mathewhe/aqua_rat huggingface dataset:
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
(E) 31/150
Rationale: 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.
Answer: (C) 14/75
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
(E) 1/5
Rationale: 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
Answer: (B) 1/2
Question: A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 298 m
(B) 279 m
(C) 500 m
(D) 289 m
(E) 800 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (500 + x)/60 = 65/3
x = 800 m.
Answer: E
Answer: (E) 800 m
Question: Which of the following integers is a divisor of(15!+14)?
(A) 15
(B) 14
(C) 13
(D) 7
(E) 2
Rationale: 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
Answer: (B) 14
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
(E) E.36
Rationale: 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
Answer: (A) A.720
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
(E) 3/11
Rationale: 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
Answer: (C) 2/3
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
(E) 15
Rationale: 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
Answer: (B) 9
Question: Express of the following as a fraction:
36%
(A) 14/25
(B) 13/25
(C) 9/25
(D) 17/25
(E) None of them
Rationale: 36% = 36/100= 9/25.
Answer is C.
Answer: (C) 9/25
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
(E) 3π
Rationale: 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
Answer: (C) 40/π
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
(E) 9 days
Rationale: Explanation:
4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
Answer: A
Answer: (A) 6 days
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
(E) 78181
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer:D
Answer: (D) 13500
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
(E) 800
Rationale: 25%= 200 fruit
100%=800 fruit
50% of 800 fruit=400 fruit
400 limes
ANSWER:C
Answer: (C) 400
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
(E) 1 and 9
Rationale: Explanation:
Standard and extended access control lists (ACLs) are used to configure security on a router.
Answer: Option A
Answer: (A) 1 and 3
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
(E) 2/6
Rationale: 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
Answer: (B) 3/2
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 5%?
(A) 0—1.5 gal
(B) 1.5—3 gal
(C) 3—4.5 gal
(D) 4.5—6 gal
(E) 6+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 5
=>100 = 50 + 5x
=> x= 50/5 = 10
Answer E
Answer: (E) 6+ gal
Question: Some quantity of coffee is sold at Rs. 22 per kg, making 10% profit. If total gain is Rs. 88, what is the quantity of coffee sold?
(A) 35 kg
(B) 36 kg
(C) 38 kg
(D) 40 kg
(E) 44 kg
Rationale: Let CP of coffee was X.
SP = X + 10% of X
22 = 1.1X
X = 22/1.1 = Rs. 20.
Now,
Rs. 2 is gain on 20.
Rs, 1 gain = 20/2
Hence, 88 gain = (20 * 88)/2 =880.
Quantity of coffee sold = 880/20 = 44 Kg.
answer : OPTION E
Answer: (E) 44 kg
Question: The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a second of its new value. What is the stock's value at the end of Monday?
(A) X.
(B) X/2.
(C) 2X/3.
(D) X/3.
(E) 3X/4.
Rationale: Stock value= X
AT sunday end= x+.5X= 1.5 X
On monday the value drop to 1/2rd of its value on sunday
1.5x/2= .75x= 3X/4
E is the answer
Answer: (E) 3X/4.
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
(E) 11
Rationale: 1/12 - 1/x = 1/14
x = 84
Answer: B
Answer: (B) 84
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
(E) 147
Rationale: 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
Answer: (B) 26
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
(E) 4500
Rationale: 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
Answer: (D) 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.
(E) 46.
Rationale: Let the width= x
x*4x=784
x^2= 196
x= 14
Length= 4*14= 56
difference= 56-14= 42
C is the answer
Answer: (C) 42.
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
(E) Cannot be determined
Rationale: Explanation :
Percentage of passed students in both the subjects = 100-(52+40-27) = 35%
Answer : C
Answer: (C) 35%
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
(E) 15000
Rationale: 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
Answer: (C) 13501
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
(E) 216
Rationale: 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
Answer: (D) 100
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
(E) 2812
Rationale: 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
Answer: (D) 285
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
(E) I, II and III
Rationale: 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.
Answer: (C) III only
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
(E) 70
Rationale: 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).
Answer: (D) 55
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
(E)  10^5
Rationale: 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
Answer: (D)  5*10^6
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
(E) 20/7 sec
Rationale: 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
Answer: (B) 80/7 sec
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%
(E) 65%
Rationale: 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
Answer: (A) 40%
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
(E) 35
Rationale: product of two no = lcm *hcf
5x*7x=320*x
x=9
ANSWER:B
Answer: (B) 9
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
(E) Rs.22000
Rationale: 3:1
4:1
------
12:1
1 ----- 4000
13 ----- ? => Rs.52,000
Answer: D
Answer: (D) Rs.52000
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
(E) Monday, 9:30 pm
Rationale: 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.
Answer: (D) Monday, 6:45 pm
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
(E) E)Rs.5430
Rationale: 100x + 400
= 125(x – 5)
x = 41
100 * 41 + 400
= 4500
Answer:D
Answer: (D) D)Rs.4500
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
(E) 11200
Rationale: 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.
Answer: (D) 10800
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
(E) 13
Rationale: 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
Answer: (D) 12
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
(E) 14
Rationale: 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.
Answer: (D) 12
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
(E) $36,140
Rationale: 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.
Answer: (C) $9,035
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
(E) 7/10
Rationale: 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
Answer: (B) 8/15
Question: When positive integer x is divided by positive integer y, the remainder is 5. If x/y = 96.2, what is the value of y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 96.2 and remainder is 5
So .2 X y = 5
hence y= 25
Ans D
Answer: (D) 25
Question: If 7 and 9 are factors of 60n, what is the minimum value of n?
(A)  2
(B)  3
(C)  7
(D)  14
(E)  21
Rationale: 60n/7*9 should be integer => 2*2*3*5*n/7*3*3 = 2*2*5*n/21 must be an integer
for this to be true n must multiple of 21, thus min of n = 21
hence E
Answer: (E)  21
Question: If x⁄2 + 9⁄4 = 5⁄4, what is the value of x?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: x⁄2 + 9⁄4 = 5⁄4
Let's multiply both sides by 4.
2x + 9 = 5
2x = -4
x = -2
The answer is A.
Answer: (A) –2
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
(A) 26
(B) 50
(C) 1000
(D) 100
(E) 90
Rationale: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million
i.e. n3 = 106 (1 million = 106)
=> n3 = (102)3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
ANSWER D
Answer: (D) 100
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
(A) 288
(B) 388
(C) 188
(D) 258
(E) None of them
Rationale: Let no of passengers in the beginning be x
After first station no passengers=(x-x/3)+280=2x/3 +280
After second station no passengers =1/2(2x/3+280)+12
½(2x/3+280)+12=248
2x/3+280=2*236
2x/3=192
x=288
Answer is A.
Answer: (A) 288
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Answer: A
Answer: (A) 5
Question: A school has 120, 192 and 144 students enrolled for its science, arts and commerce courses. All students have to be seated in rooms for an exam such that each room has students of only the same course and also all rooms have equal number of students. What is the least number of rooms needed?
(A) 11
(B) 19
(C) 00
(D) 27
(E) 271
Rationale: We have to find the maximum number which divides all the given numbers so that number of roots get minimized. HCF of 120,192 & 144 is 24. Each room have 24 students of the same course.
Then rooms needed 12024+19224+1442412024+19224+14424 = 5 +8 + 6 = 19
Answer:B
Answer: (B) 19
Question: Carlos is 8 years old. In 12 years, how old will he be?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: 8years + 12years=20 years
answer : D
Answer: (D) 20
Question: The positive integers s and t leave remainders of 2 and 3, respectively, when divided by 6. s > t. What is the remainder when s– t is divided by 6?
(A) 3
(B) 1
(C) 4
(D) 2
(E) 5
Rationale: Let's test out some values of p and q that satisfy the given information.
s leaves are remainder of 2 when divided by 6
So, s COULD equal 8
t leaves are remainder of 3 when divided by 6
So, t COULD equal 3
What is the remainder when s – t is divided by 6?
So, s - t = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5
Answer: E
Answer: (E) 5
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.28400
(D) Rs.29400
(E) Rs.16400
Rationale: Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400
Ansewer is A
Answer: (A) Rs.14400
Question: The sum of two numbers is 18. Their difference is 4. What are the numbers?
(A) 8,6
(B) 9,9
(C) 11,7
(D) 15,3
(E) 13,9
Rationale: Let two numbers be x and y.
Equation (i): x + y = 18
Equation (ii): x - y = 4
Solve system of equations:
2x=22
x=11
y=7
Answer C is correct.
Answer: (C) 11,7
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 20:15:15
(B) 20:15:11
(C) 20:15:12
(D) 20:15:19
(E) 20:15:16
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: (C) 20:15:12
Question: Bart has $150,512 dollars in his bank account. He wants to split this money evenly among his nine daughters. What is the least amount of money (in whole number of dollars) that he must remove from his account?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 150,512 = 14 and 9 is divisible by 9.
Hence we need to subtract 5 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) 5
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 287
(B) 277
(C) 500
(D) 888
(E) 212
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: (C) 500
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (7, 0), (0, -3.5), (-7, 0)?
(A) 56
(B) 88
(C) 112
(D) 49
(E) 120
Rationale: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 7+7= 14
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*14*7= 49
D is the answer
Answer: (D) 49
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 2 kmph.
(B) 4 kmph.
(C) 5 kmph.
(D) 8 kmph.
(E) 7 kmph.
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer: D
Answer: (D) 8 kmph.