mathewhe/aqua_rat huggingface dataset:
Question: Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m.
(A) 25.8
(B) 26.8
(C) 27.8
(D) 20.5
(E) 21.8
Rationale: avg speed=2*x*y/(x+y)
=2*18*24/(18+24)=20.5
ANSWER:D
Answer: (D) 20.5
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: Option C
Answer: (C) 500
Question: If the sides of a triangle are given as 5*x, 5*(x+1), 5*(x+2), then what could be the possible value of the product of their sides.
(A) 1000
(B) 2000
(C) 3000
(D) 4000
(E) 5000
Rationale: Since the sides are consecutive multiples of 5, the product will be a multiple of 125*2*3(=750).
750*4=3000
Answer:C
Answer: (C) 3000
Question: Convert 350 inches into centimeter?
(A) 812cm
(B) 820cm
(C) 850cm
(D) 889cm
(E) 854cm
Rationale: 1 inch = 2.54cm
350 inches = 100*2.54 = 889cm
Answer is D
Answer: (D) 889cm
Question: A certain box has 13 cards and each card has one of the integers from 1 to 13 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 13 cards?
(A) 1/7
(B) 1/13
(C) 1/15
(D) 1/22
(E) 1/26
Rationale: The average of the numbers is 7
The total number of ways to choose 2 cards from 13 cards is 13C2 = 78.
The ways to choose 2 cards with a sum less than the average are:
{1,2},{1,3},{1,4},{1,5},{2,3},{2,4}
The probability is 6/78 = 1/13
The answer is B.
Answer: (B) 1/13
Question: If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10?
(A) 10.5
(B) 11.5
(C) 12.5
(D) 13.5
(E) 14.5
Rationale: If a clock takes 7seconds to strike 7 , there are 6 time intervals of duration 7/6 secs.
At 10, there are 9 time intervals of 7/6 secs having total duration of 9*7/6= 10.5 secs for 10 strikes
ANSWER:A
Answer: (A) 10.5
Question: If one cat eats 1.5 rats in 1.5 days, then in howmany days 3 cats will eat 3 rats??
(A) 1 Day
(B) 2 Days
(C) 3 Days
(D) 4 Days
(E) 5 Days
Rationale: 1Cat ------ 3/2 Rat --------- 3/2 Days
1 Cat ------(3/2)*2 Rat -----(3/2)*2 Days (Rat doubled, days doubled)
1*3 Cat----- 3 Rat -----------3/3=1 Day (Cat*3 , Same rat , Days/3 )
ANSWER:A
Answer: (A) 1 Day
Question: A set of data consists of the following 4 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 0 and 8 , results in a value that would change the SD to the least. Hence E
Answer: (E) 0 and 8
Question: A contractor undertakes to built a walls in 50 days. He employs 20 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(A) 25
(B) 30
(C) 35
(D) 30
(E) None of these
Rationale: 20 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
20 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 20×25×0.6/25×0.4 = 30 men
AnswerD
Answer: (D) 30
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 602 sq.cm
(B) 620 sq.cm
(C) 200 sq.cm
(D) 605 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer: E
Answer: (E) 600 sq.cm
Question: Peter wants to get $200,000 for his house. An agent charges 20% of the selling price for selling the house for Peter.What will be the agent's commission?
(A) $25,000
(B) $35,000
(C) $60,000
(D) $80,000
(E) $50,000
Rationale: Let x be the selling price: x - 20%x = 200,000
a) Solve for x to find x = $250,000 which is the seeling price of the house,then
20% *250,000 = $50,000 the agent's commission
correct answer E)$50,000
Answer: (E) $50,000
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/38
(C) 23/18
(D) 53/18
(E) 23/22
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14)
= 36/70 + 1/7
= 46/70 = 23/35
Answer:A
Answer: (A) 23/35
Question: A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 165
(E) 225
Rationale: 1 of 5 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more than one departments.
We can choose any of the 5 candidates for the math dep., which gives as 5 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 5*45 = 225
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans E
Answer: (E) 225
Question: If p and q are positive integers and q ≠ 1, then pq(q −2) is
(A) pq^2
(B) pq^2+2pq
(C) pq^2-2pq
(D) pq^2+pq
(E) pq^2-6pq
Rationale: pq(q-2) = pq^2-2pq
Answer : C
Answer: (C) pq^2-2pq
Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, three orange ice pops, and five lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 7/11
(B) 9/22
(C) 19/33
(D) 29/44
(E) 39/55
Rationale: P(2 cherry) = 3/11 * 2/10 = 6/110
P(2 orange) = 3/11 * 2/10 = 6/110
P(2 lemon) = 5/11 * 4/10 = 20/110
P(2 of the same flavor) = 32/110
P(2 different flavors) = 1 - 32/110 = 78/110 = 39/55
The answer is E.
Answer: (E) 39/55
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the W odds that x^2+y^2>1?
(A) 1. pi/4
(B) 2. W=pi/16
(C) 3. W=1-pi/4
(D) 4. W=1-pi/16
(E) 5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: (C) 3. W=1-pi/4
Question: It takes 60 identical printing machines 2 hours to print 200,000 cards. How long would it take 50 of these machines to print the same total?
(A) 2 hr 36 min
(B) 2 hr 40 min
(C) 2 hr 30 min
(D) 2 hr 25 min
(E) 2 hr
Rationale: 50% of 60 = 30% or 0.30
2 hr x 60 min = 120 min
120 min x 0.30 = 36 min
36 min + 2 hr = 2 hr and 36 min
Answer is A
Answer: (A) 2 hr 36 min
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 288
(B) 266
(C) 299
(D) 400
(E) 827
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer:D
Answer: (D) 400
Question: A participated in cycling contest and he drove the lap at the rate of 6kmph, 12kmph, 18kmph, 24kmph..What is his average speed?
(A) 15kmph
(B) 18kmph
(C) 14.25 kmph
(D) 11.52 kmph
(E) 16kmph
Rationale: =4x/(x/6 +x/12 + x/18 +x/24)
=11.52
ANSWER:D
Answer: (D) 11.52 kmph
Question: There are some sweets in party, 1/3rd eaten by kids . Then 2/5th of the remaining by men , then 2/3rd of the remaining by women . At last 2 were remaining . How many sweets were in total ?
(A) 45
(B) 27
(C) 15
(D) 26
(E) 91
Rationale: Sol:
If x sweets were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 2
x×2/3 × 3/5 × 1/3 = 2
x = 15
Answer:C
Answer: (C) 15
Question: 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find the amount paid by him.
(A) 110
(B) 111
(C) 115
(D) 123
(E) None
Rationale: Explanation:
Average amount paid by 10 persons = Rs. 60
Increase in average due to Rs. 50 paid extra by the 11th men = Rs. 50/10= Rs. 5
Therefore, Average expenditure of 11 friends = Rs. 60 + Rs. 5 = Rs. 65
Therefore, Amount paid by the 11th men = Rs. 65 + Rs. 50 = Rs. 115
Correct Option: C
Answer: (C) 115
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 17. What is the last numbers?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A + B + C = 18
B + C + D = 15
A + D = 17
A – D = 3
A + D = 17
2D = 14
D = 7
ANSWER:D
Answer: (D) 7
Question: complete the numerical series with the correct number
6+3+2=181227
7+2+4=142840
8+6+3=482466
9+4+5=364567
6+5+5= ?
(A) 468645
(B) 303055
(C) 454585
(D) 454386
(E) 444586
Rationale: 6+5+5=303055
Answer : B
Answer: (B) 303055
Question: a television have side 6*5.its screen size is 5*4.calculate the percentage of unscreened part t.v.
(A) 30
(B) 25
(C) 33.33
(D) 44.44
(E) 28
Rationale: unscreened part=30-20=10.
%unscreened part=10/30*100=33.33%
answer C
Answer: (C) 33.33
Question: 28 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
(A) 10
(B) 6
(C) 4
(D) 7
(E) 5
Rationale: Required number of machines = 28*10/40 = 7
Answer is D
Answer: (D) 7
Question: Solve the equation :
(2x - 1)3 + 2x(2x - 3).(3 - 2x) – (3x - 1)2 = 3x2 - 2
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Solution:
We open the brackets by using the formulas for multiplication:
8x3 - 3(2x)2.1 + 3.2x(1)2 – 13 - 2x(2x - 3)2 – (9x2 - 6x + 1) = 3x2 - 2 <=>
8x3 - 12x2 + 6x - 1 - 2x(4x2 - 12x + 9) - 9x2 + 6x - 1 = 3x2 - 2 <=>
8x3 - 21x2 + 12x - 8x3 + 24x2 - 9x = 3x2 <=>
3x2 + 3x = 3x2 <=>
3x = 0 <=> x = 0
Answer A
Answer: (A) 0
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 6
(B) 5
(C) 7
(D) 4
(E) 3
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Answer: (D) 4
Question: In a 2000 m race, A beats B by 100 meters or 20 seconds. Find the speed of B?
(A) 10m/s
(B) 2m/s
(C) 5m/s
(D) 7m/s
(E) 3m/s
Rationale: Since A beats B by 100 m or 20 seconds,
it implies that B covers 100 m in 20 seconds.
Hence speed of B = 100/20 = 5 m/s.
Answer: C
Answer: (C) 5m/s
Question: A is twice as good as B. And together they finish a piece of work in 20days. In how many days will A alone finish the work
(A) 30
(B) 25
(C) 12
(D) 10
(E) 32
Rationale: (A's 1day work):(B's 1day work) = 2:1
A+B 1day work = 1/20
A's 1day work = (1/20)*(2/3) = 1/30
A alone can finish the work in 30 days
Answer is A
Answer: (A) 30
Question: Will decides to attend a basketball game with four friends.
If the party of five sits together in five consecutive seats, and Will must NOT sit in between two of his friends, how many ways
can the five friends be arranged?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 120
Rationale: Will have to sit at either of the ends.
If will sits on the left most corner, then other 4 friends can be arranged in 4! = 24
Will can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
ANS:Option( C)
Answer: (C) 48
Question: In how many ways can the letters of the word SUBMITTED be arranged?
(A) 181215
(B) 181000
(C) 181450
(D) 181220
(E) 181440
Rationale: SUBMITTED has 9 words, but T is repeated two times. Thus ways = 9! / 2! = 181440 ways
E
Answer: (E) 181440
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits are in s(99)?
(A) 350
(B) 353
(C) 354
(D) 356
(E) 357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353;
ANSWER:B
Answer: (B) 353
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 15th, 17th, and 18th terms in the sequence?
(A) 2^18
(B) 3(2^17)
(C) 7(2^16)
(D) 13(2^14)
(E) 7(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 15th term will be 2^14
17th term 2^16
18th term 2^17
adding all three
we get
2^14+(2^15)*4+(2^15)*8
so answer is 2^15(1+4+8)=>13(2^15)
answer D
Answer: (D) 13(2^14)
Question: The speed of a boat in still water in 42 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 44 minutes is:
(A) 86.6 km
(B) 46.6 km
(C) 33 km
(D) 35.6 km
(E) 26.6 km
Rationale: Speed downstream = (42 + 3) = 45 kmph
Time = 44 minutes =44/60 hour = 11/15 hour
Distance travelled = Time × speed =11/15×45 = 33 km
ANSWER:C
Answer: (C) 33 km
Question: If (-3)^(2x) = 3^(12 - x) and x is an integer, what is the value of x ?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Since x is an integer, (-3)^(2x) is always positive.
So, 3^2x = 3^(12 - x)
2x = 12 - x
3x = 12
x = 4
Answer: B
Answer: (B) 4
Question: In an election between two candidates first candidate got 70% of votes polled and second Candidate got 270 votes. The total number of votes polled was?
(A) 700 votes
(B) 750 votes
(C) 800 votes
(D) 900 votes
(E) 1000 votes
Rationale: Explanation:
Total = 100 %,
First person got 70%
second person got remaining 30 % of votes.
than 30 % = 270
30% = 30*9 = 270
100% =100*9 =900votes
Answer: Option D
Answer: (D) 900 votes
Question: In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?
(A) Rs. 48000
(B) Rs. 48200
(C) Rs. 48400
(D) Rs. 48600
(E) None
Rationale: Solution: Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 * 4/(6+4+3) = 157300*4/13
= 12100*4 = Rs. 48400.
Answer: Option C
Answer: (C) Rs. 48400
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
(A) 54
(B) 432
(C) 2,160
(D) 3024
(E) 148,824
Rationale: We have the rectangle with dimensions 9*7 (9 horizontal dots and 7 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*7C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).
9C1*7C1*8C1*6C1=3024
Answer: D.
Answer: (D) 3024
Question: How many pairs (n, n+1) have one or more prime factors common, where n is an integer and 2 ≤ n ≤9 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: n and n+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: (A) 0
Question: If (x+3)^2/(3x+5)=2, then the difference between the two possible values of x is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: (x+3)^2/(3x+5)=2
(x+3)^2=2(3x+5)
x^2+6x+9=6x+10
x^2-1=0
(x-1)(x+1)=0
x=1 or x=-1
The answer is A.
Answer: (A) 2
Question: If cost of 18 eggs be 75 rupees, then find out the cost of 5 dozen eggs.
(A) 300
(B) 400
(C) 500
(D) 252
(E) 700
Rationale: Cost of 18 eggs = 75 rupees
Cost of 1 egg = 75/18 = 4.2 rupees,
Cost of 5 dozens, i.e. 4.2 x 12 = 50.4 x 5 = 252
Answer : D
Answer: (D) 252
Question: The sum of two numbers is 64, and one of them is 12 more than the other. What are the two numbers?
(A) 26-38
(B) 50-34
(C) 60-24
(D) 42-42
(E) 21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 64:
word problem = 64
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 64 âˆ’ 12
= 52.
x = 52/2
= 26.
This is the first number. Therefore the other number is
x + 12 = 26 + 12 = 38.
The sum of 26 + 38 is 64.
A
Answer: (A) 26-38
Question: The average of 6 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?
(A)  9.5
(B)  8.0
(C)  7.2
(D)  5.0
(E)  4.0
Rationale: The average of 6 numbers is 6.8
The sum of 6 numbers will be 6.8 x 6 = 40.8
The average of 6 number after one of the number is multiplied by 3 is 9.2
The sum of the numbers will now be 9.2 x 6 = 55.2
So the sum has increased by 55.2-40.8 = 14.4
Let the number multiplied by 3 be n
Then,
3n = n+14.4
or 2n = 14.4
or n = 7.2
Answer:- C
Answer: (C)  7.2
Question: In a rectangular coordinate system, if a line passes through the points (-13,-18), (17,22) and (x,2) then what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The slope of the line m is rise/run = 22-(-18) / 17-(-13) = 4/3
4/3 = 22-2 / 17-x
68-4x = 66-6
x = 2
The answer is B.
Answer: (B) 2
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
(A) 3:1
(B) 3:2
(C) 3:5
(D) 3:7
(E) 3:4
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=27/1
=>(a/b)3=(3/1)3
a/b=3/1
=>a:b=3:1
ANSWER IS A
Answer: (A) 3:1
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200
(B) 25100
(C) 25000
(D) 26000
(E) 26100
Rationale: Explanation:
Number of ways of selecting 3 consonants from 7
= 7C3
Number of ways of selecting 2 vowels from 4
= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
= 7C3 × 4C2
=
(
7
×
6
×
5
3
×
2
×
1
)
×
(
4
×
3
2
×
1
)
=
210
=(7×6×53×2×1)×(4×32×1)=210
It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves
=
5
!
=
5
×
4
×
3
×
2
×
1
=
120
=5!=5×4×3×2×1=120
Hence, required number of ways
=
210
×
120
=
25200
Answer is A
Answer: (A) 25200
Question: If ab + c = a(b + c), which of the following must be true?
(A)  x = 0 and z = 0
(B)  x = 1 and y = 1
(C)  y = 1 and z = 0
(D)  x = 1 or y = 0
(E)  a = 1 or c = 0
Rationale: ab + c = ab + ac
c = ac
case 1: c not= 0, a = c/c = 1
case 2: c = 0, 0 = a0 = 0
Combining 2 cases: a = 1 or c =0
E. is the answer.
Answer: (E)  a = 1 or c = 0
Question: A jeep takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 52 Kmph
(C) 6o Kmph
(D) 63 Kmph
(E) 65 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
C)
Answer: (C) 6o Kmph
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
(A) 27
(B) 30
(C) 20
(D) 99
(E) 2
Rationale: M = 15
S = 15
DS = 15 + 15 = 30
Answer:B
Answer: (B) 30
Question: X can do a piece of work in 40days. He works at it for 8 days and then Y finished it in 24 days. How long will Y take to complete the work?
(A) 30
(B) 12
(C) 15
(D) 18
(E) 20
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 24 days
Whole work will be done by Y in 24*5/4 = 30days
Answer is A
Answer: (A) 30
Question: On the number line, if x is halfway between -4 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?
(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1
Rationale: x= 0 and y = 2.
The answer is E.
Answer: (E) 1
Question: Mary's income is 60 percent more than Tim's income, and Tim's income is 50 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A)  124%
(B)  120%
(C)  96%
(D)  80%
(E)  64%
Rationale: Juan's income = 100 (assume);
Tim's income = 50 (50 percent less than Juan's income);
Mary's income = 80 (60 percent more than Tim's income).
Thus, Mary's income (80) is 80% of Juan's income (100).
Answer: D.
Answer: (D)  80%
Question: A software programmer does 20% of the work in 80% of the time, and 80% of the work in the remaining 30% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
(A) 13x /15
(B) 15x/15
(C) 7x/15
(D) 2x/30
(E) 13x/30
Rationale: Take X=30 lines
80% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 80% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => E is the answer.
Answer: (E) 13x/30
Question: How many cubes of 50 cm edge can be put in a cubical box of 1 m edge.
(A) 17 cm
(B) 10 cm
(C) 8 cm
(D) 6 cm
(E) 7 cm
Rationale: Number of cubes =100âˆ—100âˆ—100/50*50*50=8
Number of cubes =100âˆ—100âˆ—10010âˆ—10âˆ—10=1000
Note: 1 m = 100 cm
Answer:C
Answer: (C) 8 cm
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams. Find the profit percent.
(A) 20
(B) 15
(C) 25
(D) 18
(E) 19
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 800
100 + g / 100 + 0 = 1000 / 800
100+g = 5/4*100
g = 25
ANSWER: C
Answer: (C) 25