MU-NLPC/Calc-aqua_rat huggingface dataset:
Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m.  Choose the correct choice from the following choices:
A) 25.8	B) 26.8	C) 27.8	D) 20.5	E) 21.8

Solution: avg speed=2*x*y/(x+y)   =2*18*24/(18+24)=20.5   ANSWER:20.5
Answer: D
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? Options.
A) 300
B) 400
C) 500
D) 600
E) 700

Solution: 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 500
Answer: C
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. Choose the most appropriate option.
A) 1000
B) 2000
C) 3000
D) 4000
E) 5000

Solution: Since the sides are consecutive multiples of 5, the product will be a multiple of 125*2*3(=750).   750*4= 
750*4 = 3_000
3000   Answer:3000
Answer: C
Convert 350 inches into centimeter?	Choose the correct answer.
A) 812cm B) 820cm C) 850cm D) 889cm E) 854cm

Solution: 1 inch = 2.54cm   350 inches = 100*2.54 = 889cm   Answer is 889cm
Answer: D
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?  Pick:
A) 1/7  B) 1/13  C) 1/15  D) 1/22  E) 1/26

Solution: 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 1/13.
Answer: B
If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10? Choose the correct choice from the following choices:
A) 10.5	B) 11.5	C) 12.5	D) 13.5	E) 14.5

Solution: If a clock takes 7seconds to strike 7 , there are 6 time intervals of duration 7/6 secs.   10.5t 10, there are 9 time intervals of 7/6 secs having total duration of  9*7/6= 
 9*7/6 = 21/2 = around 10.5
10.5 secs for 10 strikes   10.5NSWER:10.5
Answer: A
If one cat eats 1.5 rats in 1.5 days, then in howmany days 3 cats will eat 3 rats??	Choose the correct choice:
A) 1 Day B) 2 Days C) 3 Days D) 4 Days E) 5 Days

Solution: 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 )   1 DayNSWER:1 Day
Answer: A
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? Choose the most appropriate option:
A) -1 and 9  B) 4 and 4  C) 3 and 5  D) 2 and 6  E) 0 and 8

Solution: 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)= 
(4 - 2.8) = 1.2
1.2 , and one value above SD is (4 + 2.8)= 
(4 + 2.8) = 6.8
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 0 and 8
Answer: E
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?  Select:
A) 25	B) 30	C) 35	D) 30	E) None of these

Solution: 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   Answer30
Answer: D
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?	Select:
A) 602 sq.cm
B) 620 sq.cm
C) 200 sq.cm
D) 605 sq.cm
E) 600 sq.cm

Solution: 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)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer: 600 sq.cm
Answer: E
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?	Select
A) $25,000
B) $35,000
C) $60,000
D) $80,000
E) $50,000

Solution: 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 $50,000)$50,000
Answer: E
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?
Pick.
A) 23/35	B) 23/38	C) 23/18	D) 53/18	E) 23/22

Solution: 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   23/35nswer:23/35
Answer: A
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? Choices:	A) 42	B) 70	C) 140	D) 165	E) 225

Solution: 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= 
90 / 2 = 45
45.   We are multiplying our individual selections:  5*45= 
 5*45 = 225
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 225
Answer: E
If p and q are positive integers and q ≠ 1, then pq(q −2) is  Choose the correct option
A) pq^2 B) pq^2+2pq C) pq^2-2pq D) pq^2+pq E) pq^2-6pq

Solution: pq(q-2) = pq^2-2pq   Answer : pq^2-2pq
Answer: C
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? Choose one
A) 7/11 B) 9/22 C) 19/33 D) 29/44 E) 39/55

Solution: 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 39/55.
Answer: E
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?	Options.
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

Solution: 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   3. W=1-pi/4
Answer: C
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?
Pick one.
A) 2 hr 36 min
B) 2 hr 40 min
C) 2 hr 30 min
D) 2 hr 25 min
E) 2 hr

Solution: 50% of 60 = 30% or 0.30   2 hr x 60 min = 120 min   120 min x 0.30 = 36 min   36 min   + 2= 
  + 2 = 2
2 hr and 36 min   2 hr 36 minnswer is 2 hr 36 min
Answer: A
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?	Answers:
A) 288
B) 266
C) 299
D) 400
E) 827

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer:400
Answer: D
A participated in cycling contest and he drove the lap at the rate of 6kmph, 12kmph, 18kmph, 24kmph..What is his average speed? Choose the correct answer
A) 15kmph  B) 18kmph  C) 14.25 kmph  D) 11.52 kmph  E) 16kmph

Solution: =4x/(x/6 +x/12 + x/18 +x/24)   =11.52   ANSWER:11.52 kmph
Answer: D
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 ? Select
A) 45
B) 27
C) 15
D) 26
E) 91

Solution: 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:15
Answer: C
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.	Choose one: A) 110 B) 111 C) 115 D) 123 E) None

Solution: 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   115orrect Option: 115
Answer: C
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?	Select the correct option:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: A + B + C = 18   B + C + 7 = 15   A + 7 = 17   A – 7 = 3   A + 7 = 17   27 = 14   7 = 7   ANSWER:7
Answer: D
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= ? Choose the correct choice from the following choices.
A) 468645 B) 303055 C) 454585 D) 454386 E) 444586

Solution: 6+5+5=303055   Answer : 303055
Answer: B
a television have side 6*5.its screen size is 5*4.calculate the percentage of unscreened part t.v. Choose the correct option:
A) 30 B) 25 C) 33.33 D) 44.44 E) 28

Solution: unscreened part=30-20= 
30-20 = 10
10.   %unscreened part=10/30*100=33.33%   answer 33.33
Answer: C
28 machines can do a work in 10days. How many machines are needed to complete the work in 40days?  Choose the correct choice from the following answers.
A) 10 B) 6 C) 4 D) 7 E) 5

Solution: Required number of machines = 28*10/40= 
28*10/40 = 7
7   Answer is 7
Answer: D
Solve the equation :
(2x - 1)3 + 2x(2x - 3).(3 - 2x) – (3x - 1)2 = 3x2 - 2 Choose one:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: 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   0nswer 0
Answer: A
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?
Select
A) 6 B) 5 C) 7 D) 4 E) 3

Solution: 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: 4
Answer: D
In a 2000 m race, A beats B by 100 meters or 20 seconds. Find the speed of B?  Choose one.
A) 10m/s  B) 2m/s  C) 5m/s  D) 7m/s  E) 3m/s

Solution: 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= 
100/20 = 5
5 m/s.   Answer: 5m/s
Answer: C
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  Pick:
A) 30  B) 25  C) 12  D) 10  E) 32

Solution: (30's 1day work):(B's 1day work) = 2:1   30+B 1day work = 1/20   30's 1day work = (1/20)*(2/3) = 1/30   30 alone can finish the work in 30 days   30nswer is 30
Answer: A
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? Choose the correct option: A) 24 B) 36 C) 48 D) 72 E) 120

Solution: 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= 
24+24 = 48
48   ANS:Option( 48)
Answer: C
In how many ways can the letters of the word SUBMITTED be arranged?
Choose the correct choice from the following answers.
A) 181215 B) 181000 C) 181450 D) 181220 E) 181440

Solution: SUBMITTED has 9 words, but T is repeated two times. Thus ways = 9! / 2! = 181440 ways   181440
Answer: E
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)?  Pick:
A) 350  B) 353  C) 354  D) 356  E) 357

Solution: 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= 
3 + 12 + 66 + 272 = 353
353;   ANSWER:353
Answer: B
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?
Choose the correct choice from the following options: A) 2^18 B) 3(2^17) C) 7(2^16) D) 13(2^14) E) 7(2^15)

Solution: 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 13(2^14)
Answer: D
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:
Options:	A) 86.6 km	B) 46.6 km	C) 33 km	D) 35.6 km	E) 26.6 km

Solution: Speed downstream = (42 + 3)= 
(42 + 3) = 45
45 kmph   Time= 44 minutes =44/60 hour = 11/15 hour   Distance travelled = Time × speed =11/15×45 = 33 km   ANSWER:33 km
Answer: C
If (-3)^(2x) = 3^(12 - x) and x is an integer, what is the value of x ? Select the correct option
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: Since x is an integer, (-3)^(2x) is always positive.   So, 3^2x = 3^(12 - x)   2x = 12 - x   3x = 12   x = 4   Answer: 4
Answer: B
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?
Choose the correct choice from the following answers:
A) 700 votes
B) 750 votes
C) 800 votes
D) 900 votes
E) 1000 votes

Solution: Explanation:   Total = 100 %,   First person got 70%   second person got remaining 30 % of votes.   than 30 % = 270   30% = 30*9= 
30*9 = 270
270   100%=100*9= 
100*9 = 900
900votes   Answer: Option 900 votes
Answer: D
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?  Pick one:
A) Rs. 48000 B) Rs. 48200 C) Rs. 48400 D) Rs. 48600 E) None

Solution: 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 Rs. 48400
Answer: C
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?
Choose the correct option:
A) 54
B) 432
C) 2,160
D) 3024
E) 148,824

Solution: 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: 3024.
Answer: D
How many pairs (n, n+1) have one or more prime factors common, where n is an integer and 2 ≤ n ≤9 ? Choose the correct choice:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: 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.   0nswer: 0.
Answer: A
If (x+3)^2/(3x+5)=2, then the difference between the two possible values of x is: Choose the correct choice from the following answers
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: (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 2.
Answer: A
If cost of 18 eggs be 75 rupees, then find out the cost of 5 dozen eggs. Options:
A) 300	B) 400	C) 500	D) 252	E) 700

Solution: 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 : 252
Answer: D
The sum of two numbers is 64, and one of them is 12 more than the other. What are the two numbers? Select the correct option:
A) 26-38
B) 50-34
C) 60-24
D) 42-42
E) 21-63

Solution: 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= 
52/2 = 26
26.   This is the first number. Therefore the other number is   x + 12= 26 + 12= 
26 + 12 = 38
38.   The sum of 26 + 38 is 64.   26-38
Answer: A
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?	Choose the correct choice
A) 9.5 B) 8.0 C) 7.2 D) 5.0 E) 4.0

Solution: 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= 
 55.2-40.8 = 14.4
14.4   Let the number multiplied by 3 be n   Then,   3n= n+14.4   or 2n = 14.4   or n = 7.2   Answer:- 7.2
Answer: C
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? Choose the correct answer:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 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 2.
Answer: B
If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:  Choose the correct option
A) 3:1	B) 3:2	C) 3:5	D) 3:7	E) 3:4

Solution: 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   3:1NSWER IS 3:1
Answer: A
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Choose the correct answer.
A) 25200	B) 25100	C) 25000	D) 26000	E) 26100

Solution: 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   25200nswer is 25200
Answer: A
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?
Select the correct option: A) 48 Kmph B) 52 Kmph C) 6o Kmph D) 63 Kmph E) 65 Kmph

Solution: Time = 6   Distance = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   6o Kmph)
Answer: C
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? Select: A) 27 B) 30 C) 20 D) 99 E) 2

Solution: M = 15   S = 15   DS = 15 + 15= 
15 + 15 = 30
30   Answer:30
Answer: B
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?
Choose the correct choice from the following:  A) 30  B) 12  C) 15  D) 18  E) 20

Solution: 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= 
 24*5/4 = 30
30days   30nswer is 30
Answer: A
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? Choose the correct choice from the following answers: A) -1 B) -1/2 C) 0 D) 1/2 E) 1

Solution: x= 0 and y = 2.   The answer is 1.
Answer: E
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? Choose the correct choice from the following:
A) 124%
B) 120%
C) 96%
D) 80%
E) 64%

Solution: 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: 80%.
Answer: D