mathewhe/aqua_rat huggingface dataset:
Question: A shipment of 7 television sets contains 2 black-and-white sets and 6 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
(A) 1/7
(B) 1/4
(C) 6/21
(D) 11/28
(E) 13/28
Rationale: I get 6/21, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(6,2)/C(7/2)=6/21
C
Answer: (C) 6/21
Question: If x, y, and z are positive integers and 2x = 4y = 5z, then the least possible value of x + y + z is
(A) 40
(B) 50
(C) 55
(D) 60
(E) 19
Rationale: given 2x=4y=5z
x+y+z in terms of x
= x+(2x/4)+(2x/5) = 38x/20=19x/10
now checking with each of the answers and see which value gives a minimum integer value.
A x = 10/19*40 , not an integer
B,C,E can be ruled out similarly.
D is minimum value as x = 19*10/19 = 10
Answer is E
Answer: (E) 19
Question: 10^(65) Ã· 10^(64) = ?
(A) 1
(B) 10
(C) 100
(D) 1000
(E) 10000
Rationale: 10^(65) Ã· 10^(64) = 10^ (65-64) = 10^1
= 10
Answer : B
Answer: (B) 10
Question: If 4XZ + YW = 7 and XW + YZ = 14, what is the value of the expression (2X + Y)(2Z + W)?
(A) 9.
(B) 12.
(C) 35.
(D) 16.
(E) 18.
Rationale: (2x+y)*(2z+w) = 7+2(14) =35
Answer : C
Answer: (C) 35.
Question: A and B invest 3,000 and 4,000 in a business. A receives 10 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year ‘A’ totally receives 390, what does B receive?
(A) 375
(B) 360
(C) 350
(D) 260
(E) None of these
Rationale: In a year, for A, total amount as a remuneration
= 10 × 12 = 120
∴ Amount of A’s profit = 390 – 120 = 270
Ratio of investment = 3 : 4
Let total profit = x
Then, B’s profit = (x – 270)
∴ 3/3+4×x=270⇒ x = 630
∴ B’s profit = 630 – 270 = 360
Answer B
Answer: (B) 360
Question: Find the rate at Simple interest, at which a sum becomes four times of itself in 15 years.
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: Explanation:
Let sum be x and rate be r%
then, (x*r*15)/100 = 3x [important to note here is that simple interest will be 3x not 4x, beause 3x+x = 4x]
=> r = 20%
Option B
Answer: (B) 20%
Question: Find a a prime number from the options below.
(A) 37
(B) 38
(C) 39
(D) 40
(E) 42
Rationale: Clearly, 37 is a prime number.
A
Answer: (A) 37
Question: $ 3650 is divided among 4 engineers, 3 MBAs and 5 CAs such that 3 CAs get as much as 2 MBAs and 3 Engs as much as 2 CAs .Find the share of an MBA.
(A) 400
(B) 150
(C) 250
(D) 450
(E) 350
Rationale: 4E+3M+5C=3650
3C=2M, that is M=1.5C
3E=2C that is E=.66 C
Then, (4*0.66C)+(3*1.5C)+5C=3650
C=3650/12.166
C=300
M=1.5C
=450.
ANSWER : D 450
Answer: (D) 450
Question: The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years?
(A) 2500
(B) 2800
(C) 3500
(D) 3600
(E) 2050
Rationale: P = 4032
R = 20%
Required population of town = P/(1 + R/100)^T
= 4032/(1 + 20/100)^2
= 4032/(6/5)^2
= 2800(approximately)
Answer is B
Answer: (B) 2800
Question: If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
...
We can see the patterns here, so the sum of first 50 positive even integers minus the sum of first 50 positive odd integers will be 50.
Answer: C.
Answer: (C) 50
Question: The difference between the simple interest received from two different sources on Rs.1600 for 3 years is Rs.13.50. The difference between their rates of interest is
(A) 0.1%
(B) 0.28%
(C) 0.35%
(D) 0.42%
(E) 0.5%
Rationale: (1600xR1x3)/100-(100xR2x3)/100 =13.50
4800(R1-R2)=1350
R1-R2 = 1350/4800=0.28%
answer : B
Answer: (B) 0.28%
Question: A cricket bat is sold for $900, making a profit of $75. The profit percentage would be
(A) 9%
(B) 12%
(C) 10%
(D) 36%
(E) 40%
Rationale: 75/(900 - 75) = 75/825 = 0.9 bit more than 9%.
Answer: A
Answer: (A) 9%
Question: A train running at 25 km/hr takes 20 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
(A) a) 200/3m175/3m
(B) b) 90m70m
(C) c) 50m45m
(D) d) 100/3 m200/3
(E) e) none of these
Rationale: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/20*12=15m so the train covered a distance in 12 sec= 25*5/20*12=75
so the length of the train(Lt) is 15+75=90m
Now crossing the platform means length of train+length of platform(Lt+p)= 20*25*5/20=125m Now the length of platform (Lp) is= 125-90=35m
So answer is 90m and 35m Must beBeven though its mentioned 90m and 70m thinking so typo mistake...........
Answer: (B) b) 90m70m
Question: 3x^2 + 5x - 2 =
(A) (3x-1)(x+2)
(B) (3x-4)(x+2)
(C) (3x-4)(x-2)
(D) (3x-2)(x+4)
(E) none of above
Rationale: 3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x (x + 2) - (x+2)
= (3x-1) (x+2)
Option A
Answer: (A) (3x-1)(x+2)
Question: A farmer spent $33 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $36.30
(B) $38.50
(C) $39.20
(D) $39.50
(E) $40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$33=$13.2 on chicken feed, thus he spent the remaining 33-13.2=$19.8 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.2 --> x=$16.5.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 16.5+19.8=$36.3.
Answer: A
Answer: (A) $36.30
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
(A) 0.03
(B) 0.9
(C) G.C.D.=0.18
(D) 0.2
(E) 0.21
Rationale: Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C
Answer: (C) G.C.D.=0.18
Question: In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A)  172,700
(B)  172,800
(C)  172,900
(D)  173,000
(E)  173,100
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 7-3 = 4 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 4 = 172,800. Hence B.
Answer: (B)  172,800
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 19008, how much amount per month would he have spent on clothes and transport?
(A) 4038
(B) 8076
(C) 9691.2
(D) 1584
(E) 1625
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 19008⁄12 = 1584
Answer D
Answer: (D) 1584
Question: A company produces 72000 bottles of water everyday. If a case can hold 9 bottles of water .How many cases are required by the company to hold its one day production
(A) 2000
(B) 4500
(C) 5000
(D) 8000
(E) 9000
Rationale: Number of bottles that can be held in a case = 9.
Number of cases required to hold 72000 bottles = 72000/9=8000 cases.
So the answer is D =8000
Answer: (D) 8000
Question: The expression 10^14−130 is divisible by all of the following integers EXCEPT
(A) 9
(B) 2
(C) 4
(D) 8
(E) 11
Rationale: Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (A) is correct.
Answer: (A) 9
Question: If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
(A) (3x + 2y)/5
(B) (3x + 2y)/(x + y)
(C) (3x + 2y)/(xy)
(D) 5(3x + 2y)
(E) 3x + 2y
Rationale: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 3x;
Cost of prunes = 2y;
Cost per pound = (3x + 2y)/5;
Ans is (A).
Answer: (A) (3x + 2y)/5
Question: A garrison of 400 men had a provision for 31 days. After 20 days 180 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 65 days
(B) 45 days
(C) 20 days
(D) 16 days
(E) 18 days
Rationale: 400 --- 31
400 --- 11
220 --- ?
400*11 = 220*x => x =20 days.
Answer: C
Answer: (C) 20 days
Question: Cara and Dan race around a running track. Cara runs at a constant rate of one lap every 4 minutes and Dan runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Cara to get exactly one lap ahead of Dan?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: Let x be the number of minutes it takes for Cara to get one lap ahead.
Then Cara ran x/4 laps and Dan ran x/5 laps.
x/4 = 1+x/5
5x=20+4x
x=20
The answer is B.
Answer: (B) 20
Question: How many three digits odd numbers can be formed by using the digits 4,5,6,7,8,9 if the repetition of the digits not allowed?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 30
Rationale: For a number to be odd the unit place must be filled by the number 5,7 or 9 in 3 ways. Since the repetition of digits not allowed the ten's and hundred's place can be filled in by 5 and 4 ways respectively. So the required number of numbers =3*5*4 = 60. Answer : A
Answer: (A) 60
Question: The average length of the sides of triangle ABC is 12. What is the perimeter of triangle ABC?
(A) 4
(B) 6
(C) 12
(D) 24
(E) 36
Rationale: (average) = (perimeter)/3;
12 = (perimeter)/3;
(perimeter) = 36.
Answer: E.
Answer: (E) 36
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 15 kmph
(B) 40 kmph
(C) 18 kmph
(D) 19 kmph
(E) 10 kmph
Rationale: Speed downstream = 60 + 20
= 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
Answer: (B) 40 kmph
Question: How many points are there on the globe where by walking one mile south, one mile east and one mile north you reach the place where you started.
(A) South Pole
(B) North Pole
(C) east Pole
(D) west Pole
(E) none
Rationale: if you are standing on South Pole there is no going 1 mile South. I mean you are at the ultimate south.
So the answer should be only North Pole.
ANSWER:B
Answer: (B) North Pole
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
(A) 6Rs
(B) 7Rs
(C) 8Rs
(D) 4Rs
(E) 1Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer:A
Answer: (A) 6Rs
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 21
(B) 20
(C) 99
(D) 277
(E) 12
Rationale: Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed = sum of the speeds].
Answer: B
Answer: (B) 20
Question: The price of a certain motorbike this year is $8,964, which is 8 percent greater than the cost of the motorbike last year. What was the price of the motorbike last year?
(A) $8,000
(B) $8,100
(C) $8,200
(D) $8,300
(E) $8,400
Rationale: The price of the motorbike last year was $8,964/1.08=$8,300
The answer is D.
Answer: (D) $8,300
Question: A circular mat with diameter 1.4 inches is placed on a square tabletop, each of whose sides is 4 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 3/8
(B) 7/8
(C) 1/5
(D) 3/7
(E) 7/9
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (22/7)(1.4)(1.4)
Area of the Table = (4)(4)
So the quick way to estimate is looking at the fraction like this:6.16/16 nearest to 3/8
Answer: A
Answer: (A) 3/8
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
(A) 12.5%
(B) 13%
(C) 14.5%
(D) 15%
(E) 15.7%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
A)
Answer: (A) 12.5%
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 104
(B) 7778
(C) 266
(D) 288
(E) 121
Rationale: 624/6 = 104 kmph Answer:A
Answer: (A) 104
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?
(A) 33
(B) 82
(C) 67
(D) 28
(E) 18
Rationale: Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Answer:B
Answer: (B) 82
Question: the cost price of 30 items is equal to the sale price of 40 items .What is percentage profit?
(A) 20% loss
(B) 25% loss
(C) 15% loss
(D) 35% loss
(E) 5% loss
Rationale: this results in loss percentage not profit.
let cp of 1 item=1rp.
SP of 40 items=CP of 30 items=30
cp of 40 items=40
sp of 40 items-30
loss=cp-sp=10
loss percentage=(10/40*100)=25%
ANSWER:B
Answer: (B) 25% loss
Question: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [5]*[4] = ?
(A) [33]
(B) [44]
(C) [45]
(D) [88]
(E) [90]
Rationale: [5]*[4]=(2*5+1)(4/2+1)
=[33].
Ans-A
Answer: (A) [33]
Question: What percent of a day is 8 hours?
(A) 12Ã—1/2%
(B) 16Ã—1/2%
(C) 33Ã—1/3%
(D) 22Ã—1/2%
(E) None
Rationale: Solution
Required percentage	= (8/24Ã—100)%
= (100 / 3)%.
= 33Ã—1/3%.
Answer C
Answer: (C) 33Ã—1/3%
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. After how much time will the trains meet?
(A) 27/7 sec
(B) 20/7 sec
(C) 33/7 sec
(D) 21/7 sec
(E) 32/7 sec
Rationale: B
20/7 sec
They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer: (B) 20/7 sec
Question: 121,112,...?..,97,91,86
(A) 99
(B) 104
(C) 102
(D) 108
(E) 100
Rationale: 121. 112. 104. 97. 91. 86
the decreasing difference is reducing by 1 at each step
so,missing no. will be 104
answer B
Answer: (B) 104
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 2.9 kmph
(B) 9.9 kmph
(C) 1.3 kmph
(D) 1.2 kmph
(E) 5.7 kmph
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10
= 1.3 kmph.
Answer: C
Answer: (C) 1.3 kmph
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got
(A) 55%
(B) 56%
(C) 57%
(D) 58%
(E) 59%
Rationale: Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
ANSWER IS C
Answer: (C) 57%
Question: A4C,B9D,C16E,D25F,E36G,?
(A) F49G
(B) H47J
(C) F49H
(D) H64I
(E) G49I
Rationale: A _ C = 2^2
B _ D = 3^2
C _ E = 4^2
D _ F = 5^2
E _ G = 6^2
2^2, 3^2 , 4^2 , 5^2 , 6^2 ---> As per this number sequence
=> next number = 7^2 = 49
F _ H = 49 => F49H
ANSWER:C
Answer: (C) F49H
Question: A certain club has 12 members, including Harry. One of the 11 members is to be chosen at random to be the president, one of the remaining 10 members is to be chosen at random to be the secretary, and one of the remaining 9 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?
(A) 2
(B) 1
(C) 1/6
(D) 3/6
(E) 5/6
Rationale: Each member out of 12, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/12 and the probability that Harry will be selected to be the treasurer is also 1/12. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/12+1/12=2/12.
Answer: C.
Answer: (C) 1/6
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?
(A) 33 1/8 %
(B) 100 %
(C) 33 1/3 %
(D) 33 5/8 %
(E) 34 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 8.
If he buys 4 a rupee, his CP = 2
He selling at 2 a rupee, his SP = 4
Profit = SP - CP = 4 - 2 = 2
Profit Percent = 2/2 * 100 = 100 %
Answer: B
Answer: (B) 100 %
Question: A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?
(A) 6 km/hr
(B) 7.2 km/hr
(C) 7.56 km/hr
(D) 7.78 km/hr
(E) 8 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: If 20 ounces of a strong vinegar solution are diluted with 60 ounces of water to form a six-percent vinegar solution, what was the concentration of the original solution?
(A) 15%
(B) 18%
(C) 20%
(D) 21%
(E) 24%
Rationale: Let x be the concentration of the original solution.
20x = 0.06(80)
x = 0.24
The answer is E.
Answer: (E) 24%
Question: If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by
(A) 12 %
(B) 19 %
(C) 25 %
(D) 32 %
(E) 36 %
Rationale: Explanation:
Let original consumption = 100 kg and consumption = y kg.
So, 100 x 6 = y x 8
y = 75 kg
Reduction in consumption = 25 %.
ANSWER: C
Answer: (C) 25 %
Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed?.
(A) 6kilometer/hour
(B) 8kilometer/hour
(C) 12kilometer/hour
(D) 15kilometer/hour
(E) None of these
Rationale: Remaining distance = 3km and remaining time = (1/3*45)minutes=15minutes=1/4hour.
Required speed=(3*4)kilometer/hour=12km/hour.
Correct Option: C
Answer: (C) 12kilometer/hour
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
(A) 1/26
(B) 1/27
(C) 1/22
(D) 1/21
(E) 1/29
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13
= 1/26
Answer: A
Answer: (A) 1/26
Question: In a meeting of 3 representatives from each of 8 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
(A) 242
(B) 232
(C) 212
(D) 262
(E) 252
Rationale: In fact, all 24 people will shake hands with 21 others.
So, it SEEMS like the TOTAL number of handshakes = (24)(21)
HOWEVER, we need to keep in mind that we have counted each handshake TWICE.
To account for this DUPLICATION, we must divide (24)(21) by 2.
So, the TOTAL # of handshakes = (24)(21)/2 = 252
Answer : E
Answer: (E) 252
Question: At the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
(A) 15.3%
(B) 25%
(C) 30%
(D) 33%
(E) 40%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
50 = 30 + b + 30b/100
b = 15.3
Answer (A)
Answer: (A) 15.3%
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
(A) 11
(B) 10
(C) 99
(D) 88
(E) 12
Rationale: 2420 --- 242
100 --- ? => 10%Answer: B
Answer: (B) 10
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 42 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 27
(C) 50
(D) 99
(E) 12
Rationale: Relative speed = 42 + 30 = 72 km/hr.
72 * 5/18 = 20 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 /20 = 50 sec.
Answer: C
Answer: (C) 50
Question: A small bag contains full of nine yellow ball, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
(A) 16c2
(B) 5c7
(C) 4c2
(D) 32c2
(E) 48c2
Rationale: tot balls = 9+3+4 = 16
two balls drawn from 16C2 ways
ANSWER A
Answer: (A) 16c2
Question: The ratio of efficiency of A is to C is 5:3.The ratio of no.of days taken by B is to C is 2:3.A takes 6 days less than C,when A and C completes the work individually.B and C left the work after 2 days.the no of days taken by A to finish the remaining work?
(A) 4.5
(B) 5
(C) 6
(D) 28/3
(E) 7
Rationale: A : B : C
Efficiency 10 : 9 : 6
No of days 9x : 10x : 15x
given=> 15x-9x = 6
hence, x = 1
Number of days taken by A = 9 and daily work done=10
Number of days taken by B= 10 and daily work done=9 (total work =90)
Number of days taken by C = 15 and daily work done=6
work done by B and C in initial 2 days =30
rest work =60
Number of days required by A to finish = 60/10=6 days
ANSWER:C
Answer: (C) 6
Question: The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
(A) 11 : 9
(B) 11 : 18
(C) 21 : 19
(D) 21 : 19
(E) None
Rationale: Sol.
Let the numbers be x and y.
Then, x+y / x -y = 40/4 = 10
⇔ (x+y) = 10(x-y)
⇔ 9x = 11y
⇔ x/y = 11 / 9.
Answer A
Answer: (A) 11 : 9
Question: If c is a positive integer, then 3^c + 3^(c +1) =
(A) 4^a
(B) 3^a − 1
(C) 3^(2a) + 1
(D) 3^a*(a − 1)
(E) 4(3^c)
Rationale: 3^c + 3^(c +1)
= 3^c + (3^c * 3^1)
= 3^c (1 + 3)
= 3^c(4)
Ans. E) 4(3^c)
Answer: (E) 4(3^c)
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
(A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
(B) Ram = Rs.2500, Shyam = Rs.500, Mohan = Rs.250
(C) Ram = Rs.1200, Shyam = Rs.1300, Mohan = Rs.750
(D) Ram = Rs.1700, Shyam = Rs.1300, Mohan = Rs.750
(E) Ram = Rs.1000, Shyam = Rs.1300, Mohan = Rs.750
Rationale: 1/2:1/3:1/4
= 6:4:3
Ram = 6/13 * 3250
= 1500
Shyam = 4/13 * 3250
= 1000
Mohan = 3/13 * 3250
= 750
Answer:A
Answer: (A) Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) Rs.24028
(B) Rs.24000
(C) Rs.24003
(D) Rs.24029
(E) Rs.24029
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs.24000
Answer: B
Answer: (B) Rs.24000