mathewhe/aqua_rat huggingface dataset:
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 24000
(C) 34000
(D) 35000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions.
(A) 843.03 m
(B) 844.03 m
(C) 845.03 m
(D) 846.03 m
(E) 847.03 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.
= 600 * 2 * 22/7 * 22.4
= 84403 cm
= 844.03 m
Answer: B
Answer: (B) 844.03 m
Question: The probability of two events A and B are 0.15 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
(A) 0.45
(B) 0.4
(C) 0.5
(D) 0.05
(E) 0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.15+.40-.15
=.40
but the probability of neither A nor B=1-.40
=0.60
ANSWER:E
Answer: (E) 0.6
Question: The area of a square is 144 m². Find its perimeter.
(A) 18 m
(B) 28 m
(C) 38 m
(D) 42 m
(E) 48 m
Rationale: Area of square = side × side
Given; area of square = 144 m²
Therefore, side² = 144 m²
Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m
Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m
ANSWER : E
Answer: (E) 48 m
Question: In a room filled with 7 people, 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 5/21
(B) 3/7
(C) 4/21
(D) 5/7
(E) 16/21
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 6 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 2 people out of 7 is 7C2=21
first sibling pair----(A and B)--selecting 2 people --2C2=1
second sibling pair (C and D)--selecting 2 people--2C2=1
third sibling pair (E F G)--selecting 2 out of 6 --6C2=15
total= 1+1+15=17
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 2 people who are siblings
=17/21(21 is 7C2)
=1-17/21
=4/21
ANS C
Answer: (C) 4/21
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 158 m
(B) 150 m
(C) 110 m
(D) 130 m
(E) 157 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: (B) 150 m
Question: Two pipes can fill a tank in 12 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/12 + V/15 - V/10 = 3V/60 = V/20 per minute
The tank will be filled in 20 minutes.
The answer is A.
Answer: (A) 20
Question: If x% of y is the same as 4/5 of 80, then the value of xy is?
(A) 4250
(B) 6205
(C) 5260
(D) 4852
(E) 6400
Rationale: x/100 * y = 4/5 * 80
xy = 64*100 = 6400
Answer is E
Answer: (E) 6400
Question: A bag holds 5 red marbles and 5 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
(A) 1/6
(B) 2/5
(C) 3/10
(D) 2/9
(E) 1/2
Rationale: probability of selecting first red marble = 5/10
probability of selecting second red marble without replacement = 4/9
final probability = 5/10 * 4/9 = 2/9
The correct answer is D.
Answer: (D) 2/9
Question: If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?
(A) 100.2 miles
(B) 112.7 miles
(C) 120.5 miles
(D) 108.9 miles
(E) 105.6 miles
Rationale: We first convert the speed into miles per minute.
66 / 60 = 1.2 miles per minute
We now use the speed and the time to find the distance.
1.2 (miles/minute) * 99 minutes = 108.9 miles
correct answer D
Answer: (D) 108.9 miles
Question: How many pieces of 85 cm length can be cut from a rod of 17 meters long?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: Number of pieces = 1700/85 = 20
The answer is D.
Answer: (D) 20
Question: The midpoints of three of the edges of a cube are
labelled A, B, and C as shown in the diagram. What
is the measure of L ABC ?
(A) 90o
(B) 105o
(C) 120o
(D) 135o
(E) 150o
Rationale: Let D be the point on the base of the cube such that CD is perpendicular to
the base. Let s be the length of the sides of the cube. Then AB = BC = AD =
p
2s/2.
Using the Pythagorean Theorem in 4ADC, we get AC =
p
3s/
p2. By the Law of
Cosines AC2 = AB2 +BC2 −2AB · BC · cos(\ABC). We get cos(\ABC) = −1/2, so
L ABC = 120o.
correct answer C
Answer: (C) 120o
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 6?
(A) 2/3
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 6 = Integer, therefore we have 48 / 96 numbers divisible by 6
O E O / 6 = Not Integer
We cannot forget multiples of 6 from 1 to 96
We have 16 numbers that are multiple of 8
Therefore, 48/96 + 16/96 = 64/96 = 2/3
answer : A
Answer: (A) 2/3
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
(A) 720
(B) 740
(C) 770
(D) 780
(E) 790
Rationale: 720
Option 'A'
Answer: (A) 720
Question: A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:
(A) 50
(B) 90
(C) 80
(D) 28
(E) 93
Rationale: Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: Option C
Answer: (C) 80
Question: Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1235
(B) 1345
(C) 1678
(D) 1767
(E) 1659
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Large number = 274+1385 = 1659
E
Answer: (E) 1659
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that boys and girls sit alternately?
(A) 1/12!
(B) 12C6/12!
(C) 6!6!/12!
(D) 2∗6!6!/12!
(E) 6!7!/12!
Rationale: Total number of ways in which 6 boys and 6 girls can sit in a row = 12!/6!∗6!
Number of ways in which 6 boys and 6 girls can sit alternately = 2 (BGBG..... or GBGB.....)
Probability = 2∗6!∗6!/12!
Answer: D
Answer: (D) 2∗6!6!/12!
Question: A car is traveling 85 kilometers per hour. How many meters does the car travel in one minute?
(A) 1250m/min
(B) 1360m/min
(C) 2560m/min
(D) 1670m/min
(E) 1416.67m/min
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
85 kilometers per hour = 85 km/hr
= (85 × 1000 meters) / (60 minutes) = 1,416.67 meters / minute
correct answer is E)1416.67m/min
Answer: (E) 1416.67m/min
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 87 days
(B) 20 days
(C) 16 days
(D) 19 days
(E) 36 days
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Answer: (B) 20 days
Question: A certain country had a total annual expenditure of $7.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
(A)  $ 500
(B)  $1,000
(C)  $2,000
(D)  $3,000
(E)  $5,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (7,2 x 10^11) / 240 000 000 = (7,2 x 10^11) / (2,4 x 10^8) = 3 x 10^(11-8) =
3 x 10^3 = 3000.
Answer is D.
Answer: (D)  $3,000
Question: Two employees M and N are paid a total of $583 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
(A) $245
(B) $255
(C) $265
(D) $275
(E) $285
Rationale: 1.2N + N = 583
2.2N = 583
N = 265
The answer is C.
Answer: (C) $265
Question: Product of two co-prime numbers is 117. Their L.C.M should be:
(A) 1
(B) 117
(C) 116
(D) equal to their H.C.F
(E) Cannot be calculated
Rationale: H.C.F of co-prime numbers is 1.
So, L.C.M = 117/1 = 117.
ANSWER:B
Answer: (B) 117
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 1/2 brand A and 1/2 brand B. what fraction of the cost of the blend is Brand A?
(A) a. 1/3
(B) b. 2/5
(C) 3. 1/2
(D) 4. 2/3
(E) 5. 3/4
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.5 A and 0.55 B ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 150
Thus fraction of A in the blend = 0.5*200/150 = 2/3.
Answer : D
Answer: (D) 4. 2/3
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
=5
Answer:A
Answer: (A) 5
Question: Set A = {1, 2, 3, 4, 5, 6, d}
Which of the following possible values for d would cause Set A to have the smallest standard deviation?
(A)  1
(B)  2.5
(C)  3
(D)  3.5
(E)  7
Rationale: I agree. The mean of the set d=1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: (D)  3.5
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in?
(A) 18
(B) 12
(C) 11
(D) 19
(E) 114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/3
6/x = 1/3 => x = 18
So, B takes 9 hours to finish the work.
Answer: A
Answer: (A) 18
Question: Three friends Alice, Bond and Charlie divide $1105 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?
(A) $495
(B) $510
(C) $480
(D) $375
(E) $360
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 10 : y - 20 : z -15 is 11a : 18a : 24a
When $10, $20 and $15 are removed, we are removing a total of $45 from $1105.
Therefore, 11a + 18a + 24a = 1105 - 45 = 1060
i.e., 53a = 1060
or a = 20.
We know that z - 15 = 24a = 24 * 20 = 480
Therefore, z = 480 + 15 = $495
correct choice is (A)
Answer: (A) $495
Question: A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 28 years
(B) 22 years
(C) 23 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+30.
=> 2(x+2) = (x+30+2)
=> 2x+4 = x+32
=> x = 28 years
Option A
Answer: (A) 28 years
Question: The average weight of A, B and C is 42 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 33 kg
(B) 31 kg
(C) 32 kg
(D) 40 kg
(E) 37 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (42 x 3) = 126 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 40.
B's weight = 40 kg.
D
Answer: (D) 40 kg
Question: A and B can do a piece of work in 8 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 13 1/3
(B) 878
(C) 30
(D) 88
(E) 11
Rationale: C = 1/5 â€“ 1/8 = 3/40 => 40/3 = 13 1/3 days
Answer: A
Answer: (A) 13 1/3
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits Q of the larger integer?
(A) Q=2
(B) Q=5
(C) Q=8
(D) Q=10
(E) 11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: (A) Q=2
Question: Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $25 per month and Plan B costs $75 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?
(A) 25%
(B) 30%
(C) 37.5%
(D) 56.25%
(E) 50%
Rationale: If there are A customers with plan A, and B customers with plan B, then the total revenue is $25A + $75B.
Since the average customer pays $100, we know that
$100 = ($25A + $75B) / (A + B)
$100(A + B) = ($25A + $75B)
$100A + $100B = $25A + $75B
$75A = -$25B
A = 3B.
Since there are 3 times as many $75 clients as $75 clients, for every $75 received from Plan B customers, 3($25) = $75 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$75/($75 + $75) = $75/$150 = 50%.
The correct answer is choice (E).
Answer: (E) 50%
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction Q of the cookies that were placed in the other tins were placed in the green tin?
(A) 15/2
(B) 9/4
(C) 5/9
(D) 7/5
(E) 9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction Q= 5N/12 * 12/9N = 5/9 (C)
Answer: (C) 5/9
Question: If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 5, which of the following could NOT be a possible value of M+N?
(A) 84
(B) 52
(C) 34
(D) 29
(E) 14
Rationale: M=5p+1
N=5q+3
We need M+N=5p+1+5q+3=5(p+q)+4
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 5 so
p+q=0 ; M+n = 4
p+q=1 ; M+N = 9
P+q=2 ; M+N = 14
and so on, so basically you get something like - 4,9,14,19,24,29,34,..... all the other options were turning up.
Then I directly tried p+q=10 because it was closer to 52 for the first option, i got 54, .
So Answer B.
Answer: (B) 52
Question: A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6 min
(B) 8 min
(C) 7 min
(D) 9 min
(E) 1 min
Rationale: The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes
The answer is D.
Answer: (D) 9 min
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 90
(B) 100
(C) 120
(D) 130
(E) 140
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: If n and y are positive integers and 450y = n^3, which of the following must be an integer?
(A) y/(3*2^2*5)
(B) y/(3^2*2*5)
(C) y/(3*2*5^2)
(D) y/(5^3*2^2)
(E) y/(5*3*2)
Rationale: Solution:
As y and n are both integers so y is of the form of 3*5*2*2*K
where K= an integer.
to make n as an integer and 450y to be a cube of a number.
Now checking with the answers we get only 1 as K.
So the answer is (1).
Answer: (A) y/(3*2^2*5)
Question: If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?
(A) 3
(B) 4
(C) 5
(D) 9
(E) 12
Rationale: If x=5 and y=3, then x^2-y^2=16 and 16 is divisible only by 4 from the options, thus it must be correct.
Answer: B.
Answer: (B) 4
Question: How many positive integers between 1 and 300 are there such that they are multiples of 9?
(A) 31
(B) 33
(C) 35
(D) 36
(E) 23
Rationale: Multiples of 9 = 9,18,27,-----297
Number of multiples of 15 => 9*33=297
Answer is B
Answer: (B) 33
Question: A can work three times as fast as B. Together they can finish a job in 18 days. In how many days can A complete the job alone?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: B's rate is x and A's rate is 3x.
x + 3x = 1/18
x = 1/72
A's rate is 3x = 1/24
A can complete the job in 24 days.
The answer is B.
Answer: (B) 24
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 850 grams. Find the profit percent.
(A) 300/17%
(B) 100/23%
(C) 100/19%
(D) 100/13%
(E) None of these
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 850
100 + g / 100 + 0 = 1000 / 850
100+g = 20/17*100
g = 300/17 %
ANSWER: A
Answer: (A) 300/17%
Question: Three workers have a productivity ratio of 2 to 3 to 4. 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) 6 to 1
(C) 5 to 1
(D) 1 to 6
(E) 10 to 3
Rationale: The fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 40 to 12, or 10 to 3.
Answer: E
Answer: (E) 10 to 3
Question: John makes $60 a week from his job. He earns a raise andnow makes $80 a week. What is the % increase?
(A) 15%
(B) 33.33%
(C) 17.8%
(D) 19%
(E) 21%
Rationale: Increase = (20/60)*100 = (1/3)*100 = 33.33%.
B
Answer: (B) 33.33%
Question: pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
(A) 2
(B) 9
(C) 8
(D) 7
(E) 1
Rationale: x/18 + 12/24 = 1
x = 9.Answer: B
Answer: (B) 9
Question: What is log3(4) log4(5)...log80(81)?
(A) 1
(B) 4
(C) 81
(D) log80 243
(E) e81
Rationale: Recall the change of base formula
logb(a) =
ln(a)
ln(b)
:
(Alternatively, we can substitute logc for ln on the right, as long as the base is the same on
the top and on the bottom.) Using this, we can rewrite the entire expression using natural
logarithms, as
ln(4)
ln(3)
ln(5)
ln(4)
ln(81)
ln(80)
=
ln(81)
ln(3)
= log3(81) = log3(34) = 4:
correct answer B
Answer: (B) 4
Question: How many integers between 6000 and 7000 that have distinct digits and increase from left to right ?
(A) 10
(B) 20
(C) 60
(D) 80
(E) 600
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
645_ --> 4
646_ --> 3
647_ --> 2
648_ --> 1
656_ --> 3
657_ --> 2
658_ --> 1
667_ --> 2
668_ --> 1
678_ --> 1
Number of integers =20
B
Answer: (B) 20
Question: Calculate the different number of ways 3 girls and 2 boys can sit on a bench?
(A) 180
(B) 150
(C) 120
(D) 122
(E) 130
Rationale: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
C
Answer: (C) 120
Question: A seven-digit phone number is divisible by 3. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?
(A) 07
(B) 06
(C) 05
(D) 04
(E) 02
Rationale: Given that 7 digit number is divisible by 3
we know any number will not be divisible by 3 if the sum of all digits of the number is not the multiple of 3.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 3... hence answer is B
Answer: (B) 06
Question: A reduction of 40% in the price of bananas would enable a man to obtain 67 more for Rs.40, what is reduced price per dozen?
(A) 1.86
(B) 2.86
(C) 4.86
(D) 3.86
(E) 5.86
Rationale: 40*(40/100) = 16 --- 67
? --- 12 => Rs.2.86
Answer: B
Answer: (B) 2.86
Question: If M is the mean of x,y,z ; then what is the mean of z,y and x
(A) 2M
(B) 3M
(C) 10M
(D) M
(E) M-10
Rationale: order only changed
So new mean is M .
Answer (D)
Answer: (D) M
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 15 years?
(A) 30
(B) 35
(C) 40
(D) 50
(E) 60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 15 years = (20 + 15) years =35 years.
Answer : B
Answer: (B) 35
Question: A guy was asked to specify his age in years. He said, “Take my age 5 years hence, multiply it by five and subtract five times of my age 5 years ago and you will know my age.” What was the age of that guy?
(A) 18
(B) 15
(C) 33
(D) 39
(E) 50
Rationale: Current age of the guy = A years.
Then, 5 (A + 5) – 5 (A – 5) = A
(5A + 25) – (5A – 25) = A
A = 50
E
Answer: (E) 50
Question: If 3/a + 4/a + 5/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) 15/a
Rationale: 3/a + 4/a + 5/a
=12/a
Answer A
Answer: (A) 12/a
Question: The largest natural number by which the product of three consecutive even natural numbers is always divisible, is
(A) 16
(B) 24
(C) 48
(D) 96
(E) 78
Rationale: Solution
Required number	= (2×4×6)
= 48.
Answer C
Answer: (C) 48