MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the number of square tiles to cover the floor of a room measuring 10 m * 12 m leaving 0.25 m space around the room. A side of square tile is given to be 50 cms?
Choose one:  A) 277  B) 476  C) 437  D) 257  E) 212

Solution: 9 1/2 * 11 1/2 = 1/2 * 1/2 * x => x = 437   Answer:437
Answer: C
Find the value for x from below equation: x/3=-2? Choose one:
A) -6
B) -4
C) 4
D) 5
E) -5

Solution: 1. Multiply both sides by 3:   x*3/3= -2/3   2. Simplify both sides:   x = -6   -6
Answer: A
If m=9^(x−1), then in terms of m, 3^(4x−5) must be which of the following?  Choose one:	A) m/3	B) 9m	C) 9m^2	D) m^2/3	E) m^2/9

Solution: m = 9 ^ (X-1)   m = 3 ^ (2x-2)   m^2 = 3 ^ (4x-4)   m^2/3 = 3 ^ (4x-5)   Answer m^2/3
Answer: D
In the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole?	Choose the correct choice from the following choices
A) 500% B) 600% C) 800% D) 1100% E) 1200%

Solution: Say initially population was 100.   What is 200% of 100? It is   200/100 * 100= 
  200/100 * 100 = 200
200.   An increase of 200% means the new population became  100 + 200= 
 100 + 200 = 300
300   What is 300% of 300? It is   300/100 * 300= 
  300/100 * 300 = 900
900   An increase of 300% means the new population now is  300 + 900= 
 300 + 900 = 1_200
1200   So from 100, the population increased to 1200 i.e. an increase of 1100.   1100 is what percent of 100?   1100= x/100 * 100   i.e. it is 1100% 1100%
Answer: D
Find the least number which when divided by 6, 9, 14, 21 and 24 leaves 1, 4, 9, 16 and 19 as remainders respectively, but when divided by 17 leaves no remainder.  Choose the correct choice from the following choices:  A) 11277  B) 1003  C) 3277  D) 278  E) 181

Solution: LCM of 6, 9, 14, 21 and 24 is 504. Required number = (504 k–5) which is divisible by 17 for the least value of k. (504 k – 5) = (493k + 11k – 5) = (17×29)k + (11k–5) Let k = 1 ⇒ (11×1 – 5) = 7 (not divisible by 17) Let k ⇒ = 2 (11×2 – 5) = 17 (divisible by 17) ∴ (17×29)k + (11k–5) is exactly divisible by 17 for k = 2. ∴ Required Number   = (504)k – 5 = (504×2) – 5 = 1003.   Answer:1003
Answer: B
The probability that a visitor at the mall buys a pack of candy is 20%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
Answers.
A) .343 B) .147 C) .189 D) .096 E) .027

Solution: One case is: candy - candy - no candy   The probability is 1/5*1/5*4/5 = 4/125   There are 3 such cases, so we should multiply this probability by 3.   P(exactly 2 buy candy) = 4/125 * 3 = 12/125= 
12/125 = 12/125 = around 0.096
0.096   The answer is .096.
Answer: D
an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -t and a*t=0, then =?
Answers:  A) a) -a  B) b) -1/a  C) c) 1/a  D) d)0  E) e)a

Solution: If a*t=0 and a=-t then a-t = o of a=t, so answer e)a
Answer: E
find the average of all the number between 6 and 34 which are divisible by 5.
Choose the correct answer:
A) 18
B) 20
C) 24
D) 30
E) 32

Solution: Solution   Average = (10+15+20+25+30/5) =100/2 =20 Answer 20
Answer: B
Kevin purchased a house for Rs.61000 and a site for Rs.29000 respectively, if he sold the house for Rs.77000 and the site for Rs.19000, then find the resultant percentage of gain? Choose the correct choice from the following answers: A) 6.66% B) 5.55% C) 5.56% D) 6.65% E) 7.77%

Solution: Sol.   Total CP = 90000 & total SP = 96000 ⇒ gain = SP/CP = 96000/90000 = 1.0666 = 6.66%.   6.66%nswer 6.66%
Answer: A
If Scott has earned 15 dollars by working 4 days a week at a constant daily rate for 1 weeks, which of the following represents his daily wage?  Choose one:
A) 4/15
B) 1/60
C) 15/1
D) 15/3
E) 15/4

Solution: Scott total earning = 15   No days he worked = 4   Rate = 1 week   Daily wage = total / (Rate * days)   = 15/(4*1)   15/4 is correct answer...
Answer: E
8% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning? Choose the correct choice from the following answers
A) 2988  B) 4543  C) 4400  D) 2871  E) 881

Solution: X * (92/100) * (85/100) = 3553   X = 4543   Answer:4543
Answer: B
Find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm? Choices:
A) 180 cm2 B) 150 cm2 C) 168 cm2 D) 198 cm2 E) 987 cm2

Solution: 1/2 * 24(9 + 6)   = 180 cm2   180 cm2nswer: 180 cm2
Answer: A
On a wedding catering service, An experienced chef can prepare a service for a wedding in 4 hours while an novice chef would finish the preparations in 16 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?  Choose the most appropriate option:	A) 2	B) 3	C) 4	D) 6	E) 8

Solution: Experienced chefs work = 1 wedding/4 hours   Novice chefs work = 1 wedding/16 hours   Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equal x   1hr and 36mins = 8/5 an hour   x/4+ x/16 = 1 wedding / (8/5)   x/4 + x/16 = 5/8   x=2   So there are 2 novice chefs and 2 experienced chefs. In total there are 4. The answer is 4.
Answer: C
If 8 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?	Choose the correct choice:
A) 784
B) 763
C) 120
D) 160
E) 1260

Solution: parallelogram can formed by 2 horizontal and 2 vertical lines   for horizontal 8c2   for vertical 8c2   total parallelogram is 10 c2*8c2=28*28= 
28*28 = 784
784   784NSWER:784
Answer: A
A coin is tossed three times. What is the probability that there is at the least one tail?
Choose the most appropriate option.
A) 7/8	B) 31/37	C) 31/18	D) 31/10	E) 31/19

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed three times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/8 ; P(T) = 1 - 1/8 = 7/8   7/8nswer: 7/8
Answer: A
If X+Y = 2X+2Z, X-2Y = 2Z and X+Y+Z = 21, what is the value of Y/Z?  Answers.
A) -4. B) -2. C) -1.7. D) 3. E) 2.5.

Solution: X+Y = 2X+2Z   Y= X+2Z---------- 1   X-2Y = 2Z   X-2Z= 2Y--------- 2   Subtracting equation 1 from equation 2   -4Z= Y   Y/Z= -4   -4. is the answer
Answer: A
A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 22000. What is the share of C?
Choose the correct choice from the following options:
A) Rs. 2250	B) Rs. 3375	C) Rs. 6000	D) Rs. 5625	E) None of these

Solution: Explanation:   Let the investment of C be Rs. x.   The inverstment of B = Rs.(2x/3)   The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)   Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3   C's share = Rs. [(3/11) × 22000] = Rs. 6000   Answer: Option Rs. 6000
Answer: C
Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 60 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
Choose the correct choice from the following
A) 40 B) 50 C) 60 D) 110 E) 80

Solution: L+M=M+N-60 / N=2L+10   60=M+N-L-M   60=N-L   60=2L+10-L   50=L   2(50)+10=110   110
Answer: D
In a camp,there is a meal for 120 men or 200 children.If 110 children have taken the meal,how many men will be catered to with the remaining meal ? Choose the correct choice
A) 20	B) 30	C) 40	D) 50	E) 54

Solution: Solution   There is a metal for 200 children. 110 children have taken the meal.   Remaining meal is to be catered to 90 children.   Now, 200 children = 120 men   90 children =( 120/200x90)men= 54 men. Answer 54
Answer: E
How many keystrokes are needed to type numbers from 1 to 1000?
Choose the correct choice.
A) 3001	B) 2893	C) 2704	D) 2890	E) None of these

Solution: Explanatory Answer   While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.   Each of these numbers requires one keystroke.   That is 9 key strokes.   There are 90 two-digit numbers: from 10 to 99.   Each of these numbers requires 2 keystrokes.   Therefore, 180 keystrokes to type the 2-digit numbers.   There are 900 three-digit numbers: from 100 to 999.   Each of these numbers requires 3 keystrokes.   Therefore, 2700 keystrokes to type the 3-digit numbers.   1000 is a four-digit number which requires 4 keystrokes.   Totally, therefore, one requires   9 + 180 + 2700 + 4= 
  9 + 180 + 2700 + 4 = 2_893
2893 keystrokes.   Choice 2893
Answer: B
A man invests in a 16% stock at 128. The interest obtained by him is	Select the correct option:
A) 22.5%  B) 42.5%  C) 12.5%  D) 62.5%  E) 82.5%

Solution: By investing Rs 128, income derived = Rs. 16   By investing Rs. 100, income derived = = Rs.12.5   Interest obtained = 12.5%   Answer: 12.5%
Answer: C
The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is:  Choose one
A) 1/289 B) 289/290 C) 290/289 D) 289 E) None of these

Solution: Let the numbers be a and b. Then,   ab = 17, a = 1 and b = 17   So, 1/a2 + 1/b2 = (a2 + b2)/a2 b2   = (12 + 172)/(1 * 17)2 = 290/289   ANSWER:290/289
Answer: C
In the island of Hanoi is trapped a princess. To rescue her, the prince has to transfer a set of rings
numbered 1 to 7 from tower A to tower C. The rings are stacked one over the other in an order, with 1 at the top and 6 at the bottom, and have to be stacked in the same fashion on tower C. The prince can move only one ring at a time, and can store the rings in a stack, temporarily, in another tower B.Minimum how many moves of rings, between the towers, will it take the prince to arrange the rings in tower C ?	Pick one.
A) 13
B) 14
C) 15
D) 16
E) 17

Solution: As a total of 7 rings are to be transferred, it is mentioned that only 6 rings are present in Tower A. So, either 1 ring is present separately or there are 7 rings itself in tower A. In both cases, answer should be "13".   As a temporary stack can be used, therefore transfer top 6 rings of Tower A(or all 6 rings in case 7th ring is present separately) to Tower B in "Last in first out" order one ring at a time, so that the 6th ring is at the top of the stack in Tower B. .................-> 6 Moves made   Now, place the seventh ring at the bottom of the stack in Tower C.....1 move made here, so total moves till now= 6+1= 
6+1 = 7
7   Again start transferring all 6 rings from Tower B to Tower C keeping the 6th ring above 7th ring n 1st ring at the top. ...........6 moves made here. Total moves made till now= 7+6= 
7+6 = 13
13   13NSWER:13
Answer: A
In how many ways a committee consisting of 5 women and 6 men can be formed from 8 women and 10 men?  Choose the correct choice from the following answers:  A) A)12540  B) B)11450  C) C)11760  D) D)13250  E) E)12450

Solution: Required number of ways = 8117605*10117605 = 8117603*10117604 = 11760   Answer is 11760
Answer: C
Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
Choose the correct option: A) 11/12 B) 13/17 C) 13/19 D) 12/19 E) 11/19

Solution: Let Rex's income = 100, then:   Rex = 100   Paul = 60   Quentin = 48   Sam = 36   Rex gives 60 dollars to sam, so now sam has 96 dollars   Rex gives 40 dollars to Quentin, so now Quentin has 88 dollars   The fraction Q/S = 11/12   11/12NSWER:11/12
Answer: A
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Choose the correct choice from the following.
A) 2 years	B) 4 years	C) 6 years	D) 8 years	E) 10 years

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   ANSWER:6 years
Answer: C
12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
Choose the correct option.
A) 990 B) 495 C) 1980 D) none E) Cannot be determined

Solution: Explanation :   For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495Therefore, we can draw 495 quadrilaterals.   Answer : 495
Answer: B
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 36 sec. What is the length of the platform?
Choose the correct answer.
A) 389 m B) 350 m C) 289 m D) 299 m E) 25 m

Solution: Speed = 300/36= 25/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 25/3   => x = 25 m.   Answer:25 m
Answer: E
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
Choose the correct choice from the following choices: A) 10 and 20 B) 12 and 18 C) 20 and 16 D) 21 and 63 E) 22 and 88

Solution: 16 has only the prime 2 (16=2^4) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.   The answer is 20 and 16.
Answer: C
Find the value of 15 + 2 â€¢ (8 â€“ 3)  Choose the most appropriate option.
A) 25	B) 13	C) 17	D) 24	E) 15

Solution: 15 + 2 â€¢ (8 â€“ 3)   = 15 + 2 (5)   = 15 + 2 *5   = 15 + 10= 
15 + 10 = 25
25   correct answer 25
Answer: A
5 blue marbles, 3 red marbles and 4 purple marbles are placed in a bag. If 4 marbles are drawn without replacement, what is the probability that the result will not be 2 blue and 2 purple marbles? Choose the correct choice from the following.
A) 4/33	B) (5/36)^2	C) 1/2	D) (31/36)^2	E) 29/33

Solution: Answer is 29/33.   The probability of 2 blue and 2 purple marbles selected is 5C2.4C2/12C4 =4/33.   Subtracting the above from 1 we get 29/33 29/33
Answer: E
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Choose the correct choice from the following options.
A) 12/455  B) 3/19  C) 14/160  D) 8/79  E) 2/546

Solution: Explanation:   Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (Â²Câ‚)(â´Câ‚‚)/Â¹âµCâ‚ƒ   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455   12/455nswer: 12/455
Answer: A
A restaurant spends one quarter of its monthly budget for rent and two thrid of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages? Pick one
A) 23.5% B) 50% C) 35% D) 37.5% E) 75%

Solution: Spend on rent = 1/4   Spend on food and beverage= 2/4 of remaining = 2/3*3/4= 1/2   so 1/2= 50.0%   50% is the answer
Answer: B
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 108 km/hr. What is the length of the platform?	Choose the correct choice from the following choices.
A) 229
B) 240
C) 288
D) 480
E) 221

Solution: Speed = 108 * 5/18= 
108 * 5/18 = 30
30 m/sec.   Length of the train= 30 * 20= 
30 * 20 = 600
600 m.   Let the length of the platform be x m . Then,   (x + 600)/36= 30 => x = 480 m.   Answer: 480
Answer: D
One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I. 24
II. 20
III. 5
Choose the correct choice from the following answers.
A) I only	B) II only	C) III only	D) II and III only	E) I, II and II

Solution: The triangle will have a maximum area when it is a right angled triangle   The largest triangle will be formed when 8 and 5 are the base and height of triangle .   Area = 1/2 * 8 * 5= 
1/2 * 8 * 5 = 20
20   There is no lower limit on the area of any triangle whose only 2 sides are known . Area> 0   So we can also have triangle with area= 5   Suppose we want to take 8 as the hypotenuse in the right angled triangle , then one of the other sides(base or height) will be less than 8 .   Hence , product will be lesser than 20 .   Answer II and III only
Answer: D
A man took some money for borrowed, for 3 years the total will be Rs.5000 and 5 years it will be Rs.6000/-. Then how much amount he borrowed? Choose the correct choice from the following answers
A) s.2000/-
B) s.2500/-
C) s.2770/-
D) s.2800/-
E) s.3500/-

Solution: 3 years --------> Rs.5000/-   5 years --------> Rs.6000/-   ~ ~   ------------------------------   2 years ---------> Rs.1000/-   1 year ----------> Rs.500/-   3years * Rs.500/- = Rs.1500/-   P = Rs.5000/- - Rs.1500/- = Rs.3500/-   P = Rs.3500/-   s.3500/-
Answer: E
In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?	Choose the correct choice from the following options.
A) 20	B) 30	C) 24	D) 12	E) 26

Solution: Explanation :   Number of matches won by the team in June: 30% of 60 = 18   After a phenomenal winning streak the average is 50%   Let the team played x matches continuously and won all of them to achieve an average winning percentage of 50%.   So total matches played by the team = (60+x)   Total matches won by the team = (18+x)   Total matches won = 50% of Total matches played   => (18+x) = 50% of (60+x)   => 18+x = (50/100)*(60+x)   => 18+x = (1/2)*(60+x)   => 36+2x = 60+x   => x = 24   Answer : 24
Answer: C
For any 4 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.	Choose the correct choice from the following options:
A) I only B) II only C) I and II only D) II and III only E) None of the above

Solution: Let the 3 numbers be x, y and z.   Question: Which of the following is equivalent to (x + y + z)/3   I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141   II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent   III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent   I onlynswer: I only
Answer: A
A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to
pass a man standing at a crossing.  Choose the correct choice from the following options.
A) 10 seconds  B) 12 seconds  C) 14 seconds  D) 16 seconds  E) None of these

Solution: Explanation:   As we need to get answer in seconds, so never forget to convert speed into meter per second.   Speed = 30 km/hr = 30* 5/18 m/sec   = 25/3 m/sec   Distance = length of train = 100 meter   Required time =   DistanceSpeed=100253=100   ∗   325=12sec   Answer: 12 seconds
Answer: B
In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/4 the number that used Kennedy Airport and 3 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?  Choose the correct choice:
A) 18.6	B) 9.3	C) 6.2	D) 3.1	E) 1.03

Solution: number of   passengers using Kennedy airport = 37/3 =~12.43   Passengers using Miami airport = 12.43/4=~3.1   passengers using logan airport = 3.1/3 =~1.03   so 1.03
Answer: E
In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket inchours, and the hot-water leak alone would fill the same bucket inhhours, wherec < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tookthours to fill the bucket, which of the following must be true?
I. (c/2) < t < (h/2)
II. c < t < h
III. 0 < t < h Choose the correct option.
A) a) I only
B) b) II only
C) c) I and III
D) d) I and II
E) e) III only

Solution: I picked numbers for this problem   c) I and III = 2 hours   H = 3 hours   c) I and III<H   2 people working together formula is   1/c) I and III + 1/H = 1/t   1/2 + 1/3 = 1/t   t = 6/5= 
6/5 = 6/5 = around 1.2
1.2   Substitute the values of c) I and III, H and t in the 3 choices given below   Only 1, 3 are valid.Therefore c) I and III is the best answer
Answer: C
A certain boxer has agreed to pay his opponent a fee of 2.5% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in eight pounds over the specified limit, what was the boxer's purse? Choose the correct option:
A) $65,625 B) $105,000 C) $150,000 D) $131,250 E) $1,050,000

Solution: .025*8= 
.025*8 = 0.2
.2   26250/.2= $131,250   Answer: $131,250
Answer: D
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Choose the correct choice from the following.
A) 74 B) 94 C) 184 D) 364 E) None of these

Solution: EXPLANATION   L.C.M. of 6, 9, 15 and 18 is 90.   Let required number be 90k + 4, which is multiple of 7.   Least value of k for which (90k + 4) is divisible by 7 is k = 4.   Required number = (90 x 4) + 4 = 364.   Answer 364
Answer: D
A triangle having three sides 10 cm, 17 cm, and 21 cm.A square is formed by one side lying on the longest side of the triangle.What is the maximum possible Area of the square found inside the triangle? Choose one
A) 168/29	B) 178/29	C) 188/28	D) 198/28	E) 198/29

Solution: s=1/2(10+17+21)=24   a=84   84=1/2*21*h   h=8   8/21=168/29   168/29NSWER:168/29
Answer: A
The difference between two numbers is 2395. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is  Choose the correct choice from the following answers:
A) 120 B) 239 C) 476 D) 523 E) 526

Solution: Let the smaller number be x.   Then, larger number = (2395 + x)   Therefore 2395 + x = (6x + 15)   ‹=› 5x = 2380   ‹=› x = 476.   ANSWER:476
Answer: C
Five unbiased coin are tossed. What is the probability of getting atmost
one head? Choose the correct answer:
A) 31/24	B) 31/34	C) 31/32	D) 31/35	E) 31/36

Solution: Here n(S)= 2^5   Let E=event of getting atmost one head =   n(E)= 31   P(E)=n(E)/n(S)=31/32   Answer option 31/32)
Answer: C
if 8^25 divided by 7 then what is reminder	Choose the correct choice from the following options:
A) 25	B) 1	C) 0	D) 2	E) 3

Solution: 8^25/7   8 can be written as 7*1+1   (7*1+1)^25/7   (ax+1)^n/a always gives the remainder 1   here a=7,x=1,n=25   Hence remainder is 1   ANSWER:1
Answer: B
An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 4 ?	Pick one:
A) 1/9
B) 1/3
C) 1/2
D) 2/3
E) 5/6

Solution: n(n+1) to be divisible by 4 either n or n+1 must be a multiples of 4.   In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 3, or 4. Thus, the overall probability is 2/4 = 1/2.   Answer: 1/2.
Answer: C
A can do a work in 15 days B in 14 days and C in 16 days . If they work on it together then in how many days required to complete the work?  Options: A) 3360/210 B) 3360/21 C) 3360/674 D) 3360/240 E) 3360/224

Solution: Person ( A ) ( B ) ( 3360/674 ) (A+B+3360/674)   Time - (15) ( 14 ) (16)   Rate - (224) (240) (210) (674)   Work - (3360) (3360) (3360) (3360)   therefore A+B+3360/674 requires (3360/674) days to complete entire work   = 3360/674   Answer is 3360/674
Answer: C