mathewhe/aqua_rat huggingface dataset:
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Z of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) Z=4x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: (B) Z=4x
Question: The present population of a town is 1000. Population increase rate is 25% p.a. Find the population of town before 1 years?
(A) 800
(B) 1500
(C) 1000
(D) 750
(E) 500
Rationale: P = 1000
R = 25%
Required population of town = P/(1 + R/100)^T
= 1000/(1 + 25/100)
= 1000/(5/4)
= 800
Answer is A
Answer: (A) 800
Question: The speed of a boat in still water is 60kmph and the speed of the current is 12kmph. Find the speed downstream and upstream?
(A) 87 kmph
(B) 40 kmph
(C) 16 kmph
(D) 15 kmph
(E) 48 kmph
Rationale: Speed downstream = 60 + 12
= 72 kmph
Speed upstream = 60 - 20
= 48 kmph
Answer:E
Answer: (E) 48 kmph
Question: A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 104,350,400,000 pounds, how many widgets have been unloaded?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.
When we divide 104,350,400,000 by 100,000, we get 104,350,400,000 = 1,043,504 * 5^5 *2^5.
1,043,504 is not divisible by 5, thus there are 5 widgets.
The answer is D.
Answer: (D) 5
Question: How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?
(A) 10 litres
(B) 12 litres
(C) 15 litres of water
(D) 18 litres
(E) 21 litres
Rationale: C.P. of 1 litre of milk = Rs. 20×2/3 = Rs. 40/3.
C.P. of 1 litre of water =Rs 0.
Mean price = Rs. 32/3.
By the rule of alligation, we have :
C.P of 1 litre C.P of 1 litre
of water of milk
(0) (Rs. 40/3)
\ /
Mean Price
(Rs. 32/3)
/ \
40/3−32/3 32/(3−0)
8/3 32/3
The ratio of water and milk =8/3:32/3.
=8:32=1:4.
Thus, Quantity of water to be added to 60 litres of milk:
=(1/4)×60 litres.
=15 litres. ANSWER : C
Answer: (C) 15 litres of water
Question: Angelina walked 150 meters from her home to the grocery at a constant speed. She then walked 200 meters to the gym at double the speed. She spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 2
(B) 3
(C) 4
(D) 10
(E) 12
Rationale: let the speed be X...
so time taken from home to grocery= 150/x..
the speed to gym = 2x..
so time taken = 200/2x=100/x..
its given 150/x-100/x=10
50/x=10
x=5m/secs..
so grocery to gym=2*5=10m/s...
Answer : D
Answer: (D) 10
Question: In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 100 sec.
(B) 50 sec
(C) 25 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1000/5 = 200 sec.
Time taken by Baley to complete the race is D = 1000/4 = 250 sec.
Hence, D-B = 50 sec
ANSWER:B
Answer: (B) 50 sec
Question: If a person walks at 16 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
(A) 50 km
(B) 56 km
(C) 60 km
(D) 70 km
(E) 33.3 km
Rationale: Let the actual distance travelled be x km.
x/10 = (x+20)/16
16x = 10x + 200
6x = 200
x = 33.3 km.
answer :E
Answer: (E) 33.3 km
Question: Insert the missing number. 2, 7, 10, 22, 18, 37, 26
(A) 26
(B) 22
(C) 2
(D) 52
(E) 18
Rationale: There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
Answer is D
Answer: (D) 52
Question: How many ways are there for 3 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
(A) 6
(B) 12
(C) 72
(D) 100
(E) 720
Rationale: Lets first sit the 3 man, 2! ways.
Now since one position is fixed for women, there are 2 women left and they have 2! ways
2! X 2! = 4 answer is diff this way.
or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, ANS:B
Answer: (B) 12
Question: How many different values of positive integer x, for which |x+9|<x, are there?
(A) 0
(B) 2
(C) 3
(D) 8
(E) 16
Rationale: Answer C
I opted to put the random value option.
i used 0 , 9 , -9 and the the extreme of 10 and -10..
i was able to solve it in 1:09
C
Answer: (C) 3
Question: A man buys an article for 14% less than its value and sells it for 14% more than its value. His gain or loss percent is:
(A) no profit, no loss
(B) 20% profit
(C) less than 30% profit
(D) more than 30% profit
(E) None
Rationale: Let the article be worth Rs. x.
C.P. 86% of Rs. x = Rs. 86x/100
S.P. = 114% of Rs. x = Rs. 114x/100
Gain = (114x/100 - 86x/100) = Rs. 7x/25
Gain % = 7x/25 * 100/86x * 100 = 32 24/43 % > 30%
ANSWER:D
Answer: (D) more than 30% profit
Question: If x is negative and y is positive, which of the following must be positive?
(A) x/y
(B) xy
(C) 2y + x
(D) (x + y)^2 + 1
(E) 3x/y
Rationale: A. x/y
-ve/+ve=-ve
will be negative
B. xy
-ve*+ve= -ve
will be negative
C. 2y + x
might be positive or negative . The sign will be depend on the absolute values of x and y . The expression will be positive if 2y>x
D. (x + y)^2 + 1
= (x+y)^2 will be positive irrespective of the absolute values of x and y
will be positive always
E. 3x/y
=- ve/ +ve
will be negative
Answer D
Answer: (D) (x + y)^2 + 1
Question: In an election between 2 candidates, 50% of the voters cast their votes, out of which 10% of the votes were declared invalid. A candidate got 5000 votes which were 50% of the total valid votes. Find the total number of votes enrolled in that election?
(A) 16200
(B) 18000
(C) 17500
(D) 15823
(E) 15000
Rationale: Let the total number of votes enrolled be x.
Then, number of votes cast = 50% of x.
Valid votes = 90% of (50% of x)
50% of (90% of (50% of x)) = 4050
(50/100)*(90/100)*(50/100)x = 4050
x = 18000
Answer is B
Answer: (B) 18000
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/45
(D) 1/50
(E) 1/900
Rationale: If it takes 9 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/9 = 20. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases = 20. Now, we need to figure out the total # of cases.
The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3 = 900
So, the probability that the police will find the transmitter within three hours = 20/900 = 1/45. Option C
Answer: (C) 1/45
Question: Prathik purchased 40 shirts for rs 3000.he spends 10% for transportation. What should be the selling price per shirt to earn profit of 20% ?
(A) 96 rs
(B) 97 rs
(C) 98 rs
(D) 99 rupees
(E) 100 rs
Rationale: total CP = 3000 + 3000*10/100 = 3300
to gain 20% profit, SP = (100+20)*3300/100 = 3960
selling price per shirt = 3960/40 = 99 rs/shirt
ANSWER:D
Answer: (D) 99 rupees
Question: A can do a certain job in 16 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 11 1/4 days
(B) 8 days
(C) 5 days
(D) 10 days
(E) None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 16 : x = 8x = 5 x 16 =x = 10 days.
Answer is D.
Answer: (D) 10 days
Question: A can do a work in 22 days. B is 30% more efficient than A. How many days does B alone take to do the same job?
(A) 222/13
(B) 221/13
(C) 220/13
(D) 219/13
(E) 218/13
Rationale: Ratio of times taken by A and B = 130:100 = 13:10
suppose B alone to take x days to do the work
then, 13:10::22:x
13x= 10*22
x=220/13 days
correct option is C
Answer: (C) 220/13
Question: When Q is divided by X, the quotient is R and the remainder is E. Which of the following expressions is equal to E?
(A) -RX + Q
(B) RX - Q
(C) Q + RX
(D) QX - R
(E) Q/R
Rationale: Q/X = R + E/W
Q -RX = E
Amswer: A
Answer: (A) -RX + Q
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
(A) 69
(B) 78
(C) 96
(D) 56
(E) 48
Rationale: let the digits be x,y
x + y = 15
x - y = 3
2x = 18, x = 9 so y = 6
hence the number is 96
so the correct answer is option C) 96.
Answer: (C) 96
Question: If n is a natural number, then(6n^2+6n) is always divisible by?
(A) 6 only
(B) 6 and 12
(C) 12 only
(D) by 18 only
(E) None of these
Rationale: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B
Answer: (B) 6 and 12
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
(A) 9/7
(B) 5/8
(C) 3/7
(D) 5/12
(E) 4/7
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12.
Ans: D
Answer: (D) 5/12
Question: Kul is 22 years old and Saras is 33 years. Find the ratio of Saras's age to Kul's age.
(A) 3/1
(B) 3/2
(C) 5/2
(D) 5/3
(E) None of these
Rationale: Explanation :
Kul is 22 years old.Saras is 33 years old.Saras's age : Kul's age = 33 : 22 = 3 : 2
Answer : B
Answer: (B) 3/2
Question: If 2/a + 3/a + 6/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 6/a
(D) 9/a
(E) 11/a
Rationale: 2/a + 3/a + 6/a
=11/a
Answer E
Answer: (E) 11/a
Question: What percent is 240 of 90?
(A) 133 1/3 %
(B) 134 1/3 %
(C) 135 1/3 %
(D) 266 2/3 %
(E) 143 1/3 %
Rationale: 240/90 = 8/3
8/3 × 100 = 800/3 = 266 2/3 %
D
Answer: (D) 266 2/3 %
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 46800, how much amount per month would he have spent on clothes and transport?
(A) 4038
(B) 8076
(C) 9691.2
(D) 4845.6
(E) 3900
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 46800⁄12 = 3900
Answer E
Answer: (E) 3900
Question: How long does a train 125 m long running at the speed of 78 km/hr takes to cross a bridge 125 m length?
(A) 12.7 sec
(B) 10.1 sec
(C) 11.5 sec
(D) 12.1 sec
(E) 11.7 sec
Rationale: Speed = 78 * 5/18
= 21.7 m/sec
Total distance covered
= 125 + 125 = 250 m.
Required time = 250/21.7 '
= 11.5 sec.
Answer:C
Answer: (C) 11.5 sec
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 23. What is the middle number?
(A) 25
(B) 27
(C) 15
(D) 32
(E) 34
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 23 = 111
So, the middle number is (126 - 111 ) = 15
C
Answer: (C) 15
Question: The compound ratio of 5:6, 5:2 and 4:5?
(A) 1:1
(B) 5:3
(C) 1:6
(D) 1:9
(E) 1:2
Rationale: 5/6 * 5/2 * 4/5 = 5/3
5:3
Answer: B
Answer: (B) 5:3
Question: A car runs at the speed of 40 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced?
(A) 8 hours 12 minutes
(B) 12 hours
(C) 16 hours
(D) 17 hours
(E) None
Rationale: Explanation :
Time = 80*8 / 40 = 16 hours
Answer â€“ C
Answer: (C) 16 hours
Question: The Julie's father's age is two more than thrice Julie's age. If Julie will be 15 after 4 years, what is her father's present age?
(A) 35 years
(B) 33 years
(C) 32 years
(D) 34 years
(E) 30 years
Rationale: LET AGE OF JULI BE 'J'
AGE OF HER FATHER BE 'F'
then given 3J+2=F
AND J+4=15
====>J=11 at present
then F=3*11+2
F=35
ANSWER:A
Answer: (A) 35 years
Question: Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series?
(A) 34.25
(B) 34.28
(C) 24.252
(D) 64.28
(E) 34.21
Rationale: Explanation:
Average runs scored by Virat Kohli in 10 matches: Total runs scored/10—(1)
Average runs scored by Virat Kohli in 6 matches: (Total runs in 6 matches)/6
=> 42 = Runs/6
=>252 runs
Using (1):
=>38.9 = Runs/10
=>389 runs
Runs scored in rest 4 matches: 389 - 252 runs
=> 137 runs
Average runs scored by Virat Kohli in 4 matches: 137/4 = 34.25 runs
ANSWER: A
Answer: (A) 34.25
Question: The speed of boat in still water is 20 km/hr. If it travels 26 km downstream and 14 km upstream in same time, what is the speed of the stream?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: Explanation:
Let X be speed of stream
Speed of boat downstream = (20 + X )
Speed of boat upstream = (20 – X)
It is given that boat takes same time to travel 26 km downstream and 14 km upstream
[26/(20 +X)] = [14 / (20 – X)]
520 – 26 X = 280 + 14X
40X = 240
X = 6 km/hr
ANSWER: A
Answer: (A) 6
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel Q if the median is 10 gallons?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel Q= 2
Answer: (B) 2
Question: Set J consists of 5 consecutive even numbers. If the smallest term in the set is -2, what is the range of the positive integers in set J?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: Since there are only 5 integers, another approach is the just list all 5.
We get: -2,0,2, 4, 6
Range of POSITIVE INTEGERS =6 - 2= 4
Answer: C
Answer: (C) 4
Question: What is the measure of the acute angle between the hour and minute hands of a correctly
working clock at 4:18 ?
(A) 12◦
(B) 15◦
(C) 18◦
(D) 21◦
(E) 24◦
Rationale: Consider an axis through the center of the clock with direction, the direction of the hands of the
clock at 12:00. At 4:18 the angle between the axis and the hour hand is
(4+18/60)*360◦/12=129◦
The angle between the axis and the minute hand is 18/60*360◦=108◦
correct answer D
Answer: (D) 21◦
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 15.5 days
(B) 19.5 days
(C) 17.5 days
(D) 16.5 days
(E) 18.5 days
Rationale: C = 1/5 – 1/7 = 2/35 => 17.5 days
ANSWER:C
Answer: (C) 17.5 days
Question: A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
Answer: B
Answer: (B) 18
Question: Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 59
(C) 166
(D) 285
(E) 334
Rationale: I solve it using the tough luck technique:
According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.
80 books of the same science subjects is possible only for two subjects: Physics=90>80 OR Chemistry=110>80
Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books
What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.
We picked:
50 Botany Books
75 Zoology Books
50 Geology Books
Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!
Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick
79*2+1 books
Because, we could have picked the books in following order;
1st book picked: Physics
2nd book picked: Chemistry
3rd book picked: Physics
Thus, Total= 50+75+50+79*2+1=175+1+158=334
Ans:E
Answer: (E) 334
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 13/213
(B) 36/145
(C) 25/113
(D) 27/137
(E) 31/128
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: A can finish a work in 36days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
(A) 15days
(B) 12days
(C) 6days
(D) 7days
(E) 8days
Rationale: B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/36 work is done by A in 1day
5/12 work is done by A in 36*5/12 = 15days
Answer is A
Answer: (A) 15days
Question: The numbers of students speaking English and Hindi are in the ratio of 4 : 5. If the number of students speaking English increased by 35% and that speaking Hindi increased by 20%, what would be the new respective ratio?
(A) 19 : 20
(B) 7 : 8
(C) 8 : 9
(D) Cannot be determined
(E) None of these
Rationale: Reqd ratio = 4×13/55×120=9:10
Answer E
Answer: (E) None of these
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
(A) 7 days
(B) 2 days
(C) 5 days
(D) 3 days
(E) 6 days
Rationale: B
2 days
Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days.
Answer: (B) 2 days
Question: An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 34%
(E) 25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*525 = 315
Percent of total membership that voted for winning candidate = (315/1260)*100 = 25%
Answer E
Answer: (E) 25%
Question: A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180 m
(B) 160 m
(C) 240 m
(D) 207 m
(E) 202 m
Rationale: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 32 = 15
x + 300 = 480
x =180m.
Answer: A
Answer: (A) 180 m
Question: In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
(A) 231
(B) 150
(C) 200
(D) 450
(E) 451
Rationale: (3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: C
Answer: (C) 200
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29.25
(B) 29.28
(C) 79.28
(D) 29.22
(E) 29.21
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
Answer: A
Answer: (A) 29.25
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 6
(B) 7
(C) 8
(D) 5
(E) 3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: (C) 8
Question: A train covers a certain distance at a speed of 340kmph in 4 hours. To cover the same distance in 2 3/4 hours, it must travel at a speed of
(A) 495km/hr
(B) 420km/hr
(C) 450km/hr
(D) 550km/hr
(E) 650km/hr
Rationale: Explanation:
Distance = 340Ã—4 = 1360km
Required speed = (1360Ã— 4/11) = 495km/hr
Answer: Option A
Answer: (A) 495km/hr
Question: 6 people meet for a business breakfast. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 30
(B) 21
(C) 18
(D) 15
(E) 10
Rationale: Let's look at the logic.
Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people
But in this 30 we have counted two times the total handshakes (c shakes hand with d and d shakes hand with c)
So just divide 30/2= 15 total handshakes
Answer is D
Answer: (D) 15
Question: Find the odd man out?
396, 462, 572, 427, 671, 264.
(A) 2378
(B) 427
(C) 297
(D) 2678
(E) 187
Rationale: Explanation:
In each number except 427, the middle digit is the sum of other two.
Answer: C) 427
Answer: (C) 297
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
(A) 347
(B) 3667
(C) 387
(D) 675
(E) 711
Rationale: Let xx be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−10025x=75+30(x−3)−100
25x=75+30x−90−10025x=75+30x−90−100
190−75=30x−25190−75=30x−25
115=5x115=5x
x=23x=23
So the company worked 23 days and they made 23⋅25+100=67523⋅25+100=675 pieces.
Answer:D
Answer: (D) 675
Question: The average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 65 kg
(C) 55 kg
(D) 97 kg
(E) 25 kg
Rationale: Total weight increased = (8 x 4) kg = 32 kg.
Weight of new person = (65 + 32) kg = 97 kg.
Answer: D
Answer: (D) 97 kg
Question: Which of the following statements is not correct?
A.	log10 (10) = 1
B.	log (2 + 3) = log (2 x 3)
C.	log10 (1) = 0
D.	log (1 + 2 + 3) = log 1 + log 2 + log 3
(A) log10 (10) = 1
(B) log (2 + 3) = log (2 x 3)
(C) log10 (1) = 0
(D) log (1 + 2 + 3) = log 1 + log 2 + log 3
(E) none of these
Rationale: (a) Since loga (a) = 1, so log10 (10) = 1.
(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
log (2 + 3) log (2 x 3)
(c) Since loga (1) = 0, so log10 (1) = 0.
(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.
So, (b) is incorrect.
Answer is B.
Answer: (B) log (2 + 3) = log (2 x 3)