MU-NLPC/Calc-aqua_rat huggingface dataset:
A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 3 games?	Choose the correct choice from the following answers
A) x + 3y/(n + 3) B) x + y/(n + 3) C) (x + 3y)/(n + 3) D) (nx + 3y)/(n + 3) E) (3x + ny)/(n + 3)

Solution: Total points in first n games = nx   Total marks in next 3 games is 3y   So, Average marks in n + 3 games = (nx+3y)/(n+3)   Hence, correct answer will be ((nx + 3y)/(n + 3))
Answer: D
How should a profit of Rs.500 be divided into two partners, if one of them invested Rs.6000 for 5 months and other invested Rs.5000 for 4 months? (in Rs.) Choose the most appropriate option:
A) 1000,5000
B) 3000,2000
C) 500,400
D) 2000,3000
E) 300,200

Solution: ratio come as 3:2, pofit become as 300,200.   ANSW300,200R:300,200
Answer: E
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 7? Select the correct option
A) 180  B) 196  C) 286  D) 324  E) 288

Solution: We have to find the total number of 3-digit odd numbers not having 7 as a digit.   Units digits will be among 1,3,5,9   Tenth digits will be among 0,1,2,3,4,6,5,8,9   Hundredth digits will be among 1,2,3,4,6,5,8,9   So total numbers = 4*9*8= 
4*9*8 = 288
288   Answer : 288
Answer: E
There are two decks of 11 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?  Choose the most appropriate option:  A) 0.23  B) 0.36  C) 0.4  D) 0.42  E) 0.46

Solution: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:   11 = 11   12 = 2*2*3   13 = 13   14 = 7*2   15 = 5*3   16 = 2*2*2   17 = 17   18 = 3*2*3   19 = 19   20 = 5*2*2   Combos that have a 2 and a 3 as factors (first + second card):   12 + anything - 19 of these possibilities (we count 12 + 12 only once)   14 + 15 - 2 of these possibilities   15 + 16 - 2 of these possibilities   15 + 20 - 2 of these possibilities   18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities   Total possibilities that will be a multiple of 6: 42   Total possibilites:   10*10= 
  10*10 = 100
100   Probability= 42/100 = 0.46   Answer:0.46
Answer: E
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?  Choose the correct choice from the following answers
A) 729	B) 362	C) 154	D) 653	E) 234

Solution: The first ring can be worn in any of the 3 fingers (3 ways).   Similarly each of the remaining 5 rings also can be worn in 3 ways.   Hence total number of ways   =3×3×3×3×3×3=36=729   729ns: 729
Answer: A
Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 22,the first number is :	Choices:
A) 22	B) 21	C) 77	D) 99	E) 25

Solution: 25xplanation:   Let the numbers be a,b,c,d   Given, a + b + c = 48, b + c + d = 45   Now, d = 22   thus, b + c + 22 = 45 ⇒ b + c = 23   Putting the value of b + c in a + b + c = 48   a + 23 = 48 ⇒ a = 25   Answer: 25
Answer: E
25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?  Answers.
A) 625 B) 600 C) 576 D) 676 E) 700

Solution: we can go in any bus out of the 25 buses.   Hence He can go in 25 ways.   Since we can not come back in the same bus that he used for travelling,   we can return in 24 ways.   Total number of ways = 25 x 24 = 600   ANSWER:600
Answer: B
if m^3 has 16 factors then m^4 will have how many factors ????? and m is not a prime no. Choose the most appropriate option.
A) 24	B) 25	C) 26	D) 27	E) 28

Solution: 25 m^3 = (3+1)(3+1) = 16   then m^4 = (4+1)(4+1)=25   ANSWER:25
Answer: B
The area of a triangle is with base 3m and height 6m?	Choose the most appropriate option:
A) 88 m2
B) 9 m2
C) 66 m2
D) 77 m2
E) 31 m2

Solution: 1/2 * 3 * 6= 
1/2 * 3 * 6 = 9
9 m2   Answer: 9 m2
Answer: B
If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?	Choose the correct choice from the following answers.
A) 1/12  B) 1/15  C) 1/19  D) 1/13  E) 1/11

Solution: X * (120/100)   ---------------- = 2/15   Y * (75/100)   X/Y = 1/12   1/12nswer: 1/12
Answer: A
How many words can be formed by using all the letters of the word “DAUGHTER” so that vowels always come together & vowels are never together?	Choose the correct choice from the following answers:
A) 5120 B) 1240 C) 4320 D) 6512 E) 1204

Solution: Given word contains 8 different letters   When the vowels AUE are always together we may suppose   them to form an entity ,treated as one letter   then the letter to be arranged are DAHTR(AUE)   these 6 letters can be arranged in 6p6 = 6!   = 720 ways   The vowels in the group (AUE) may be arranged in 3! = 6 ways   Required number of words = 760 * 6 =4320   Ans: 4320
Answer: C
5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.
Choices.
A) 10 B) 7 C) 6 D) 12 E) 13

Solution: 1 man can do the work of 8/5= 
8/5 = 8/5 = around 1.6
1.6 women   equivalent of   3*1.6 + 5= 
  3*1.6 + 5 = 9.8
9.8 women take 10 days   so women needed to do the work in 14 days= [10/14]*9.8   = 7   ANSWER:710/14 *9.8= 
10/14 *9.8 = 7
7   ANSWER:7
Answer: B
A meeting has to be conducted with 6 managers. Find the number of ways in which the managers be selected from among 10 managers, if 2 managers will not attend the meeting together?	Choose the most appropriate option.
A) 120	B) 110	C) 105	D) 140	E) 135

Solution: we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together   so 8C6 + (8C5 * 2C1)   this is   28 + 112= 
  28 + 112 = 140
140   Answer : 140
Answer: D
The first three terms of a proportion are 3, 9 and 12. The fourth term is?  Answers:	A) 22	B) 28	C) 27	D) 36	E) 88

Solution: (9*12)/3= 
(9*12)/3 = 36
36   Answer:36
Answer: D
5000 voted in an election between two candidates.14% of the votes were invalid.The winner won by a margin approximately closer to 15%.Find the number of votes secured by the person
Pick one.
A) 2128  B) 2472  C) 2689  D) 26707  E) 17191

Solution: nvalid Votes = 14 % (5000) = 700   Valid Votes = 5000 - 700= 
5000 - 700 = 4_300
4300= R (say)   Assume the looser got 'L" votes and winner got "W" votes.   W - L = 15% (R)   W + L = R   Solving we get W = 57.5% and L = 42.5%   So Winner got 57.5%(4300) = 2472   Answer:2472
Answer: B
A store reduced the price of all items in the store by 10% on the first day and by another 14% on the second day. The price of items on the second day was what percent of the price before the first reduction took place? Select the correct option
A) 80.0
B) 80.9
C) 77.4
D) 81.1
E) 81.9

Solution: consider price of the all items as $100   after a initial reduction of 10% price becomes = 0.9 *100= 
0.9 *100 = 90
$ 90   after the final reduction of 14% price becomes= 0.86* 90= 
0.86* 90 = 77.4
$ 77.4   price of all items on second day is 77.4% of price on first day   correct answer option 77.4
Answer: C
A contractor undertook to do a certain piece of work in 6 days. He employed certain number of men, but 5 of them being absent from the very first day, the rest could finish the work in 10 days. The number of men originally employed were :
Choose the correct choice from the following choices:
A) 12 B) 10 C) 13 D) 11 E) None of these

Solution: Explanation :   Let there be x men at the beginning. Less men, More days (Indirect Proportion)   12 : 6 :: x : (x - 5) 12 (x - 5) = 6x <=> 6x = 60 x = 10   Answer : 10
Answer: B
Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 3 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?  Answers.
A) 4 minutes	B) 32/7 minutes	C) 192/7 minutes	D) 224/7 minutes	E) 32/5 minutes

Solution: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;   Pipe B can fill the same tank3 times fasterthan pipe A --> the rate of B = 1/32 + 3/32 = 4/32 tank/minute.   Their combined rate = 1/32 + 4/32 = 5/32tank/minute;   Therefore, A and B can fill the tank in 32/5minutes.   Answer: 32/5 minutes
Answer: E
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 70%?
Select the correct option:
A) 6	B) 5	C) 8	D) 9	E) 10

Solution: We need on-time departure rate to be higher than 7/10, so it should be at least 8/11, which means that 8 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then  8-3= 
 8-3 = 5
5 subsequent flights need to depart on-time.   Answer: 5
Answer: B
If 2x+y = 10, 2y+z = 20 and 2x+z = 30. Where x, y,and z are real number. What is the value of 2x ?  Choose the correct choice from the following choices.
A) 3/2  B) sqrt(15)  C) sqrt(6)/2  D) 15  E) 18

Solution: Explanation :   Let, 2x = a, 2y = b and 2z = c   Then from the question:   2x+y = 2x * 2y = ab = 10   Similarly, bc = 20 , ac = 30   ab/bc = 1/2   => a/c = 1/2   and ac = 30   (a/c)*ac = 1/2*30= 
1/2*30 = 15
15   a= sqrt(15)   Answer : sqrt(15)
Answer: B
The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 4. If p is any prime number then f(p)=  Choices:	A) p-1	B) p-2	C) (p+1)/2	D) (p-1)/2	E) 2

Solution: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.   Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).   If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.   Answer: (p+1)/2.
Answer: C
A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $3 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Choose the correct choice:
A) $28  B) $82  C) $110  D) $138  E) $193

Solution: by the question, the equation would be 150 p - 83*150 - 16500 = 0   p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.   solving the equation, we get p = $ 193. Answer $193 for me.
Answer: E
At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 42 liters of forest green to change it to Verdant green?  Answers:
A) 14  B) 12  C) 15  D) 11  E) 10

Solution: 42 liter of Forset green have 24 liter of blue and 18 liter of yellow   Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is   Blue/yellow =24/(18+x) = ¾   54+3x=96 => x =14   14nswer : 14
Answer: A
Insert the missing number
1, 2, 4, 8, 16, 32, 64, ..., 256
Choose the correct choice
A) 128	B) 148	C) 154	D) 164	E) 174

Solution: The sequence is just like multiples of 2..   i.e., 1 = 1   1 * 2= 
1 * 2 = 2
2   2 * 2= 
2 * 2 = 4
4   4 * 2= 
4 * 2 = 8
8   8 * 2= 
8 * 2 = 16
16   8 * 2= 32   32 * 2= 
32 * 2 = 64
64   64 * 2= 
64 * 2 = 128
128   128*2= 
128*2 = 256
256   128NSWER:128
Answer: A
The slant height of a conical mountian is 2.5 km and the area of its base is 1.54 km². The height of the mountain is:  Choose the correct choice from the following options:
A) 2.4 km
B) 2.6 km
C) 4.5 km
D) 5.4 km
E) None

Solution: Sol.   Let the radius of the base be r km. Then,   ∏r² = 1.54 ⇒ r² = [1.54 * 7 / 22= 
1.54 * 7 / 22 = 0.49
0.49 ⇒ r= 0.7 km.   Now, l = 2.5 km, r = 0.7 km.   ∴ h = √(2.5)² = (0.7)² km = √6.25 - 0.49= 
6.25 - 0.49 = 5.76
√5.76 km= 2.4 km   2.4 kmnswer 2.4 km
Answer: A
Which one of the given numbers is completely divisible by 45? Choose the correct choice from the following.
A) 202860  B) 165642  C) 112330  D) 112333  E) None of these

Solution: We know that 45 = 9 × 5 where 9 and 5 are co-prime numbers. Also 9 and 5 are   factors of 45. Hence   if a number is divisible by 5 and 9, the number will be divisible by their product 45 also.   If a number is not divisible by 5 or 9, it is not divisible by 45   You must learn Divisibility Rules to say whether a given number is divisible by another number   Answer is A   without actually performing the division. Please go through divisibility rules before proceeding   further.   112330 is divisible by 5 but not divisible by 9 => 112330 is not divisible by 45   202860 is divisible by 5 and 9 => 202860 is divisible by 45   165642 is not divisible by 5 and 9 => 165642 is not divisible by 45
Answer: A
In a dairy farm, 16 cows eat 16 bags of husk in 16 days. In how many days one cow will eat one bag of husk?	Select.
A) 16 B) 40 C) 20 D) 26 E) 30

Solution: Explanation :   One bag of husk = 16 cows per day   ⇒ 16 × 1 × 16 = 1 × 16 × x   For one cow = 16 days   16nswer : 16
Answer: A
Which of the following must be equal to zero for all real numbers x ?
I. −1x−1x
II. x + (-x)
III. x^0 Choose the correct choice from the following answers:
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II , and III

Solution: I. -1/x will not be 0 for any real number; The value will be undefined if x is 0;   II. The value will be 0 for any real number. (ex.,) 2 + (-2) = 2-2= 
2-2 = 0
0;   III. x^0= 1 for real numbers;   II only.   Ans is (II only)
Answer: B
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 5 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?  Answers.
A) 45  B) 65  C) 77  D) 89  E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 5= 
68 + 5 = 73
73   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 73 + 4= 
73 + 4 = 77
77   77
Answer: C
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?  Choose the correct choice from the following options:
A) 4
B) 8
C) 12
D) 16
E) 20

Solution: 4 pairs = 4*2= 
4*2 = 8
8 people total   8C4= 8!/4!4! = 70 total outcomes   Total – unfavorable = favorable   Unfavorable outcomes   Assuming one pair of twins in the committee, we have two spaces left. Since we plugged a pair of twins in the committee, we have 8-2= 
8-2 = 6
6 people to fill 2 spaces.   6C2= 6!/2!4! = 15 ways to fill the two remaining slots   We only filled the slots with one pair, and we have to account for arrangements of the pairs. Now, we have 4 pairs. 4*15= 60 total arrangements   When we place members into the remaining slots, there may be an additional set of twins. There are 2 remaining slots to which we can fit a pair of twins. If it were one remaining slot, we cannot fit a pair of twins, so we wouldn’t have to account for duplicates.   Now we account for the number of duplicates.   # of duplicates = Total arrangements - # of unique combinations   To find the # of duplicates of twins, we need treat a pair of twins as one unit.   This means the 4 slots are really 2 slots.   Total ways of arranging four pairs of twins in two slots   4P2 = 4*3= 
4*3 = 12
12 total ways   Total # of unique combinations   Choosing two pairs out of 4 pairs= 4C2   = 6   Therefore, # of duplicates = 12 - 6= 
12 - 6 = 6
6 duplicates   70 – 60 + 6= 16   ANS:16
Answer: D
A train is moving at 6/7 of its usual speed. The train is 30 minutes too late. What is the usual time for the train to complete the journey?	Choose one.
A) 1 hour	B) 30 minutes	C) 3 hours	D) 2 hours 30 min	E) 2 hours

Solution: new time = d / (6v/7) = 7/6 * usual time   30 minutes represents 1/6 of the usual time.   The usual time is 3 hours.   The answer is 3 hours.
Answer: C
A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?
Choose the correct choice from the following answers
A) 46  B) 64  C) 164  D) 146  E) 56

Solution: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the 164ombination Formula: n164r= n!/r!(n-r)!   n = 12   r = 3   So, total groups is 121643 = 12!/(3!(12 - 3)!) = 220, and   n = 12 - 4= 
12 - 4 = 8
8   r= 3   for groups without a triangle is 81643 = 8!/(3!(8 - 3)!) = 56,   so, groups with at least 1 triangle = 220 - 56= 
220 - 56 = 164
164   Answer: 164
Answer: C
Helen went to the stationers and bought things worth Euro 50, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Choose the correct choice from the following answers: A) Euro 15 B) Euro 15.7 C) Euro 19.7 D) Euro 44.7 E) None

Solution: Explanation: Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = Euro [50 - (5 + 0.30)= 
50 - (5 + 0.30) = 44.7
Euro 44.70   Answer: Option Euro 44.7
Answer: D
A student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
.	Choose the correct option:
A) 50 B) 80 C) 110 D) 220 E) 360

Solution: 1) preferred one   as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five   choose 2 in first 5 and all 5 from later half..   ways = 5C2 = 10..   total ways = 101103 = 120   ans = 120-10= 
120-10 = 110
110   ANSWER:110
Answer: C
The cricket team of 11members is 25yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?	Choose the correct choice from the following choices.
A) 21	B) 22	C) 23	D) 25	E) 28

Solution: Let the average age of the whole team be x years.   11x - (25 + 28) = 9 (x - 1)   => 11x - 9x = 44   => 2x = 44   => x = 22.   So, average age of the team is 22 years.   22
Answer: B
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 6 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Choose the correct choice from the following answers:
A) 48%
B) 80%
C) 100%
D) 120%
E) 125%

Solution: For A, r=8/2pi. Its capacity = (4pi)^2 * 6= 96pi   For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi   48%/B = 96pi/200pi = 0.48   48%96  /200= 
96  /200 = 12/25 = around 0.48
0.48   48%
Answer: A
What is the chance that a leap year selected at random contains 53 fridays?
Select the correct option:
A) 1/7
B) 2/7
C) 3/7
D) 4/7
E) 5/7

Solution: normal year =365 days   leap year = 366 days   now there are 52 weeks i.e. 364 days+2 odd days   the 2 odd may have Friday over a week has 7 days   so probability = 2/7   ANSWER:2/7
Answer: B
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 4 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 2 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?	Choose the most appropriate option: A) 16:00. B) 18:00 C) 20:00 D) 22:00. E) 24:00.

Solution: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 4 hours   Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 2 hours   Time taken by both buses to meet again in St. Louis will be LCM of 4 and 2 = 4   If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours   16:00.nswer 16:00.
Answer: A
If a trader sold two cars each at $ 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Choose the correct choice from the following answers:
A) 3.44% B) 2.44% C) 6.44% D) 1.44% E) 7.44%

Solution: D   1.44%   SP of each car is $ 325475, he gains 12% on first car and losses 12% on second car.   In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: D
The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Choose the correct choice from the following answers:
A) 40%  B) 45%  C) 50%  D) 60%  E) 70%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length = x .   2   New breadth = 3y.   New area = x x 3y = 3 xy.   2 2   Increase % = 1 xy x 1 x 100 % = 50%.   2 xy   50%
Answer: C
If U is an odd number and V and W are different integers, which of the following must be even?	Choose the correct choice from the following choices: A) UV+UW B) U+VW C) UVW D) U+V+W E) None of these

Solution: Let U = 3.   a. UV + UW   If V = 1 and W = 2 -> UV + UW = 3*1 + 3*2= 
3*1 + 3*2 = 9
9 (Odd)   b. U + VW   If V= 1 and W = 2 -> U+VW = 3 + 1*2= 
3 + 1*2 = 5
5 (Odd)   c. UVW   If V= 1 and W = 5 -> UVW = 1*3*5= 
1*3*5 = 15
15 (Odd)   d. U + V + W   If V= 1 and W = 5 -> U + V + W = 1 + 3 + 5= 
1 + 3 + 5 = 9
9 (Odd)   Answer is None of these.
Answer: E
What is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.  Choose one.
A) 1/144 B) 1/36 C) 1/12 D) 1/16 E) 1/3

Solution: Solution -   Rolling dices is an independent event.   The combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16.   The probability of getting 5 in first attempt is 4/16=1/4.   Probability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS 1/16
Answer: D
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	Select:
A) 16 sec
B) 12 sec
C) 17 sec
D) 21 sec
E) 23 sec

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.   Answer: 12 sec
Answer: B
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: Choose the correct choice from the following answers:
A) 18  B) 24  C) 42  D) 81  E) 28

Solution: Let the ten's and unit's digit be x and 8/x respectively.   Then,   (10x + 8/x) + 18 = 10 * 8/x + x   9x2 + 18x - 72 = 0   x2 + 2x - 8 = 0   (x + 4)(x - 2) = 0   x = 2   So, ten's digit = 2 and unit's digit = 4.   Hence, required number = 24.   ANSWER:24
Answer: B
Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days? Choose the correct choice from the following:	A) 1/5	B) 1/1	C) 1/6	D) 1/3	E) 1/7

Solution: A's one day's work = 1/30   B's one day's work = 1/45   (A + B)'s one day's work = 1/30 + 1/45 = 1/18   The part of the work completed in 3 days = 3 (1/18) = 1/6.   Answer: 1/6
Answer: C