MU-NLPC/Calc-aqua_rat huggingface dataset:
In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 3 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?	Choose the correct choice from the following:
A) 5/21
B) 3/7
C) 4/7
D) 5/7
E) 32/35

Solution: There are suppose A B C D 32/35 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 32/35FG are 3 people who have exactly 3 siblings....(32/35 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);(32/35FG)   Now first selecting 3 people out of 7 is 7C3=35   first sibling pair----(A and B)--selecting 3 people --3C3=1   second sibling pair (C and D)--selecting 3 people--3C3=1   third sibling pair (32/35 F G)--selecting 3 out of 3 --3C3=1   total= 1+1+1= 
1+1+1 = 3
3   but,a/c to formula P(success)-1-p(fail)   here,p(failure)is selecting 3 people who are siblings=3/35(35 is 7C3)   =1-3/35   =32/35   ANS 32/35
Answer: E
Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 4 hours to paint a wall with dimensions a and c. He takes 2 hours to paint a wall with dimensions b and c and 6 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 3, then what is the volume of the room? Choose the correct choice from the following choices
A) 4.5 cubic meters
B) 2.4 cubic meters
C) 3.0 cubic meters
D) 3.6 cubic meters
E) It can’t be determined.

Solution: Time to paint each wall as given in problem:   4.5 cubic metersC = 4 hours   BC = 2 hours   4.5 cubic metersB = 6 hours   Since he works at constant rate and it takes him twice as long to paint 4.5 cubic metersC compared to BC   4.5 cubic metersC=2BC   Plug in 6 for 4.5 cubic meters and you find that B=1.5 Since painting 4.5 cubic metersB takes 3 times as long compared to BC,   4.5 cubic metersB=3BC   Plug in 6 for 4.5 cubic meters and 3 for B and you find that C=1   4.5 cubic meters*B*C=3*1.5*1= 
3*1.5*1 = 4.5
4.5 cubic meters   4.5 cubic metersnswer: 4.5 cubic meters
Answer: A
If ABC us a three digit number such that no one number is similar to other than how many possible values of ( a + 4b + c ) will be divisible by 40 :  Pick
A) 18	B) 16	C) 15	D) 12	E) 11

Solution: a b c   4 9 0 *1 because if 0 comes in first it is not a three digit number   1 9 3 *2   1 8 7 *2   2 8 6 *2   3 8 5 *2   3 7 9 *2   4 7 8 *2   7 6 9 *2   15   ANSWER:15
Answer: C
The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter?
Choose the correct choice from the following choices
A) 91.5 cm B) 11.5 cm C) 104.6 cm D) 92.5 cm E) 99.5 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 24) + 2(24)   = 56.6 + 48= 
56.6 + 48 = 104.6
104.6 cm   Answer:104.6 cm
Answer: C
Find the number of square tiles to cover the floor of a room measuring 4.5 m * 10 m leaving 0.60 m space around the room. A side of square tile is given to be 11 cms?  Choose the correct choice from the following answers: A) 2710 B) 4764 C) 2772 D) 4000 E) 2400

Solution: 3.30 *8.80 = 11/100 * 11/100 * x => x = 2400   Answer: 2400
Answer: E
Find the HCF of
23,46,827	Answers.
A) 227  B) 83  C) 23  D) 827  E) None of these

Solution: Answer: Option A   Explanation:   Whenever we have to solve this sort of question, remember the formula.   HCF =   HCF of Numerators LCM of Denominators   So answers will be option 1   227nswer: Option 227
Answer: A
A certain school principal must choose 6 students to attend a field trip out of a group of 10 students. In addition, out of the 6 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 6 students and then select the treasurer and the note-taker?	Options
A) 1,260
B) 2,520
C) 5,040
D) 6,300
E) 10,080

Solution: 5 students can be selected out of 10 students in 10C6 ways.   out of the remaining 6 students,Note taker can be chosen in 6 ways.   Finally only 5 students remain from which we can choose a treasurer in 5 ways.   Total number of ways = 210 * 6 *5= 
210 * 6 *5 = 6_300
6300   correct answer - 6,300
Answer: D
City A to city B, Andrew drove for 1hr at 42 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?	Choices:	A) 55.5	B) 57.5	C) 61	D) 61.5	E) 62.5

Solution: The total distance is 1×42+3×60=222   And the total time is 4 hours. Hence,   55.5verage Speed=(Total Distance/Total Time)   =222/4= 
222/4 = 111/2 = around 55.5
55.5   55.5
Answer: A
A password of a computer consists of five digits 1 through 6. What is the probability that all digits are divisible by 3 ? Choose the correct choice from the following options.
A) 1/3  B) 1/6  C) 1/27  D) 1/243  E) 1/486

Solution: For each digit there are six possibilities. Two of them (3 and 6) are divisible by three, so there is a one in three chance for each digit, and since the digits are independent of each other, overall probability is 1 / 3^5 or 1/243
Answer: D
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Answers: A) 29 Years B) 32 Years C) 37 Years D) 49 Years E) 50 Years

Solution: Total age of students is 32X16 = 512 Years   Total age inclusive of teacher = 33X (16+1) = 561   So, Teacher's age is 561-512= 
561-512 = 49
49 Yrs   There is a shortcut for these type of problems   Teacher's age is 16+(33X1)= 49 Years   49 Years
Answer: D
A bag contains 10 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?	Choose the correct choice: A) 3/11 B) 5/23 C) 7/30 D) 9/37 E) 11/48

Solution: Total possible ways to choose three scarves is 10C3 = 120   We need to choose the red scarf and two of 8 other scarves (not the green scarf).   The number of successful possibilities is 87/302 = 28   P(red scarf but not green scarf) = 28/120 = 7/30   The answer is 7/30.
Answer: C
The water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)	Select
A) 100  B) 250  C) 4500  D) 1200  E) 5625

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  60*20*1/2= 
 60*20*1/2 = 600
600 feet^3 of water must be removed, which equals to   600*7.5= 
  600*7.5 = 4_500
4500 gallons.   Answer: 4500.
Answer: C
On dividing a certain number by 342, we get 47 as remainder. if same number is divided by 18 . what will be the remainder? Choose the correct choice from the following answers.
A) 7*9k+86 B) 7*9k+56 C) 8*4k+56 D) 18*19K+47 E) 19*6k+9

Solution: number =324k+47   =(18*19k)+(18*2)+11   = 18*(19k+2)+11   = 18*19K+47   Answer(18*19K+47)
Answer: D
What is the probability that Carol and Bernie will get selected for a job they both applied for in a company, given that their chances of getting selected is 4/5 and 3/5 respectively?	Choose one:  A) 8/25  B) 11/24  C) 12/25  D) 12/25  E) 12/23

Solution: Explanation:   P(Carol) = 4/5   P(Bernie) = 3/5   E = {Carol and Bernie both get selected}   P(E) = P(Carol)*P(Bernie)   = 4/5 * 3/5   = 12/25   ANSWER: 12/25
Answer: D
A train which has 390 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?  Pick:  A) 26 sec  B) 39 sec  C) 36 sec  D) 29 sec  E) 30 sec

Solution: Time taken to cross a moving person = length of train/ relative speed   Time taken = 390/((45-9) (5/18) = 390/ 36*(5/18) = 390/10= 
390/10 = 39
39 sec   Answer: 39 sec
Answer: B
one gear of pulley rotates at a speed of 3 rev/sec another gear roates at 5 rev/sec. if both start together after how many seconds will they be together again Choose the correct choice
A) 3 sec  B) 5sec  C) 15 sec  D) 20 sec  E) 25 sec

Solution: 3 rotates 3,6,9,12,15   5 rotates 5,10,15   ans is 15   ANSWER:15 sec
Answer: C
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 7 m, the volume of the box (in m3) is: Pick
A) 4830	B) 5236	C) 6420	D) 8960	E) 7960

Solution: Clearly, l = (48 - 14)= 
(48 - 14) = 34
34 m,   b= (36 -14)= 
(36 -14) = 22
22 m,   h= 8 m.   Volume of the box = (34 x 22 x 7) m3 = 5236 m3. Answer: Option 5236
Answer: B
A king has 1000 bottles of wine,A queen wants to kill the king and sends a servant to poison the wine .Fortunately the king's guard's catch d servant after he has only poisoned one bottle and the guard don't know which bottle is poisoned .Furthermore it takes one month to have an effect,and there is an anniversary party coming up in 5 weeks time!the king decides he will get some of the prisoners in his vast dungeons to drink the wine.how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time?  Choose the correct choice
A) 1	B) 499	C) 500	D) 999	E) 10

Solution: Since you need 10 digits to represent 1000 numbers in binary, you will need 10 prisoners.   Now the logic is this: Every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000.   Now you have 10 prisoners. Each bottle will be tasted by the prisoners depending on the binary representation of the bottle. Wherever there is 1, the bottle will be tasted by that prisoner (assuming units digit represents the 1st prisoner, tens digit the 2nd prisoner and so on...)   1st bottle is 0000000001 so it will be tasted by only the 1st prisoner.   2nd bottle is 0000000010 so it will be tasted by only the 2nd prisoner.   3rd bottle is 0000000011 so it will be tasted by the 1st and 2nd prisoners.   and so on...   1000th bottle is 1111101000 so it will be tasted by 4th, 6th, 7th, 8th, 9th and 10th prisoners.   At the end of a month, we see which prisoners die. Say, only the 3rd prisoner dies. This means the poisoned bottle number is 0000000100 = 3.   Say 1st, 7th and 9th prisoners die. This means the poisoned bottle number is 0101000001 = 321   ANS:10
Answer: E
A train running at the speed of 90 km/hr crosses a pole in 6 seconds. What is the length of the train?
Choose one.
A) 255 B) 205 C) 502 D) 225 E) 235

Solution: Speed=(90 * 5/18) m/sec = (25) m/sec Length of the train = (Speed x Time) = (25 * 9)= 
(25 * 9) = 225
225 m.   Answer: 225
Answer: D
A train 180 m long is running with a speed of 55 km/hr. In what time will it pass a man who is running at 7km/hr in the direction opposite to that in which the train is going?	Choose the correct choice from the following
A) 5.5	B) 10.45	C) 7	D) 8	E) 9.5

Solution: Speed of train relative to man = 55+ 7= 
55+ 7 = 62
62 km/hr.= 62 * 5/18 = 155/9 m/sec.   Time taken to pass the men = 180 *9/155 = 10.45 sec.   Answer: Option 10.45
Answer: B
The greatest number by which the product of three consecutive multiples of 2 is always Select:	A) 54	B) 48	C) 162	D) 243	E) None of these

Solution: Explanation:   2*4*6= 
2*4*6 = 48
48   Option 48
Answer: B
Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 25 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?	Choose the correct answer:
A) 12.5 minutes.	B) 25 minutes	C) 35 minutes.	D) 35 minutes	E) 75 minutes

Solution: If the distance between the two houses is D. Then   Speed of Danny = (D/25)   Speed of Steve = (D/50) [ Steve takes 50 minutes to reach Danny's house. double the time taken by Danny)   Obviously speed of Danny is Twice that of Steve.   Now in order to cover distance (D/2) [They meet in middle], Steve will take:   (D/2) / (D/50) = 25 minutes.   Distance is same and Danny's speed is twice of Steve. Thus he will take 12.5 minutes to cover this same distance.   Steve take   25-12.5= 
  25-12.5 = 12.5
12.5 minutes longer.   12.5 minutes. is the answer.
Answer: A
100 is increased by 50%. Find the final number.
Answers:  A) 100  B) 110  C) 150  D) 155  E) 160

Solution: Final number = Initial number + 50%(original number) = 100 + 50%(100) = 100 + 50= 
100 + 50 = 150
150.   Answer 150
Answer: C
Of the four numbers, whose average is 50, the first is one-fourth of the sum of the last three. The first number is ?
Choose the correct choice from the following answers.
A) 28 B) 29 C) 11 D) 48 E) 40

Solution: Explanation:   Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 50 or x = (50 * 4) / 5= 
(50 * 4) / 5 = 40
40   Answer: 40
Answer: E
While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?  Choose the correct choice from the following choices.
A) 3 B) 3.5 C) 4 D) 4.5 E) 5

Solution: Both computers together process files at a rate of 240/12 + 240/6 = 20+40= 
20+40 = 60
60 files per hour.   The time required to process 240 files is  240/60= 
 240/60 = 4
4 hours   The answer is 4.
Answer: C
What is the smallest integer that satisfies the inequality (x - 3)/ (x^2 - 8x - 20) > 0> 0?
Choose the correct choice:
A) -2	B) 10	C) 3	D) -1	E) 0

Solution: Explanatory Answer   Let us factorize the denominator and rewrite the expression as x−3 /(x−10)(x+2) > 0   Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.   The values that are relevant to us are x = 3, x = 10 and x = -2.   Let us arrange these values in ascending order: -2, 3 and 10.   The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.   Interval 1: x < -2.   Pick a value in that range and check whether the inequality holds good.   Let us take x = -10. When x = -10, x−3 /(x−10)(x+2) < 0; the inequality DOES NOT hold good in this interval.   Interval 2: -2 < x < 3.   Let us take x = 0. When x = 0, x−3/(x−10)(x+2) = 0−3 /(0−10)(0+2) > 0; the inequality holds good in this interval.   The least integer value that x can take if x > -2 is x = -1.   So, the correct answer is -1. Choice D.   Remember: We have to find out the least integer value. And we have arrived at -1.   Do, not waste time computing the entire range of values of x that satisfy the inequality.   Note: In any inequality question, when the question asks us to determine the intervals in which the inequality holds good, we have to eliminate values of x that will result in the denominator becoming zero.   Choice -1
Answer: D
If r = 199,999 and s = 991,999, which of the following is the units digit of r^4 + s^4? Choose the correct answer
A) 0	B) 1	C) 2	D) 8	E) 9

Solution: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).   Then the sum of r^4+s^4 will have the units digit of 1+1= 
1+1 = 2
2 as a units digit.   The answer is 2.
Answer: C
What is the area of a square with perimeter 4P ?  Choose the correct answer
A) p^2  B) 4P  C) P^2/4  D) P/16  E) P^2/16

Solution: Each side is p   p^2 = (p)^2   p^2nswer p^2
Answer: A
Rahul and Bharti are partners in a business. Rahul contributes 1/4th capital for 15 months and Bharti received 2/3 of profit. For how long Bharti money was used. Answers:  A) 8 months  B) 10 months  C) 11 months  D) 17 months  E) None of these

Solution: Explanation:   Let the total profit be Rs. Z   10 monthsharti's share = (2/3)Z   Rahul's Share = Z-(2/3)Z = Z/3   Rahul:10 monthsharti = Z/3:(2/3)Z = 1:2   Now let the total capital be Rs X, and 10 monthsharti capital was used for Y months   then, Rahul capital will be (1/4)X and 10 monthsharti capital wil be X-(1/4)X = 3X/4   14X∗15/ 3/4X∗Y=1/2   Y=15∗2/3=10   So 10 monthsharti's money was used for 10 months   Option 10 months
Answer: B
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?  Choose the most appropriate option:
A) 35%
B) 30%
C) 40%
D) 42 6/7%
E) None of these

Solution: Explanation:   SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer IS 42 6/7%
Answer: D
If n divided by 7 has a remainder of 2, what is the remainder when 2 times n is divided by 7?  Choose the correct option
A) 1  B) 2  C) 3  D) 4  E) 6

Solution: As per question => N=7P+2 for some integer p   hence 2N => 14Q + 4 => remainder => 4 for some integer Q   Alternatively => N=2 > 2N=> 4 =>4 divided by 7 will leave a remainder 4   hence 4
Answer: D
A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball?
Choose the most appropriate option:
A) 5⁄7
B) 10⁄21
C) 2⁄7
D) 11⁄21
E) None of these

Solution: Reqd probability = 5C2/7C2=5×4/7×6=10/21   Answer 10⁄21
Answer: B
If the product of the integers r, s, t and u is 770, and if 1 < r< s< t< u, what is the value of r+ u?  Answers:
A) 10
B) 13
C) 16
D) 18
E) 21

Solution: 770 = 2 * 5 * 7 * 11   So r= 2, s= 5, t= 7, u= 11   r+ u= 2 + 11= 
2 + 11 = 13
13   Answer - 13
Answer: B
At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 11'o clock.	Pick one: A) 60sec B) 62sec C) 66sec D) 64sec E) 76sec

Solution: At 6'0 clock, clock ticks 6 times.   So, there must be 5 intervals between clock ticks.   Time Between first and last ticks = 30sec   So, 1 interval = 30/5= 
30/5 = 6
6sec   So 6'o clock 5 *6= 
5 *6 = 30
30sec   7'o clock 6 *6= 
6 *6 = 36
36sec   .   .   .   10'o clock 9 *6= 
9 *6 = 54
54sec   11'o clock 10*6= 
10*6 = 60
60sec   So, 60sec at 11'o clock.   60secNSWER:60sec
Answer: A
In how many different R ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?	Choose the most appropriate option:
A) 70 B) 288 C) 576 D) 10,080 E) 20,160

Solution: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways   And there are 4! ways to arrange ladies among themselves   Answer R= (4!)^2 = 576 or 576
Answer: C
The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the sum of the numbers left on the board at the end?	Choose the correct option:  A) 820  B) 821  C) 781  D) 819  E) 780

Solution: Explanation :   Initial sum of the numbers is 1 + 2 + …40.   Initial sum = 40 * 41/2= 
40 * 41/2 = 820
820. (A.P. with common difference 1 and 1st term 1, last term 40).   Two numbers, a, b are erased and replaced by a+b-1, that means, the sum is now 819.   This is done 39 times. So, sum after 39 time replacement is 820 – 39= 781.   Answer : 781
Answer: C
If December 3rd, 1999 is a Friday, what day is January 7th, 2000? Choose the correct choice from the following answers
A) Wednesday B) Thursday C) Friday D) Saturday E) Sunday

Solution: There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000.   35/7 has a remainder of 0.   Jan. 7th is: Friday + 0 days = Friday   The answer is Friday.
Answer: C
Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm.
Choose the correct answer
A) 221 cm2	B) 211 cm2	C) 231 cm2	D) 236 cm2	E) 241 cm2

Solution: Given: length = 17 cm, breadth = 13 cm   Perimeter of rectangle = 2 (length + breadth)   = 2 (17 + 13) cm   = 2 × 30 cm   = 60 cm   We know that the area of rectangle = length × breadth   = (17 × 13) cm22   = 221 cm2 221 cm2NSWER :221 cm2
Answer: A
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? Choose one.
A) 87 days
B) 20 days
C) 66 days
D) 77 days
E) 44 days

Solution: C = 1/2 - 1/4 - 1/5 = 1/20   => 20 days   Answer: 20 days
Answer: B
The difference between a number and its two-fifth is 45. What is the number?  Pick.
A) 76  B) 56  C) 88  D) 66  E) 75

Solution: Explanation:   Let the number be x.   x – (2 / 5) x = 45   (3/5) x = 45   x = 75   ANSW75R: 75
Answer: E
What is the total number of prime numbers less than 50?	Options:
A) 17  B) 18  C) 19  D) 15  E) 21

Solution: Solution   Prime numbers less than 50 are	=15.   2,3,5,7,11,13,17,19,23,29,31,37,41,43,47   Their number is 15.   Answer 15
Answer: D
What will be the compound interest on Rs. 30000 after 3 years at the rate of 12 % per annum Choose the correct choice from the following options:
A) Rs 10123.20
B) Rs 12147.84
C) Rs 10123.40
D) Rs 10123.50
E) None of these

Solution: Explanation:   (30000×(1+12/100)3)   =>30000×28/25×28/25×28/25   =>42147.84   So Compound interest will be   42147.84 - 30000= 
  42147.84 - 30000 = 12_147.84
Rs 12147.84   Option Rs 12147.84
Answer: B
A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the physics club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs. Choose the correct choice from the following:
A) 80
B) 70
C) 60
D) 50
E) 30

Solution: A-Club has 200 members (1/2 of 400)   B-Club has 250 members (5/8 of 400)   C-Club has 300 members (3/4 of 400)   We can create an equation to solve this:   200+250+300 = n + x + 2y   where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.   The question provides y for us (150).   750 = 400 + x + 300   x = 50   50
Answer: D
In how many different ways can the letter of the word 'JUDGE ' be arranged in such a way that the vowels always come together?  Pick one:
A) 48
B) 89
C) 56
D) 74
E) 25

Solution: It has 5 different letters.   when the vowels UE are always together, they can be supposed to form one letter.   then we have to arrange the letter JD   now 4 letters can be arranged in 4!=24ways   the vowels UE can be arranged amoung themselves in 2!=2 ways   required number of ways =24*2= 
24*2 = 48
48   48nswer(48)
Answer: A
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was: Choose one:
A) 900
B) 750
C) 250
D) 600
E) 800

Solution: Number of valid votes = 80% of 2000 = 1600   Valid votes polled by other candidate = 45% of 2000   =(45/100)X2000 =900   900NSWER = 900
Answer: A
Set S has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? Select
A) {2, 10}  B) {16, 16}  C) {9, 11}  D) {7, 13}  E) {10, 18}

Solution: answer A, B,C, and D mean is not 9 therefore not accepted . E mean is 9 but S.D is one unit. therefore accepted   answer is E mean is 9 and S.D decreases minimum.   {10, 18}
Answer: E
if the ratio of s.i earned on certain amount on same rate is 4:5.what is the ratio of time?
Choose one:
A) 1:2	B) 6:9	C) 4:5	D) 2:3	E) not possible to calculate

Solution: s.i1/s.i2=[(p*r*t1)/100]/[(p*r*t2)/100]   4/5=t1/t2   ratio=4:5   answer 4:5
Answer: C
A man sitting in a train which is traveling at 36 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 240 m long, find its speed	Choose the correct choice from the following
A) 50 kmph B) 56 kmph C) 58 kmph D) 62 kmph E) 72 kmph

Solution: Explanation:   Relative speed = 240/10 m / sec = ((240/10)×(18/5)) kmph = 86 kmph.   Speed of goods train = (86 - 36)= 
(86 - 36) = 50
50 kmph   50 kmphnswer: Option 50 kmph
Answer: A