MU-NLPC/Calc-aqua_rat huggingface dataset:
A completes a work in 12 days and B complete the same work in 20 days. If both of them work together, then the number of days required to complete the work will be  Options:
A) 8 days B) 9 days C) 7.5 days D) 12 days E) 13 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 12 × 20/ 32 = 7.5 days.   7.5 days
Answer: C
Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L  Pick one.
A) 3.	B) 1/2.	C) 2.	D) 1/3.	E) 6.

Solution: Difference = Average   H - L = (H + L)/2,   Solving for H/L gives 3. 3. quick check, H be 24 and L be 8, 24 - 8 = (24 + 8 )/2   3.
Answer: A
A bag contains 8 red and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Choose the most appropriate option:  A) 8/15  B) 2/3  C) 5/8  D) 1/4  E) 5/7

Solution: Total number of balls = 8+7= 
8+7 = 15
15   number of white balls= 8   Probability = 8/15   8/15nswer is 8/15
Answer: A
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?	Choose the most appropriate option.
A) 54 B) 63 C) 75 D) 86 E) 98

Solution: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)   Therefore, the product should have factors with a difference of 2.   63 = 7*9, so this is a possible value for the original expression.   The answer is 63.
Answer: B
a light flashes every 12 seconds, how many times will it flash in ? of an hour?	Choose the correct choice from the following:	A) 550	B) 300	C) 650	D) 700	E) 750

Solution: 1flash=12sec   for 1 min=5flashes   so for 1 hour=5*60= 
5*60 = 300
300 flashes.   ANSWER:300
Answer: B
If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be	Choose the correct choice
A) 6x
B) 4x
C) 5x/3
D) 3x/2
E) 3x/5

Solution: Note that we have 5positivetemperatures.   Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<d<5x --=""> only option B fits.   Answer: 4x.</d<5x>
Answer: B
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
Choose the most appropriate option:
A) 120990
B) 120950
C) 120970
D) 120960
E) 120980

Solution: 8!(2!)(2!)=8×7×6×5×4×3×2×1/(2×1)(2×1)   =10080   In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.   Number of ways to arrange these vowels among themselves =4!/2!=4×3×2×12×1=12   Hence, required number of ways   =10080×12=120960   Answer: 120960
Answer: D
How many odd, positive divisors does 440 have?  Choose the correct choice from the following options:
A) 3  B) 8  C) 12  D) 15  E) 24

Solution: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=3 factors.   Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.   3nswer: 3.
Answer: A
Three integers are at random chosen between 0 and 9 inclusive. What is the probability W that each number is different ? Choose the most appropriate option.
A) A.18/25 B) B.4/5 C) C.81/100 D) D.9/10 E) E.1

Solution: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10   Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8   Probability W= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25   A.18/25nswer: A.18/25
Answer: A
In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required is:  Choices:	A) 4	B) 5	C) 6	D) 8	E) 9

Solution: Explanation :   Let the required number of men be x.   Less days, More men (Indirect Proportion)   More working hrs per day, Less men (Indirect Proportion)   8ays 8 : 10   Working Hrs 15 : 8 :: 12 : x   => 8 x 15 x x = 10 x 8 x 12   => x = 10 x 8 x 12 / (8 x 15)   => x = 8   Answer : 8
Answer: D
In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, what part of the total number of students is present ? Choose the correct choice from the following options:
A) 17/25
B) 18/49
C) 23/30
D) 23/36
E) 29/36

Solution: Girls = 3/5, boys are 2/5   Absentees are (2/9)*(3/5) + (1/4)*(2/5) = 7/30   Present Students are 23/30   ANSWER:23/30
Answer: C
For any positive integer b, the sum of the first b positive integers equals b(b+1)/2 . If a and b are positive integers and a > b, what is the sum of all the integers between a and b, inclusive?
Select:
A) a(a+1)/2 + b(b+1)/2
B) a(a+1)/2 - b(b-1)/2
C) a(a+1)/2 - b(b+1)/2
D) a(a+1)/2 + b(b-1)/2
E) a(n+1)/2 - b(a-1)/2

Solution: The sum of all the integers between a and b,inclusiveis the sum of the first a positive integersminusthe sum of the first b-1 positive integers.   The sum of the first a positive integers is a(a+1)/2;   The sum of the first b-1 positive integers is (b-1)b/2;   Therefore the answer is a(a+1)/2 - (b-1)b/2.   Answer: a(a+1)/2 - b(b-1)/2.
Answer: B
Two pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 20 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank? Pick one
A) 150 liters	B) 540 liters	C) 200 liters	D) 560 liters	E) 580 liters

Solution: 1/10 + 1/15 - 1/x   = 1/15   x = 10   10 * 20= 
10 * 20 = 200
200   Answer:200 liters
Answer: C
If 2x = 3√32, then x is equal to :	Choose the most appropriate option
A) 3/5  B) 5/3  C) 15  D) 25  E) NOne

Solution: Sol.   2x = 3√32 ⇔ 2x = (32)1/3 = (25)1/3 = 25/3 ⇔ x = 5/3.   Answer 5/3
Answer: B
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?	Choices
A) 7:9
B) 7:3
C) 7:2
D) 7:9
E) 7:1

Solution: Let the age of father and son 10 years ago be 3x and x years respectively.   Then, (3x + 10) + 10 = 2[(x + 10) + 10]   3x + 20 = 2x + 40 => x = 20.   Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3   Answer:7:3
Answer: B
The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 50 kmph. Find the speed of the boat in still water and the speed of the stream?	Choose the correct choice: A) 40,10 kmph B) 38,10 kmph C) 40,70 kmph D) 78,10 kmph E) 70,12 kmph

Solution: Speed of the boat in still water   = (30+50)/2= 
(30+50)/2 = 40
40 kmph. Speed of the stream= (50-30)/2= 
(50-30)/2 = 10
10 kmph.   40,10 kmphnswer:40,10 kmph
Answer: A
An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?  Choose the correct answer:
A) 211
B) 216
C) 1075
D) 1080
E) 2160

Solution: For the case when the hundreds digit is repeated: XXY or XYX   X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).   Y can take 9 values (10 digits minus the one we used for X).   To account for XXY or XYX case we are multiplying by 2.   So, for this case we'd have 8*9*2.   For the case when the tens and units digits are repeated: XYY   X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).   Y can take 9 values (10 digits minus the one we used for X).   Now, 8*9 also give number 200 and we need numbers greater than 200, so for this case we'd have 8*9 - 1.   Last step, since there are 5 vowels, then the final answer would be 5*(8*9*2 + 8*9 - 1) = 1,075.   Answer: 1075.
Answer: C
The positive two-digit integers a and b have the same digits, but in reverse order. Which of the following must be a factor of a + b?	Select.
A) 6 B) 9 C) 10 D) 55 E) 14

Solution: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9   and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187   55 is multiple of 11   So, Answer 55
Answer: D
A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?  Pick one
A) 2/7  B) 3/5  C) 3/11  D) 1/4  E) 7/16

Solution: Total number of balls = 3+5+4= 
3+5+4 = 12
12   n(S)= 123/113 = 12*11*10 / 3*2 = 220   n(E) = 33/111 * 53/111 * 43/111 = 3*5* 4= 
3*5* 4 = 60
60   Probability= 60/220 = 3/11   Answer is 3/11
Answer: C
By selling 15 pencils for a rupee a man loses 25%. How many for a rupee should he sell in order to gain 25%?
Choose the correct choice from the following options.
A) 8 B) 9 C) 7 D) 6 E) 5

Solution: 75% --- 15   125% --- ?     75/125 * 15= 
  75/125 * 15 = 9
9   Answer: 9
Answer: B
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?  Answers
A) 11	B) 40	C) 88	D) 76	E) 26

Solution: Let 1 man's 1 day work = x and 1 woman's 1 day work = y.   Then, 4x + 6y = 1/8 and 3x + 7y = 1/10   Solving these two equations, we get:   x = 11/400 and y = 1/400   1 woman's 1 day work = (1/400 * 10) = 1/40.   Hence, 10 women will complete the work in 40 days.   Answer:40
Answer: B
A and B invest money in the ratio 3:4 and they has loss of Rs.8400 at the end of year. what is the share of loss of B?	Choose the correct choice from the following options
A) Rs.4800	B) Rs.4700	C) Rs.4600	D) Rs.4500	E) None of the above

Solution: et ratio of Rs.4800 and B be 3x & 4x   so net loss = 3x+4x= 8400   x=1200   Rs.4800=3x=3(1200)=3600   B= 4x=4(1200)=4800   so, B= 4800   Rs.4800NSWER:Rs.4800
Answer: A
A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Then number is	Pick:
A) 21  B) 23  C) 27  D) 72  E) 57

Solution: Sol.   Let the ten's digit be x and unit's digit be y.   Then, 10x + y = 3(x+y) ⇒ 7x - 2y = 0   10x + y + 45 = 10y + x ⇒ y - x = 5   Solving (i) and (ii), we get : x = 2 and y = 7.   ∴ Required number = 27.   Answer 27
Answer: C
The tax on a commodity is diminished by 10% and its consumption increased by 15%. The effect on revenue is?  Choose the correct choice from the following answers
A) 2% decrease B) 3.5% increase C) 9% decrease D) 3% decrease E) 2% increase

Solution: 100 * 100= 
100 * 100 = 10_000
10000   90 * 115= 
90 * 115 = 10_350
10350   -----------   10000-----------350   100-----------?=> 3.5% decrease   Answer: 3.5% increase
Answer: B
In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?  Pick one:
A) 10
B) 20
C) 40
D) 50
E) 80

Solution: His height was = 5 feet 5 inch = 5 + 60= 
5 + 60 = 65
65 inch. Required % correction=65*(1.25-1)* 100 = 20   20
Answer: B
In how many ways can you seat 8 people on a bench if one of them does not want to sit at either end? Choose the correct choice from the following options
A) 26,360 B) 27,480 C) 28,120 D) 29,860 E) 30,240

Solution: One person can choose 6 possible chairs to sit. The remaining 7 people can sit in 7! ways.   The number of arrangements is 6*7! = 30,240.   The answer is 30,240.
Answer: E
A car takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Choices:  A) 50 Kmph  B) 60 Kmph  C) 32 Kmph  D) 70 Kmph  E) None

Solution: Time = 6   Distence = 288   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 288/9= 
288/9 = 32
32 Kmph   32 Kmph)
Answer: C
The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:  Choose the most appropriate option.
A) 400  B) 500  C) 600  D) 800  E) 1000

Solution: Let the sum be $. P.   (P(1+10/100)^2-P)=525   P((11/10)^2-1)=2500   SUM = 2500   So SI = 500   ANSWER 500
Answer: B
[1/4(2/5) + 1/2(4/9)] = ?  Choose one.
A) 7/11	B) 5/11	C) 2/11	D) 1/11	E) 2/11

Solution: Explanation:   [1/4(2/5) + 1/2(4/9)] = 1/(22/5) + 1/(22/9)   = 5/22 + 9/22 = 14/22 = 7/11   7/11nswer: Option 7/11
Answer: A
Two trains of length 90 m and 95 m are 250 m apart. They start moving towards each other on parallel tracks, at speeds 64 kmph and 92 kmph. After how much time will the trains meet?
Pick one
A) 53/10	B) 55/10	C) 56/10	D) 57/10	E) 58/10

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (64 + 92)*5/18 = 43.3 mps.   The time required = d/s = 250/43.3 = 58/10sec.   Answer:58/10
Answer: E
A store reported total sales of $416 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?	Choose the correct answer: A) 2% B) 17% C) 30% D) 65% E) 83%

Solution: New Value – Old Value)/Old Value x 100   We are given:   February sales this year = 416 million   February sales last year = 320 million   We need to determine the percent increase between sales from last year to sales this year.   Thus, the new value = 416 million and the old value = 320 million. Let’s plug them into our percent change formula.   (New Value – Old Value)/Old Value x 100   [(416 – 320)/320] x 100 =30%   The answer is 30%.
Answer: C
The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 3.6 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
Choose one:
A) 31  B) 35  C) 39  D) 43  E) 47

Solution: (3.6 miles / 8 minutes)*60 minutes/hour = 27 mph   Let x be the original speed.   x - 4(3) = 27   x = 39 mph   The answer is 39.
Answer: C
A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ? Choose the correct choice from the following answers.
A) 20 km/hr  B) 35 km/hr  C) 42 km/hr  D) 45 km/hr  E) 50 km/hr

Solution: Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr   35 km/hr
Answer: B
What is the perimeter of a triangle with sides 5 and 3 that has the maximum possible area? Choose the correct option:	A) 8 + √34	B) 7 + √26	C) 12	D) 8 + 3√5	E) 8 + 3√6

Solution: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(25+9)= 
(25+9) = 34
√34   The perimeter is 8 + √34   The answer is 8 + √34.
Answer: A
A man buy a book in Rs50 & sale it Rs60. What is the rate of profit ???
Pick:  A) 10%  B) 20%  C) 30%  D) 25%  E) 28%

Solution: cp=50   sp=60   profit=60-50= 
60-50 = 10
10   %=10/50*100= 
10/50*100 = 20
20%   ANSWER:20%
Answer: B
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 75 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?	Choose the correct choice:	A) 15 sec	B) 16 sec	C) 14 sec	D) 67 sec	E) 13 sec

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 75   D = 75 * 100/18 = 1250/3   RS = 60 + 50 = 100 * 5/18   T = 1250/3 * 18/500= 
1250/3 * 18/500 = 15
15 sec   15 secnswer: 15 sec
Answer: A
If daily wages of a man is four times to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.  Choose the correct choice from the following choices: A) 12 B) 4 C) 6 D) 8 E) 20

Solution: Explanation :   Wages of 1 woman for 1 day = 21600/40Ã—30   Wages of 1 man for 1 day = 21600Ã—4/40Ã—30   Wages of 1 man for 25 days = 21600Ã—4Ã—25/40Ã—30   Number of men = 14400/(21600Ã—4Ã—25/40Ã—30)=144/(216Ã—100/40Ã—30)= 8   Answer : Option 8
Answer: D
Arrange the following in descending order :
A) 111(4),
B) 110 x 109 x 108 x 107,
C)109 x 110 x 112 x 113	Choose the correct choice from the following
A) all are equal	B) B,A.C	C) A,B,C	D) A,C,B	E) None

Solution: Explanation :   if you see option B...you can easily say it is the lowest value. Now about A and C you can see the sum of the values on both side is equal on this type of cases the side which as more number of values closer than other side and to the maximum value among given numbers will be the biggest value..If you couldn't understand the explanation take two sample and compare   Answer : A,C,B
Answer: D
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options.
A) 10  B) 15  C) 20  D) 30  E) None

Solution: Sol.   Due to stoppages, it covers 9 km less.   Time taken to cover 9 km = [9/54 * 60= 
9/54 * 60 = 10
10 min.   10nswer 10
Answer: A
Find the next number in the sequence ?
2 11 25 44 68 ?  Answers:  A) 65  B) 78  C) 99  D) 97  E) 91

Solution: D   97   Explanation:   Difference between number sequence is below:   9,14,19,24,29   Now the difference between above sequence is 5.   So next number is 68 + 29= 
68 + 29 = 97
>97
Answer: D
Two trains 140 m and 160 m long run at the speed fo 60 k/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: Choose the correct answer: A) 7 B) 8.6 C) 10.8 D) 11 E) 12

Solution: Sol.   Relative speed = (60 + 40) km/hr = [100 * 5/18] m/sec = [250/9] m/sec.   Distance covered in crossing each other = (140 + 160)= 
(140 + 160) = 300
300 m.   Required time= [300 * 9/250] sec = 54/5= 
54/5 = 54/5 = around 10.8
10.8 ec.   Answer 10.8
Answer: C
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? Choose the most appropriate option.
A) 140
B) 150
C) 160
D) 170
E) 180

Solution: 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: Option 150
Answer: B
John was thrice as old as Tom 6 years ago. John will be 7/5 times as old as Tom in 6 years. How old is Tom today?
Pick one.
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: J-6 = 3(T-6), so J = 3T-12   J+6 = 7/5 * (T+6)   5J + 30 = 7T + 42   5(3T-12) + 30 = 7T + 42   8T = 72   T = 9   The answer is 9.
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 seconds. What is the length of the fast train?
Pick one:
A) 23 m
B) 33 (1/3)m
C) 27 (7/9)m
D) 29 m
E) 28 m

Solution: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.   Therefore Length of faster train =	((50/9)	x 6) m =	(300/9)m = 33	(1/3)	m.   33 (1/3)m
Answer: B
Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?  Choices:
A) $5.85
B) $2.85
C) $4.85
D) $8.85
E) $7.85

Solution: John spent and gave to his two friends a total of   1.25 + 1.20 + 1.20= 
1.25 + 1.20 + 1.20 = 3.65
$3.65   Money left    8.50 - 3.65= 
 8.50 - 3.65 = 4.85
$4.85 correct answer $4.85
Answer: C
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.	Choose the correct option:	A) 1/36	B) 1/216	C) 1/48	D) 1/55	E) 1/90

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   1/36NSWER 1/36
Answer: A
A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
Options:
A) 10.5  B) 10.8  C) 10.9  D) 10.4  E) 10.2

Solution: Total distance traveled = 10 + 12= 
10 + 12 = 22
22 km /hr.   Total time taken= 10/12 + 12/10 = 61/30 hrs.   Average speed = 22 * 30/61 = 10.8 km/hr.   Answer: 10.8
Answer: B
In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?  Pick one
A) 199 sec	B) 190 sec	C) 240 sec	D) 127 sec	E) 128 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/40= 
(1000 * 10)/40 = 250
250 sec.   Time taken by A= 250 - 10= 
250 - 10 = 240
240 sec.   Answer: 240 sec
Answer: C
The average age of a class of 20 students is 19 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
Choices.
A) 40 years	B) 41 years	C) 42 years	D) 43 years	E) 44 years

Solution: If age of the teacher was 19, average would not have changed.   Since average increased by 2,   Age of the teacher=19+22×1=41   ANSWER:41 years
Answer: B
The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 142. What is the number of frogs in the pond ?
Options.
A) 148
B) 152
C) 156
D) 145
E) None

Solution: Solution:   Ratio of Ducks and Frogs in Pond,   = 37 : 39.   Average of Ducks and Frogs in Pond,   = 142.   So, total number of Ducks and Frogs in the Pond,   = 2* 142= 
2* 142 = 284
284.   Therefore,   Number of Frogs,= (284 *39)/76 = 145.   Answer: Option 145
Answer: D
The probability that A speaks truth is 2/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A) 17/35  B) 18/35  C) 18/36  D) 18/33  E) 18/32

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 2/5 * 4/7 + 3/5 * 3/7   = 8/35 + 9/35 = 17/35   17/35nswer: 17/35
Answer: A
If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)Q of x, x^2, x^3, x^4 and x^5 is equal to which of the following?	Choose the correct choice from the following choices:
A) 12x	B) 13x	C) 14x	D) 16x	E) 20x

Solution: 1 + x^4 + x^3 + x^2 + x = 81   i.e. 1 +x+ x^2+ x^3+ x^4 = 81   x+ x^2+ x^3+ x^4 = 80   x(1 +x+ x^2+ x^3) = 80   x(81-x^4) = 80   81x - x^5 = 80   x^5 = 81x -80   Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x   Average of Q{x, x^2, x^3, x^4, x^5} 80 + 81  -80= 
80 + 81  -80 = 81
81x   Average of Q{x, x^2, x^3, x^4, x^5}= 81x/5 ~ 16x   Answer16x
Answer: D
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 3, she will stop rolling the cube. What is the probability that Molly will roll the die less than 4 times before stopping?  Choose the correct choice from the following:
A) 11/180	B) 125/216	C) 11/36	D) 91/216	E) 27/128

Solution: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:   The probability that Molly will roll the die once: P=1/6 (she gets 3 on the first roll);   The probability that Molly will roll the die twice: P=5/6*1/6 (not 3, 3);   P = 1/6 + 5/6*1/6 = 11/36   Answer: 11/36
Answer: C
The average monthly income of P and Q is Dollar 5050. The average monthly income of Q and R is Dollar 6250 and the average monthly income of P and R is Dollar 5200. The monthly income of P is:	Choose one:
A) $ 4000 B) $ 3000 C) $ 7000 D) $ 8000 E) $ 2000

Solution: A   $ 4000   Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 x 2) = 10100 .... (i)   Q + R = (6250 x 2) = 12500 .... (ii)   P + R = (5200 x 2) = 10400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)   Subtracting (ii) from (iv), we get P = 4000. P's monthly income = $ 4000.
Answer: A
If √10 = 3.16, find the value of If √5/2	Choose the most appropriate option:
A) 1.3
B) 1.58
C) 2.03
D) 2.15
E) 3.15

Solution: Explanation:   √(5/2) =√(5×2/2×2)= √(10)/2 =3.16/2= 
3.16/2 = 1.58
1.58   ANSWER: 1.58
Answer: B