MU-NLPC/Calc-aqua_rat huggingface dataset:
In a certain game of dice, the player’s score is determined as a sum of four throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 26 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?  Pick:
A) 41/50
B) 1/221
C) 1/1296
D) 1/84
E) 1/42

Solution: Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6+6= 
6+6+6+6 = 24
24, because if he gets even one less than that so 23, someone can get 24 and Jim will get nothing.   P(24)=1/6^4=1/1296.   Answer: 1/1296.
Answer: C
If each side of a square is increased by 25%, find the percentage change in its area?	Choose the correct choice.
A) 28.88  B) 56.25  C) 22.89  D) 29.18  E) 21.21

Solution: let each side of the square be a , then area = a x a   As given that The side is increased by 25%, then   New side = =   New area =   increased area=   Increase %= % = 56.25%   Answer: 56.25
Answer: B
A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?	Pick.
A) 3 days  B) 4 days  C) 5 days  D) 6 days  E) 7 days

Solution: Explanation:   To calculate the answer we need to get 1 man per day work and 1 woman per day work.   Let 1 man 1 day work =x   and 1 woman 1 days work = y.   => 6x+5y = 1/6   and 3x+4y = 1/10   On solving, we get x = 1/54 and y = 1/90   (9 men + 15 women)'s 1 days work =   (9/54) + (15/90) = 1/3   9 men and 15 women will finish the work in 3 days   Option 3 days
Answer: A
Machine E and machine B are each used to manufacture 660 sprockets. It takes machine E 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine E. How many sprockets per hour does machine E produces?  Choices.
A) 6
B) 6.6
C) 60
D) 100
E) 110

Solution: I think the correct answer is A.   Machine E produces at a speed of E sp/hour and B at a speed of B sp/hour.   so, 660/E=(660/B)+10 and E=1,1 E--->1,1*660=660+11E--->6=6, so answer 6 is correct
Answer: A
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?	Choose the correct option:
A) 144 B) 152 C) 90 D) 168 E) 176

Solution: The first digit can be filled in 6 ways   For second digit , it can either be 0 or 1   90ase 1 -   If second digit is 1 ,Third digit can take 8 values   number of codes = 6 * 1 * 8= 
6 * 1 * 8 = 48
48   90ase 2 -   If second digit is 0,Third digit can take 7 values ( Third digit can't be zero)   number of codes= 6 * 1 * 7= 
6 * 1 * 7 = 42
42   Total number of codes= 90   Answer 90
Answer: C
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is -.
Choose the correct choice.
A) 25/42 B) 9/20 C) 10/23 D) 41/42 E) 1/42

Solution: Total fruits = 9   Since there must be at least two apples,   (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.   25/42NSWER:25/42
Answer: A
Bilal and Ahmed play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Bilal goes first, which of the following is a value of n such that Ahmed can always win no matter how Bilal plays?
Pick one:  A) 7  B) 10  C) 11  D) 12  E) 16

Solution: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).   Consider n=6, no matter how many stick will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.   The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.   Answer: 12.
Answer: D
There are five different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
Choose the correct option
A) 96
B) 48
C) 64
D) 24
E) 8

Solution: Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1= 
3*2*1 = 6
6 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2*2= 16). So we have 6*16= 
6*16 = 96
96.   Please correct me if im wrong.   96nswer 96.
Answer: A
81, 64, 27, 16...	Choose one
A) 12 B) 4 C) 9 D) 3 E) 1

Solution: 81/3= 
81/3 = 27
27   64/4= 
64/4 = 16
16   27/3= 
27/3 = 9
9   ANSWER: 9
Answer: C
The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.99 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?	Options.
A) $1.63
B) $1.64
C) $1.68
D) $1.72
E) $1.79

Solution: Average price = (550*1.99)+(270*1.38)/550+270=1.79 (Approx)   Answer $1.79
Answer: E
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Select:
A) 2 sec
B) 12 sec
C) 24 sec
D) 50 sec
E) 36 sec

Solution: Explanation:   Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:36 sec
Answer: E
Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $12,000 and the marginal cost is $200, and the total cost is $16,000, what is the value of n? Choose the correct choice from the following:	A) 20	B) 50	C) 60	D) 80	E) 100

Solution: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $12,000 + n * $200 --> n = 20.   20nswer: 20.
Answer: A
A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?	Choose the correct choice from the following answers
A) 53	B) 50	C) 60	D) 79	E) 80

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 8) km/hr.   x - 8 = 45 => x = 53 km/hr.   53nswer: Option 53
Answer: A
A shop owner sells 110 eraser and gains SP of 22 metres. Find the gain %?
Choose the correct choice from the following options:
A) 25%	B) 35%	C) 27%	D) 23%	E) 32%

Solution: Gain=22 orangesTotal 110 orangesCP 110-22= 
110-22 = 88
88(22/88)*100=25%25%ns 25%
Answer: A
What number is 75 more than three-fourth of itself? Select
A) 138
B) 225
C) 300
D) 324
E) 336

Solution: 3/4x+75= x   That means 75=1/4x   x= 75*4= 
75*4 = 300
300   300 is the answer
Answer: C
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is
Choose the correct choice from the following choices:  A) 51:52  B) 52:53  C) 53:54  D) 54:55  E) None of these

Solution: Explanation:   Let the Cost price of article is Rs. x   Required ratio =   104% of x/ 106% of x   =104/106=52/53=52:53   Option 52:53
Answer: B
If c and d are both negative and cd < d^2, which of the following must be true?
Choose the correct choice from the following answers:  A) c < d < c^2 < d^2  B) c < d < d^2 < c^2  C) d < c < c^2 < d^2  D) c^2 < d^2 < d < c  E) d^2 < c^2 < d < c

Solution: Because cd <d^2 and both are negative, I thought c < d. So I crossed off answers c), d), and e).   And because c < d , c^2 < d^2   ans d < c < c^2 < d^2
Answer: C
The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the age of Mary.  Answers:
A) 11yrs
B) 12yrs
C) 13yrs
D) 14yrs
E) 15yrs

Solution: a:m=4:7   let the ages of a & m be x &22-x   x/22-x=4/7   x=8   a=8yrs   m=14yrs   ANSWER:14yrs
Answer: D
How much time will take for an amount of Rs. 400 to yield Rs. 81 as interest at 4.5% per annum of simple interest?  Choose the correct answer.
A) 4 1/2 years  B) 6 1/2years  C) 7 1/2years  D) 12 1/2years  E) 15 1/2years

Solution: Time = (100 * 81) / (400 * 4.5) = 4 1/2years   4 1/2 yearsNSWER:4 1/2 years
Answer: A
After replacing an old member by a new member, it was found that the average age of five numbers of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?
Choose the correct choice from the following answers
A) 2 years
B) 4 years
C) 8 years
D) 15 years
E) NOne

Solution: Sol.   Age decrease = (5 × 3) years = 15 years.   So, the required difference = 15 years.   Answer 15 years
Answer: D
Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(3a) if a is even. Then (2#3) + (2#3) – (3#3) is equal to Choose the most appropriate option:
A) 64 B) 82 C) 128 D) 729 E) 1522

Solution: Answer:   3^6 + 3^6 - 3^6 = 3^6 = 729   ANs 729
Answer: D
What is the area of a square field whose diagonal of length 20 m?	Pick
A) 300 sq m	B) 250 sq m	C) 200 sq m	D) 400 sq m	E) 800 sq m

Solution: d2/2 = (20 * 20)/2= 
(20 * 20)/2 = 200
200   ANSWER:200 sq m
Answer: C
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?	Select:  A) 430  B) 570  C) 480  D) 520  E) 550

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172   => 4x = 1720 => x = 430.   430NSWER:430
Answer: A
If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 1. Pick one:
A) 8
B) 5
C) 2
D) 3
E) 4

Solution: 6 * 15 * 1 = (√(6 + 2)(15 + 3) )/ (1 + 1)   = (√8 * 18) / 2   = (√144) / 2   = 12 / 6= 
12 / 6 = 2
2   Answer is 2.
Answer: C
A certain school implemented a reading program for its students, with the goal of getting each student to read 6 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?	Choose one:	A) 20cs	B) cs/2	C) 72cs	D) (2cs)/12	E) (24c)/s

Solution: Ans: 72cs   Solution: simple multiplication s students , c classes , 6 books/ month= 72 books a year   total number of books = 72cs
Answer: C
Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 20 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?
Answers:
A) a) 6  B) b) 8  C) c) 10  D) d) 12  E) e) 15

Solution: Gear L -- 20 rotations per 60 seconds -- 2 rotation per 6 seconds.   Gear R -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.   First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 2 rotations   Hence every 6 seconds the difference between the number of rotations of R and L gear is 2 units.   Required net difference should be 6 rotations => 3 (6 seconds later) ==> 18 seconds.   a) 6nswer: a) 6
Answer: A
In one hour, a boat goes 11 km along the stream and 3 km against the stream. the sped of the boat in still water (in km/hr) is :
Answers:	A) 3	B) 5	C) 7	D) 9	E) 10

Solution: Solution   Speed in still water= 1/2(11+3) km/hr= 7kmph. Answer 7
Answer: C
Given that X and Y are events such that
Z(X)= 0.02
Z(Y)=0.10
Z(XnY)=0.10
Z(X|Y)=
find Z (X|Y) and Z(X|Y)  Choose one:
A) 1/5
B) 1/6
C) 1/6
D) 1/4
E) 1/2

Solution: Here, X and Y are events   Z(X|Y) = Z(XnY)/Z(Y) = 0.10/0.10= 
0.10/0.10 = 1
1   Q(G|H)= Z(XnY)/Z(X) = 0.4/0.02 = 1/5   1/5nswer is 1/5
Answer: A
Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 16 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils?  Pick:	A) 0.75	B) 1.2	C) 1.8	D) 2.4	E) 4.25

Solution: Say the cost price of 80 pencils was $80 ($1 per pencil) and the selling price of 1 pencil was p.   Selling at a loss: 80 - 80p = 16p --> p = 5/6.   (cost price)/(selling price) = 1/(5/6) = 6/5 = 1.2.   Answer: 1.2.
Answer: B
Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 97% water by weight. What is the new weight of the cucumbers, in pounds?	Select:
A) 2  B) 33  C) 92  D) 96  E) 98

Solution: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 97% water and 3% of non-water, so now 1 pound of non-water composes 3% of cucucmbers, which means that the new weight of cucumbers is 1/0.03=34 pounds.   Answer: 33.
Answer: B
Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many E applicants majored in political science and had a GPA higher than 3.0?  Choose one.
A) 5	B) 10	C) 15	D) 25	E) 35

Solution: Total applicants = 40   Political science = 15 and Non political science = 40 - 15= 
40 - 15 = 25
25   GP5 > 3.0= 20 and GP5 <= 3.0 = 20   10 Non political science students had GP5 <= 3.0 --> 15 Non political science students had GP5 > 3.0   GP5 > 3.0 in political science = Total - (GP5 > 3.0 in non political science) E= 20 - 15= 
20 - 15 = 5
5   5nswer: 5
Answer: A
One night a certain hotel rented 2/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
Choose the correct choice from the following options.
A) 20% B) 25% C) 33% D) 36% E) 40%

Solution: The rooms which were not rented is 3/5   The A33% rooms which were not rented is (1/3)*(3/5) = 1/5   The percentage of unrented rooms which were A33% rooms is (1/5) / (3/5) = 1/3 = 33%   The answer is 33%.
Answer: C
A can do a job in 30 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?	Choose the correct choice from the following options:
A) 14 days
B) 26 days
C) 30 days
D) 31 days
E) 39 days

Solution: 30 days   1/30 + 1/30 = 1/15   15*2= 
15*2 = 30
30 days
Answer: C
If [x] is the greatest integer less than or equal to x, what is the value of [-5.6]+[3.4]+[12.7]?
Choose the correct choice from the following
A) 3 B) 5 C) 7 D) 9 E) 10

Solution: You are asked what the closest lesser integer value to [x] is.   [-5.6] = -6.0   [3.4] = 3.0   [12.7] = 12.0   Therefore , answer is: -6.0 + 3.0 + 12.0= 
-6.0 + 3.0 + 12.0 = 9
9.0   Option D.
Answer: A
In how many different number of ways the letters of the word 'ENGINEERING' can be arranged Choose the correct choice from the following:
A) 276800	B) 277000	C) 277200	D) 277400	E) 278400

Solution: 11!/(3! × 3! × 2! × 2! × 1!)   = (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 3 × 2 × 2 × 2 × 1)   = 11 × 10 × 8 × 7 × 5 × 3   = 277200   277200)
Answer: C
If x < y < 0, which of the following must be true? Choose the most appropriate option:
A) x/y is a negative integer
B) xy is a negative integer
C) x+y is a negative integer
D) x-y is a positive integer
E) (-x)+ (-y) is positive integer

Solution: Given x, y are less than 0. So both will be negative integers   negative + negative = negative   negative * negative = positive   negative / negative = positive   x-y is false since x<y eg. x=-2, y=-1 then -2-(-1)=-1   So, option (-x)+ (-y) is positive integer is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)   Answer : (-x)+ (-y) is positive integer
Answer: E
If W is an integer greater than 6, which of the following must be divisible by 3? Choices
A) W(W+1)(W-4) B) N(N+2)(N-1) C) N(N+3)(N-5) D) N(N+4)(N-2) E) N(N+5)(N-6)

Solution: Now take W = 3k , W = 3k+1 W = 3k+2..put in all the choices. If by putting all the values of W we get it is divisible by 3, then it is correct answer choice.   A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: A
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?  Pick one
A) 81:121  B) 81:122  C) 81:129  D) 81:120  E) 21:121

Solution: Ratio of the sides = ³√729 : ³√1331   = 9 : 11   Ratio of surface areas = 92 : 112   = 81:121   81:121nswer: 81:121
Answer: A
The price of a table is marked at $12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it? Choose the most appropriate option:  A) 8721  B) 2304  C) 7720  D) 6221  E) 7493

Solution: 8721   8721   8721ctual price = 95% of 90% of 85% of $12000   = 95/100 * 90/100 * 85/100 * 12000= 
95/100 * 90/100 * 85/100 * 12000 = 8_721
$8721.
Answer: A
Difference between two numbers is 4, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?	Select the correct option
A) 5,9 B) 7,9 C) 9,8 D) 11,12 E) 13,3

Solution: Explanation:   x – y = 4   4x – 6y = 6   x = 9 y = 5   5,9)
Answer: A
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?  Select the correct option:  A) 50  B) 72  C) 84  D) 90  E) 108

Solution: A is the answer....   D = TS where D=distance, T=Time and S=Speed   To travel half distance, (2+2T) = 8T ==> T = 1/6 ==> 10 minutes   To travel double distance, 2(2+2T) = 8T ==> 1 ==> 60 minutes   Difference, 50 minutes   50
Answer: A
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?	Choose the correct choice from the following choices:
A) 16 km/hr
B) 17 km/hr
C) 60 km/hr
D) 15 km/hr
E) 19 km/hr

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer: 60 km/hr
Answer: C
An investment of $3000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $3000 increased to $12000 by earning interest. In how many years after the initial investment was made the $3000 have increased to $24000 by earning interest at that rate?
Pick:  A) 16  B) 22  C) 20  D) 18  E) 30

Solution: In 12 years the investment quadrupled (from $3,000 to $12,000).   Thus, at the same rate compounded annually, it would need additional   12/2= 
  12/2 = 6
6 years to double (from $12,000 to $24,000).   Therefore, 12+6=18 years are needed $3,000 to increase to $24,000.   Answer: 18.
Answer: D
John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $15, what was the price before the first discount? Choose the correct answer:  A) $45.10  B) $34.31  C) $28.44  D) $26.66  E) $65.23

Solution: let x be the price before the first discount. The price after the first discount is   x - 25%x (price after first discount)   A second discount of 25% of the discounted price after which the final price is 15   (x - 25%x) - 25%(x - 25%x) = 15   Solve for x   x = $26.66   correct answer $26.66
Answer: D
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?  Select the correct option:
A) 8 hrs B) 6 hrs C) 7 hrs D) 3 hrs E) 9 hrs

Solution: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20   (A + C)'s 1 hour work = (1/12 + 1/20) = 2/15   Part filled in 2 hrs = (3/20 + 2/15) = 17/60   Part filled in 6 hrs = 3 * 17/60 = 17/20   Remaining part = 1 - 17/20 = 3/20   Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.   Total time taken to fill the tank = (6 + 1)= 
(6 + 1) = 7
7 hrs.   Answer: 7 hrs
Answer: C
(3X+2)(2X-5)=AX^2+ KX+N;
THEN WHAT IS THE VALUE OF A-N+K? Choose the most appropriate option.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: (3x+2)(2x-5)=6x^2-11x-10   So,A=6, K=-11, N=-10   Finally,   A-N+K=6-(-10)+(-11)   =6+10-11= 
6+10-11 = 5
5   ANSWER:5
Answer: B
when W is divided by 14, the reminder is 0. if W is three more than it value and when divided by 9 its remainder is 0. what is the value of W ? Pick.
A) 42  B) 14  C) 28  D) 30  E) 70

Solution: W is divided by 14 so that is multiple of 14 as 14,28,42...   W+3 is divided by 9 the remainder is 0 so it is divisible by 9. Consider from option let us take the number is 42 it is divisible by 14 but 42+3 is divisible by 9 so ans is 42
Answer: A
If 20 men can build a water fountain 56 metres long in 21 days, what length of a similar water fountain can be built by 35 men in 3 days? Choose one.
A) 10 m	B) 14 m	C) 17 m	D) 19 m	E) 20 m

Solution: Explanation :   Let the required length be x metres   More men, More length built (Direct Proportion)   Less days, Less length built (Direct Proportion)   Men 20: 35   Days 21: 3 : : 56 : x   Therefore (20 x 21 x x)=(35 x 3 x 56)   x=(35 x 3 x 56)/420=14   Hence, the required length is 14 m.   Answer : 14 m
Answer: B
A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Choose the correct option.
A) 3 days
B) 4 days
C) 5 days
D) 6 days
E) None of these

Solution: Explanation:   1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days   ANSWER IS 4 days
Answer: B
A password for a computer uses five digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
Select the correct option
A) 1/32 B) 1/16 C) 1/8 D) 2/5 E) 1/2

Solution: Favorable outcomes will be obtained by making Password using {0, 2, 3, 5, 7} i.e. 5 digits   Total Such Passwords = 5*5*5*5*5 = 5^5   Total Possible Password = 10*10*10*10*10 = 10^5   Probability = (5^5) / (10^5) = 1/2^5 = 1/32   1/32nswer: option 1/32
Answer: A
A truck driver starts with the speed of 70 kmph with the truck driver decreasing speed every two hours by 10 kmph. The truck driver's speed does not drop below 50 kmph. In how many hours will it take the truck driver to travel 500 kms? Choose the correct choice from the following answers:
A) 480 minutes B) 492 minutes C) 504 minutes D) 528 minutes E) 540 minutes

Solution: Distance covered in first two hours = 70 Ã— 2 = 140 km   Distance covered in next two hours = 60 Ã— 2 = 120 km   Distance covered in next two hours = 50 Ã— 2 = 100 km   Distance covered in next two hours = 50 Ã— 2 = 100 km   Distance covered in first eight hours    140 + 120 + 100 + 100= 
 140 + 120 + 100 + 100 = 460
460 km   Remaining distance= 500 â€“ 460 = 40 km.   Now, this distance will be covered at the speed of 50 km/hr.   âˆ´ Time taken = 40â„50 = 4â„5 hour.   Total time= 8 + 4â„5 = 8 4â„5 hour   Answer 528 minutes
Answer: D
In a game, a player can win by getting five consecutive tails in six throws of a coin. What is the probability of winning if the player gets a tail on the first throw?	Choose the correct answer.
A) 1/32
B) 1/16
C) 3/16
D) 1/8
E) 3/8

Solution: The only way to win is to get a tail on each of the next four throws.   P(four tails)=(1/2)^4=1/16   The answer is 1/16.
Answer: B