mathewhe/aqua_rat huggingface dataset:
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 29?
(A) 17
(B) 27
(C) 37
(D) 47
(E) 57
Rationale: (1056 / 29) gives remainder 12
17 + 12 = 29, So we need to add 17
A
Answer: (A) 17
Question: If a is an integer, what is the greatest possible value for a that would still make the following statement true: 11*10^a < 1/10 ?
(A)  –4
(B)  –3
(C)  –2
(D)  –1
(E)  0
Rationale: Just putting values, the LHS becomes
a=0 --> 11
a=-1 --> 11/10
a=-2 --> 11/100
a=-3 --> 11/1000
Anything lower will be smaller than 11/1000. a=-2, equality does not hold but it does for a=-3.
Answer is B.
Answer: (B)  –3
Question: The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest whe there are 40 guests in the hotel?
(A) Rs.30
(B) Rs.32
(C) Rs.31
(D) Rs.39
(E) Rs.12
Rationale: Answer: A) Rs. 30
Explanation:
Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then
x + 10y = 600 ---------(1)
x + 20y = 800 ----------(2)
10y = 200
y = Rs. 20 and x= 400
Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200
average expenditure ={1200}/{40}
= Rs. 30
Answer: A
Answer: (A) Rs.30
Question: If x - 2 < 8 and x + 6 > 4, which of the following inequalities expresses all possible values of x?
(A) 2 < x < 10
(B) 4 < x < 8
(C) -2 < x < 10
(D) -4 < x < 8
(E) -8 < x < 4
Rationale: x - 2 < 8
So, x < 10
2. x + 6 > 4
So, x > -2
Combine the two you get -2 < x < 10
Answer will be (C)
Answer: (C) -2 < x < 10
Question: Glen is having his big family over for Christmas. Out of 25 people coming, 40 percent are lactose intolerant and 72% are vegetarians. Glen wants to prepare the good in advance. Can you calculate how many of the guests are both vegetarians and lactose intolerant?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The total number of guests coming over for Christmas is n=25.
The number of lactose intolerant guests is 40% of it, thus
n (A)=40/100×25=40/4=10.
The number of guests who are vegetarians is 72%, thus
n (B)=72/100×25=72/4=18.
In order to calculate the number of guests who are both lactose intolerant and vegetarians we can use the following equation:
n (AnB)=n (A)+n (B) -n =10+18-25=28-25=3.
So, 3 of Glen's guests are both lactose intolerant and vegetarians.
ANSWER: C
Answer: (C) 3
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.6
(B) 12.0
(C) 12.1
(D) 12.3
(E) 12.2
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.Answer: B
Answer: (B) 12.0
Question: A bag contains 8 red and 3 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 2/3
(C) 8/11
(D) 1/4
(E) 5/7
Rationale: Total number of balls = 8+3 = 11
number of white balls = 8
Probability = 8/11 = 8/11
Answer is C
Answer: (C) 8/11
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 18. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
(A) 1
(B) 13
(C) 15
(D) 19
(E) 47
Rationale: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (C)
Answer: (C) 15
Question: A shopkeeper bought 150 calculators at the rate of 250 per calculator.He spent 2500 on transportation and packing. If the marked price of calculator is 320 per calculator and the shopkeeper gives a discount of 5% on the marked price then what will be the percentage profit gained by the shopkeeper?
(A) 20%
(B) 14%
(C) 15%
(D) 16%
(E) None of these
Rationale: CP of 150 calculators = 150 × 250 = 37,500.
\ total CP = 37,500 + 2500 = 40,000
Marked price of 150 calculators = 150 × 320 = 48,000
Selling price after discount = 4800 × 95⁄100
= 45,600
\ Percentage profit = 45,600−40,000/40,000×100 = 14%
Answer B
Answer: (B) 14%
Question: The 20th term of the series a, b , b, c, c, c, d, d, d, d, e, e, e, e, e, .... is
(A) a
(B) b
(C) c
(D) d
(E) e
Rationale: a is one time, b,2 times so on...
so 20=n(n+1)/2..
0r n(n+1)= 40... now 6*7=30... 5*6<40 so n= 6.. and 20th alphabet is E..ans E
Answer: (E) e
Question: After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?
(A) 1400
(B) 1240
(C) 1200
(D) 1100
(E) 1500
Rationale: CP* (50/100) = 620
CP= 12.4 * 100 => CP = 1240
ANSWER:B
Answer: (B) 1240
Question: A researcher computed the mean, the median, and the standard deviation R for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
Rationale: If we add or subtract a constant to each term in a set the standard deviation R will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Answer: (D) The mean and the median
Question: CP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?
(A) $10,500
(B) $10,500
(C) $11,500
(D) $12,000
(E) $12,500
Rationale: Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = $17,500
C.P of 1st buffalo = $17,500
C.P of 2nd buffalo = 30,000 - 17,500 = $12,500
E
Answer: (E) $12,500
Question: Ben is driving on the highway at y miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of x feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
(A) 5,280(x/y)
(B) 5,280(y/x)
(C) 5,280(xy)
(D) 5,280/(xy)
(E) (xy)/5,280
Rationale: In one hour, at the rate of y miles per hour, Ben covers y miles, so 5,280y feet.
The number of revolutions = distance/circumference = 5,280y/x.
Answer: B.
Answer: (B) 5,280(y/x)
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 20 seconds. Its length is?
(A) 188 m
(B) 876 m
(C) 251 m
(D) 300 m
(E) 145 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 20 = x / 15
x = 300 m.
Answer: D
Answer: (D) 300 m
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $92. If $2,000 is the total amount invested, how much is invested at 8 percent?
(A) $600
(B) $700
(C) $800
(D) $900
(E) $1000
Rationale: 0.1x = 0.08(2000-x)+92
0.18x = 252
x = 1400
Then the amount invested at 8% is $2000 - $1400 = $600
The answer is A.
Answer: (A) $600
Question: A grocer has a sale of Rs. 5435, Rs. 5927, Rs. 5855, Rs. 6230 and Rs. 5562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5500?
(A) 4991
(B) 5991
(C) 3991
(D) 6542
(E) 6995
Rationale: Total sale for 5 months = Rs. (5435 + 5927 + 5855 + 6230 + 5562) = Rs. 29009.
Required sale = Rs. [ (5500 x 6) - 29009 ]
= Rs. (33000 - 29009)
= Rs. 3991
Answer: Option C
Answer: (C) 3991
Question: P is faster than Q. P and Q each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, P's speed is equal to ?
(A) 9 km/hr
(B) 4 km/hr
(C) 6 km/hr
(D) 5 km/hr
(E) 3 km/hr
Rationale: Explanation:
Let P's speed = x km/hr. Then, Q's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
- 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, P is faster than Q,
so P's speed = 4 km/hr and Q's speed = 3 km/hr.
Answer: B
Answer: (B) 4 km/hr
Question: John got Rs.6000 as his share out of a total profit of Rs.9000 which he and Rick earned at the end of one year. If John invested Rs.20,000 for 6 months, where as Rick invested his amount for the whole year, what was the amount invested by Rick?
(A) 3400
(B) 3500
(C) 4500
(D) 5000
(E) 5500
Rationale: (D)
Let the amount invested by Ramesh = Rs.x.Then, 20000×6 : 12x=6000:3000
or 12000012x=21 or x = 5000
Answer: (D) 5000
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^70?
(A) 120
(B) 140
(C) 130
(D) 150
(E) 160
Rationale: Put in simple words, we need to find the highest power of 2 in 100^70
100 = 2^2*5^2
Therefore 100^70 = (2^2*5^2)^70 = 2^140*5^140
Answer : B
Answer: (B) 140
Question: A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?
(A) M :23.50 w:22.50
(B) M :27.50 w:22.50
(C) M :27.50 w:22.51
(D) M :27.50 w:22.53
(E) M :27.50 w:22.66
Rationale: Let the daily wage of a man be Rs. x.
Then, daily wage of a woman = Rs. (x - 5).
Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.
Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50.
Answer: B
Answer: (B) M :27.50 w:22.50
Question: Two good train each 100 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 1.2 sec
(B) 2.4 sec
(C) 4.8 sec
(D) 9.6 sec
(E) None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (100+ 100) m = 1000 m.
Required time = (200 x 6 / 125) sec = 9.6 sec.
Answer D
Answer: (D) 9.6 sec
Question: If PINTU is coded as 79523 in a certain code language, how would you code JUMBO in the same language?
(A) 13426
(B) 14236
(C) 13436
(D) 14263
(E) 15263
Rationale: 1 2 3 4 5 6 7 8 9
a b c d e f g h i
j k l m n o p q r
s t u v w x y z
sooo...JUMBO is 13426...
ANSWER:A
Answer: (A) 13426
Question: A person crosses a 800 m long street in 6 minutes. What is his speed in km per hour?
(A) 5.2 km/hr.
(B) 8.0 km/hr.
(C) 7.2 km/hr.
(D) 3.2 km/hr.
(E) 4.2 km/hr.
Rationale: B
8.0 km/hr.
Speed=(800/6 * 60) m/sec
= 2.2 m/sec.
Converting m/sec to km/hr
=(2.2*18/5) km/hr
= 8.0 km/hr.
Answer is B
Answer: (B) 8.0 km/hr.
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.
How many matches were played?
(A) 99 matches
(B) 79 matches
(C) 69 matches
(D) 99 matches
(E) 59 matches
Rationale: D
99 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.
Answer: (D) 99 matches
Question: The average age of 5 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?
(A) 10years
(B) 15years
(C) 20years
(D) 25years
(E) 18years
Rationale: Total age of 5 boys = 25*5 = 125
ratio of their ages = 3:5:7
Age of the youngest = 125*3/15 = 25 years
Answer is D
Answer: (D) 25years
Question: What is the least integer that is a sum of four different prime numbers?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 23
Rationale: The sum of the four smallest primes is 2+3+5+7=17.
The answer is B.
Answer: (B) 17
Question: The value of x + (xx) when x = 2 is:
(A) A)36
(B) B)6
(C) C)18
(D) D)64
(E) E)10
Rationale: x + (xx)
Put the value of x = 2 in the above expression we get,
2 + (22)
= 2 +(2 × 2)
= 2 + (4)
= 2 + 4
= 6
B
Answer: (B) B)6
Question: A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 99%
(B) 47%
(C) 84%
(D) 96%
(E) 43%
Rationale: g% = 40 + 40 + (40*40)/100
= 96%
Answer: D
Answer: (D) 96%
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 12880
(B) 12789
(C) 27108
(D) 17600
(E) 18291
Rationale: Explanation:
Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600
Answer: (D) 17600
Question: If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is ?
(A) 1/25
(B) 1/28
(C) 1/27
(D) 1/24
(E) 1/22
Rationale: We have 1, 8, 27 and 64 as perfect cubes from 1 to 100.
Thus, the probability of picking a perfect cube is
4/100 = 1/25.
Answer: A
Answer: (A) 1/25
Question: an article with cost price of 192 is sold at 25% profit. what is the selling price?
(A) 198
(B) 200
(C) 204
(D) 240
(E) 210
Rationale: sp=1.25*192=240
ANSWER:D
Answer: (D) 240
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
(A) 4 1/6 %
(B) 6 1/6 %
(C) 8 1/3 %
(D) 20 %
(E) 10%
Rationale: C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %
ANSWER:C
Answer: (C) 8 1/3 %
Question: What quadrants do the line y = 2x - 4 go through?
(A) 1 and 2
(B) 1 and 3
(C) 1 and 4
(D) 1,2 and 3
(E) 1,3 and 4
Rationale: Find the x-intercept and the y-intercept of the line.
To find the x intercept, set y = 0 and solve for x.
0 = 2x - 4
x = 2
To find the y intercept, set x = 0 and solve for y.
y = 0 - 4
y = -4
Draw the line using the two intercepts.
Thus, the line goes through the 1st, 3rd and 4th quadrants.
Answer is E
Answer: (E) 1,3 and 4
Question: January 13, 2016, fell on a Wednesday. On which day of the week did June 25, 2016, fall? (Note: 2016 was a leap year.)
(A) Sunday
(B) Tuesday
(C) Thursday
(D) Friday
(E) Saturday
Rationale: The date range contains a partial year. The number of days in the partial year is:
January - 18, February - 29, April - 30, March and May - 31, and June - 25.
18 + 29 + 30 + (2 * 31) + 25 = 164 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 164 / 7 = 23 remainder 3.
Since the first date was a Wednesday, advance the day of the week by 3; the second date fell on a Saturday. The answer is E.
Answer: (E) Saturday
Question: Anand and Deepak started a business investing Rs. 20,500 and Rs. 30,000 respectively. Out of a total profit of Rs. 13,000, Deepak's share is?
(A) Rs. 9400
(B) Rs. 8900
(C) Rs. 8400
(D) Rs. 7722.8
(E) Rs. 8440
Rationale: Ratio of their shares = 20500 : 30000 = 41 : 60
Deepak's share = 13000 * 60/101 = Rs. 7722.8
Answer:D
Answer: (D) Rs. 7722.8
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 7 days
(B) 3 days
(C) 9 days
(D) 8 days
(E) 2 days
Rationale: C
9 days
C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days
Answer: (C) 9 days
Question: For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-seventh of his earnings for the entire year, what is the value of N?
(A) 31/4
(B) 33/4
(C) 29/4
(D) 27/4
(E) 25/4
Rationale: Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/5 = 1/7(11x + Nx);
11/10 + N/5 = 1/7(11 + N)
11+2N/10 = 11+N/7 =>77+14N = 110+10N =>4N=33
N = 33/4
Answer: B
Answer: (B) 33/4
Question: The number of circles that can be drawn out of 10 points of which 7 are collinear is
(A) 130
(B) 85
(C) 45
(D) 72
(E) 82
Rationale: For drawing a circle we need 3 non collinear points.
This can be done in:
3C3 + 3C2 x 7C1 + 3C1 x 7C2 = 1 + 21 + 63 = 85
ANSWER:B
Answer: (B) 85
Question: A number is increased by 11% and then reduced by 10%. After these operations, the number :
(A) does not change
(B) decreases by 1%
(C) increases by 1%
(D) increases by 0.1%
(E) None of these
Rationale: Let the original number be 100.
Then, the new number = 100 × 1.1 × 0.9 = 99
i.e. the number decreases by 1%.
Answer B
Answer: (B) decreases by 1%
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 7 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
(A) 12
(B) 24
(C) 36
(D) 60
(E) 72
Rationale: the difference of the speed is 2m per second so in one minute Sacha will be 120 m ahead of Bruno..
Bruno will cover this in 120/5=24 secs..
B
Answer: (B) 24
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2160 less than the principal. What was the principal?
(A) 1500
(B) 2500
(C) 2700
(D) 3200
(E) 11500
Rationale: P - 2160 = (P*5*4)/100
P = 2700
Answer: C
Answer: (C) 2700
Question: 39! is divided by 41. Then what is the remainder for this?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: (A) 1
Question: 4x − 12 = 4y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: 4x − 12 = 4y
=> 4x - 4y = 12
=> x- y =3 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 6
=> x=3
y=0
Therefore , the given system will have Exactly one solution
D
Answer: (D) Exactly one
Question: 4840÷8÷4=?
(A) 151
(B) 156
(C) 189
(D) 134
(E) 167
Rationale: 4840 ÷ 8 = 605
605 ÷ 4 = 151
Answer is A
Answer: (A) 151
Question: Three workers have a productivity ratio of 1 to 2 to 6. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 12 to 1
(B) 10 to 1
(C) 5 to 1
(D) 1 to 6
(E) 1 to 5
Rationale: The fastest worker who does 6 units of job worked for all 10 hours, so he did 6*10=60 units of job;
The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;
The ratio thus is 60 to 6, or 10 to 1.
Answer: B
Answer: (B) 10 to 1
Question: Someone on a skateboard is traveling 5 miles per hour. How many feet does she travel in 45 seconds? (1 mile = 5280 feet)
(A) 380 ft
(B) 400 ft
(C) 410.05 ft
(D) 329.85 ft
(E) 420.85 ft
Rationale: per second => 5*5280 ft/60*60 =7.33 ft
45 seconds => 7.33 * 45 = 329.85 ft
Answer : D
Answer: (D) 329.85 ft
Question: In Set T, the average (arithmetic mean) equals the median T. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
(A) I only
(B) I and II
(C) II and III
(D) I, II, and III
(E) IV only
Rationale: This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median T you might fall for 'D'.
Ans: E
Answer: (E) IV only
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 65 km/hr
(B) 76 km/hr
(C) 36 km/hr
(D) 45 km/hr
(E) 41 km/hr
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Answer: (C) 36 km/hr
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 90 kmph. After how much time will the trains meet?
(A) 20/8 sec
(B) 20/4 sec
(C) 5/2 sec
(D) 22/7 sec
(E) 60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 90)*5/18 = 8*5 = 40 mps.
The time required = d/s = 100/40 = 5/2 sec.Answer:C
Answer: (C) 5/2 sec
Question: A train is running at a speed of 40 km/hr and it crosses a post in 19.8 seconds. What is the length of the train?
(A) 190 metres
(B) 160 metres
(C) 200 metres
(D) 220 metres
(E) 250 metres
Rationale: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 19.8 s
Distance Covered, d = vt = (400/36)Ã— 19.8 = 220 m
Distance covered is equal to the length of the train = 220 m
Correct answer is 220 metres
D
Answer: (D) 220 metres
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 3.5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 15/14
(C) 4/5
(D) 6/5
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /(7/2) = 84/7
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill = (84/7)/10 = 84/70 =6/5
Answer D
Answer: (D) 6/5
Question: In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 10a then which of the following is c equal to?
(A) a/12
(B) a/8
(C) 6a
(D) 8a
(E) 16a
Rationale: The sum of the roots is = -b/a = -10a/a = -10. Let the other root be x. Thus, x-2 = -10
x = -8. Again, the product of the roots is -2*-8 = 16. Thus, c/a = 16. c = 16a.
E.
Answer: (E) 16a
Question: Rahim bought 52 books for Rs.1200 from one shop and 32 books for Rs.480 from another. What is the average price he paid per book ?
(A) s.17
(B) s.18
(C) s.12
(D) s.20
(E) s.10
Rationale: Average price per book
= (1200+ 480) / (52 + 32) = 1680/ 84
= Rs.20
Answer:D
Answer: (D) s.20
Question: John walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 8 hours 40 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways.
(A) 8 h 40 min
(B) 10 h 40 min
(C) 9 h 40 min
(D) 11 h 45 min
(E) 8 h 25 min
Rationale: 1.Walking to to a viewpoint+Driving back=8 hours 40 minutes
2.Driving to a viewpoint+Driving back=8 hours 40 minutes - 2 hours=6 hours 40 minutes, thereforeone way driving=6 hours 40 minutes/2 =3 hours 20 minutes.
3. From 1.one way driving=8 hours 40 minutes-3 hours 20 minutes=5 hours 20 minutes.
4.Walking to to a viewpoint+Walking back=5 hours 20 minutes+5 hours 20 minutes=10 hours 40 minutes.
Answer: B
Answer: (B) 10 h 40 min