B
Question: A cistern is normally filled in 12 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
A.33
B.84
C.40
D.99
Answer: B.84
Explanation: 1/12 - 1/x = 1/14
x = 84
Answer: B
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 114 ounces, what is the volume, in cubic inches, of 63 ounces of this substance?
A.27
B.26
C.42
D.64
Answer: B.26
Explanation: 112 ounces of a substance has a volume of 48 cubic inches
63 ounces of a substance has a volume of (48/114)*63 = 26 cubic inches
Answer B
Question: Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is how much price?
A.2500
B.2800
C.3000
D.5000
Answer: D.5000
Explanation: Assume that face value of both stocks are Rs.100 as it is not given.
Hence, dividend per share in 1st case is Rs.9
and dividend per share in 2nd case is Rs.10
Let investment in 9% stock = Rs.x
and investment in 10% stock = Rs.(9800-x)
Market value of a 9% stock= Rs.75
Number of 9% stocks he can purchase with Rs.x = x/75
Total dividend from 9% stocks = (x×9)/75
Market value of a 10% stock = Rs.80
Number of 10% stocks he can purchase with Rs.(9800-x) = (9800-x)/80
Total dividend from 10% stocks = (9800−x)×10/80
incomes fom both of the investments is same
(x×9)/75=(9800−x)×10/80
(x×3)/25=(9800−x)/8
24x=25×9800−25x
49x=25×9800
x=(25×9800)/49=25×200=5000
Answer is D.
ie, investment in 9% stock = Rs.5000
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 784 feet squared, what is the difference between the length and the width of the roof?
A.38.
B.40.
C.42.
D.44.
Answer: C.42.
Explanation: Let the width= x
x*4x=784
x^2= 196
x= 14
Length= 4*14= 56
difference= 56-14= 42
C is the answer
Question: In a test, 52% students failed in Hindi, 40% failed in English and 27% failed in both. What percentage of students passed in both the subjects?
A.25%
B.48%
C.35%
D.None of these
Answer: C.35%
Explanation: Explanation :
Percentage of passed students in both the subjects = 100-(52+40-27) = 35%
Answer : C
Question: If n is a positive integer, write s(n) for the sum of the digits of n. What is
s(1) + s(2) + s(3) +...+ s(1000)?
A.9991
B.10000
C.13501
D.14999
Answer: C.13501
Explanation: We start by computing S := s(0) + s(1) + s(2) + s(3) + ...+ s(999). Each digit,
0 through 9, appears equally often: 100 times in the hundreds place, 100 times in the tens
place, and 100 times in the ones place. (Here we write, e.g., 3 as 003.) Therefore,
S = 300* 0 + 300 * 1 + + 300 * 9 = 300(0 + 1 +...+ 9) = 300 *45 = 13500:
Since s(0) = 0 and s(1000) = 1 we obtain the answer.
correct answer C
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
A.299
B.278
C.277
D.100
Answer: D.100
Explanation: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer: D
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.282
B.229
C.277
D.285
Answer: D.285
Explanation: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer:D
Question: If 1< x < 2, which of the following must be true?
I. x^3 < x^2
II. x^2 < 2 + x
III. x^2 < x^4
A.I only
B.I and II only
C.III only
D.I and III only
Answer: C.III only
Explanation: I. x^3 < x^2 --> for values greater than 1 x^3 > x^2, so this statement is false.
II. x^2 < 2 + x --> x(x-1) < 2 --> 2*(2-1)= 2 !< 2, so this statement is also false.
III. x^2 < x^4 --> for values of x between 1 and 2 x^2< x^4, so this statement is true.
Answer: C.
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour?
A.30
B.40
C.50
D.55
Answer: D.55
Explanation: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D).
Question: The product of all the prime numbers less than 10 is closest to which of the following powers of 10 ?
A. 10^9
B. 10^8
C. 10^7
D. 5*10^6
Answer: D. 5*10^6
Explanation: 2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
1000*5000
5,000,000
D
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 54 kmph and 72 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
Answer: B.80/7 sec
Explanation: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Question: After a storm deposits 110 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 220 billion gallons, the reservoir was approximately what percentage full before the storm?
A.40%
B.48%
C.54%
D.58%
Answer: A.40%
Explanation: When the storm deposited 110 billion gallons, volume of water in the reservoir = 220 + 110 = 360 billion gallons
If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 330/0.6 = 550 billion gallons
Therefore percentage of reservoir that was full before the storm = (220/550)*100 = 40%
Option A
Question: if the ratio of two number is 5:7 and LCM of the number is 320 then what is the number.
A.15
B.9
C.10
D.11
Answer: B.9
Explanation: product of two no = lcm *hcf
5x*7x=320*x
x=9
ANSWER:B
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for fourtime as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was
A.Rs.32000
B.Rs.62000
C.Rs.42000
D.Rs.52000
Answer: D.Rs.52000
Explanation: 3:1
4:1
------
12:1
1 ----- 4000
13 ----- ? => Rs.52,000
Answer: D
Question: Randy'sbar serves customers every weeknight from 5 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 8:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
A.Monday, 7:30 pm
B.Monday, 9 pm
C.Monday, 7 pm
D.Monday, 6:45 pm
Answer: D.Monday, 6:45 pm
Explanation: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 6:45 pm
Answer is D.
Question: In a hostel there were 100 students. To accommodate 25 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A.A)Rs.5800
B.B)Rs.5480
C.C)Rs.5400
D.D)Rs.4500
Answer: D.D)Rs.4500
Explanation: 100x + 400
= 125(x – 5)
x = 41
100 * 41 + 400
= 4500
Answer:D
Question: What is the smallest five digit number that is divisible by 16, 36, 45, and 54?
A.10200
B.10400
C.10600
D.10800
Answer: D.10800
Explanation: 16 = 2^4
36 = 2^2 * 3^2
45 = 3^2 * 5
54 = 2 * 3^3
LCM = 2^4 * 3^3 * 5 = 2160
The smallest five-digit number that is a multiple of 2160 is 5*2160 = 10,800
The answer is D.
Question: 3 pumps,working 8 hours a day,can empty a tank in 2 days.How many hours a day must 4 pumps work to empty the tank in 1 day ?
A.9
B.10
C.11
D.12
Answer: D.12
Explanation: Solution
Let the required number of working hours per day be x.
More pumps,Less working hours per day (Indirect Proportion)
Less days,More working hours per day (Indirect Proportion)
∴ 4 × 1 × x = 3 × 2 × 8 ⇔ x = 3x2x8/4 = x= 12, Answer D
Question: A train 110 m long is running with a speed of 30 km/h. In how many seconds will the train pass a man who is running at 3 km/h in the direction opposite to that in which the train is going?
A.6
B.8
C.10
D.12
Answer: D.12
Explanation: The speed of the train relative to the man = 30 + 3 = 33 km/h.
33000 m/h * 1h/3600 s = (330/36) m/s
(110 m) / (330/36 m/s) = (110 * 36) / 330 = 36/3 = 12 seconds
The answer is D.
Question: Tough and Tricky questions: Word Problems.
AM Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
A.$4,035
B.$4,036
C.$9,035
D.$16,140
Answer: C.$9,035
Explanation: The AM company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Question: A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A.1/2
B.8/15
C.7/12
D.2/3
Answer: B.8/15
Explanation: Total selection ways: 6C2=6!/2!4!=15
Selecting one blue chip out of two: 2C1=2!/1!1!=2
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (2C1*4C1)/6C2=(2*4)/15=8/15
ANSWER:B