MU-NLPC/Calc-aqua_rat huggingface dataset:
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 64, the dividend is:
Choose the correct choice from the following choices:
A) 10301	B) 10302	C) 10303	D) 10304	E) 10305

Solution: Divisor = (5 * 64)= 
(5 * 64) = 320
320= 10 * Quotient = Divisor   => Quotient = 320/10= 
320/10 = 32
32   Dividend= (Divisor * Quotient) + Remainder   Dividend = (320 * 32) + 64 = 10305.   10305
Answer: E
A dinner has to be hosted with 5 managers.Find the number of ways in which the managers may be selected from among 9 managers,if 2 managers will not attend the meeting together.  Choose the correct choice from the following options.
A) 1.35 B) 2.None of these C) 3.12 D) 4.126 E) 5.15

Solution: 9 managers, but two of them cannot attend the meeting together.   We can split it into two cases.   1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 7 which is 7C5 = 21   2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 7, which is 2C1 X 7C4 = 70.   So, answer is   21 + 70= 
  21 + 70 = 91
91.   Answer : 2.None of these
Answer: B
Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 6 times his original investment. What is the value of n?  Choose the correct answer.
A) 50 years	B) 25 years	C) 62 years 6 months	D) 37 years 6 months	E) 40 years

Solution: Explanatory Answer   Let us say Braun invested $100.   Then, at the end of 'n' years he would have got back $600.   Therefore, the Simple Interest earned = 600 - 100= 
600 - 100 = 500
$500.   We know that Simple Interest= (Principal * number of years * rate of interest) / 100   Substituting the values in the above equation we get 500 = (100 * n * 8) / 100   Or 8n = 500   Or n = 62.5 years.   correct choice is (62 years 6 months)
Answer: C
The cost price of a cow and a horse is 3 lakhs. The cow is sold at 20% profit and horse at 10% loss.Overall gain is Rs.4200. What is the cost price of the cow?
Choose one:  A) 113000  B) 114000  C) 115000  D) 116000  E) 124000

Solution: let costs of cow and horse are x,y so x+y=300000------(1)   (x*120/100)+(y*90/100)=304200   120x+90y=30420000------(2).   solve equations (1) and (2)   x=114000   ANSWER:114000
Answer: B
If u, v and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^(uv)?
I. u+v
II. v^u
III. u^2 * v^2	Choose the correct choice from the following options.
A) I only B) II only C) III only D) I and II E) II and III

Solution: given that p and q are factors of r.   so we can picture it this way r=u*v*n (n-some another factor of r)   so, r^uv= (u*v*n)^uv   I. u+v .since the question is MUST BE TRUE, we eleminate this option   II. (u*v*n)^uv / v^u= integer YII and IIIS!   III.(u*v*n)^uv/ u^2 * v^2 YII and IIIs, since we are said that integer u>1 and integer v>1
Answer: E
A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?	Pick:  A) 1/10  B) 1/5  C) 3/10  D) 2/5  E) 1/2

Solution: We have three units - Tom (T), Mary (M) & the Rest (R).   Total ways of making a community of 3 from 6 people = 6 x 5 x 4 = 120   Now ways the community can be formed with Tom in it and Mary NOT in it:   TRR   RTR   RRT   TRR posb = 1 (way of picking Tom) x 4 (4 people left excluding Tom and Mary) x 3 (3 people left after excluding Tom, Mary and the person selected before) = 12   RTR and RRT have the possibility as TRR. Therefore possibilities the community can be formed with Tom in it and Mary NOT in it = 12 + 12 + 12= 
12 + 12 + 12 = 36
36   Hence probability=36/120=3/10   Option 3/10
Answer: C
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Choose the correct choice from the following choices.
A) 40  B) 28  C) 26  D) 27  E) 21

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40nswer: 40
Answer: A
If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, the cost of the article is?	Choose the correct choice from the following:
A) 127 B) 688 C) 400 D) 121 E) 123

Solution: Let C.P. be Rs. x.   Then, 5% of x = 360 - 340= 
360 - 340 = 20
20   x/20= 20 => x = 400   Answer: 400
Answer: C
Difference between the length &breadth of a rectangle is 15m. If its perimeter is 206 m, then its area is?  Choose the correct choice from the following answers:  A) 1400 m^2  B) 2500 m^2  C) 2520 m^2  D) 1800 m^2  E) 2580 m^2

Solution: Solving the two equations, we get: l = 45 and b = 40.   Area = (l x b) = (45 x 40) m2 = 1800 m^2   1800 m^2
Answer: D
By selling 8 pens for a rupee a woman loses 25%. How many for a rupee should he sell in order to gain 25%? Choose the most appropriate option:  A) 2  B) 14  C) 3  D) 5  E) 6

Solution: 5   75% --- 8   125% --- ?   75/125 * 8 = 5
Answer: D
If the wheel is 10 cm then the number of revolutions to cover a distance of 1056 cm is?  Select:
A) 16.8 B) 26 C) 14 D) 12 E) 91

Solution: 2 * 22/7 * 10 * x = 1056 => x   = 16.8   16.8nswer: 16.8
Answer: A
If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by	Choose the correct choice from the following choices:
A) 25
B) 62
C) 27
D) 19
E) 71

Solution: Explanation:   Let original consumption = 100 kg and consumption = y kg.   So, 100 x 6 = y x 8   y = 75 kg   Reduction in consumption = 25 %.   25NSWER: 25
Answer: A
If the area of circle is 616 sq cm then its circumference?	Choose the correct choice from the following options:  A) 22  B) 88  C) 99  D) 66  E) 41

Solution: 22/7 r2 = 616 => r = 14   2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88.Answer:88
Answer: B
If x+y=25 and x^2y^3 + y^2x^3=25, what is the value of xy?
Choices:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: x^2*y^3 + y^2*x^3=25   => x^2*y^2*(y+x)=25   => x^2*y^2*25=25 [given, x+y=25]   => (xy)^2 = 1   => xy = 1   ANSWER:1
Answer: B
The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.4.50, Rs.5.50, Rs.8.00 and Rs.10.00 each. As Rahul wanted 40 cards, he took five each of two kinds and fifteen each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?  Choose the correct choice from the following choices.
A) 25	B) 20	C) 24	D) 32	E) 30

Solution: Explanation :   Let the four cards be a, b ,c and d. 'x' be the number of notes.   Then, according to the question,   => 5a + 5b + 15c + 15d = 10*x.   => a + b + 3(c+d) = 2 * x . -----------------------------(i)   Since, a + b = 4.5+5.5= 
4.5+5.5 = 10
10.   And,=> c + d = 8+10= 
8+10 = 18
18   Putting these values in (i), we get :-=> 10+ 3 * 18 = 2 * x.   => x =32 .   Answer : 32
Answer: D
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?  Choose one
A) 38 5/7 years
B) 31 5/7 years
C) 81 5/7 years
D) 31 9/7 years
E) 41 5/7 years

Solution: Required Average   = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)   = (134 + 70 + 18)/7 = 31 5/7 years.   Answer:31 5/7 years
Answer: B
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance V that he will have a matched pair?	Options
A) V=2/5	B) V=3/5	C) 1/5	D) 1/2	E) 7/5

Solution: P(both doves) + P(both rabbits) = p(matched pair)   (3/5)*(2/4) + (2/5)*(1/4) = 2/5   Hi How did you get the probability 2/4 and 1/4???   You have 3 doves and 2 rabbits i.e. a total of 5 animals.   The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)   The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)   Similarly,   The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)   The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. V=2/5lso only 4 animals are left to choose from)   Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: A
Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 32 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales?	Choose the correct choice from the following answers:
A) $ 18,687	B) $ 22,000	C) $ 24,000	D) $ 26,000	E) $ 28,000

Solution: Let x be the total sales in $.   For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$   For the remaining (x-11000) $, you get 32% ---> 0.32*(x-11000)   Thus, 0.32*(x-11000) + 2200 = 7300 ----> x= 18,687 $   $ 18,687 is thus the correct answer.
Answer: A
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 200 m is?  Pick one:  A) 299 m  B) 777 m  C) 200 m  D) 100 m  E) 128 m

Solution: 2(l + 200) = 600 => l   = 100 m   Answer:100 m
Answer: D
A 140 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
Choices
A) 41.1 sec	B) 20.2 sec	C) 31.8 sec	D) 43.2 sec	E) none of the above

Solution: Speed = 55 Km/hr   (to convert km/hr in to M/s)   = 55 x 5/18 M/s   43.2 secistance = 140 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )   = 660 m   Time = 43.2 secistance / Speed   = 660 x 18 / (5 x 55)   = 43.2 sec   Ans is :43.2 sec
Answer: D
If S is the sum of the reciprocals of the consecutive integers from 71 to 80, inclusive, which of the following is less than S?
I. 1/7
II. 1/8
III. 1/9
IV. 1/7>S >1/8  Choose one.
A) I  B) IV  C) II  D) III  E) I&II

Solution: Since we summarize the reciprocals from 80 to 71, we can say also that we add ten numbers who are all (with one exception 1/80) greater than 1/80, so that the sum must be greater than 1/8.   On the other side we can say that we add the reciprocals from 71 to 80, so that the sum has to be less than the sum of ten times 1/81.   sum has to be greater than 1/8 and less than 1/7   IV
Answer: B
A ship sails 4 degrees north, then 13 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?  Choose one.
A) STARTED WITH EQUATOR	B) STARTER WITH NORTH POLE	C) STARTER WITH SOUTH POLE	D) STARTER WITH 80 DEGREE NORTH POLE	E) STARTER WITH NORTH OF SOUTH POLE

Solution: Let x = the latitude sought.   Then marking the northings +, and the southings -;   By the statement x + 4 - 13 + 17 - 19 = -11   STARTED WITH EQUATORnd x = 0.
Answer: A
A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 6% special additives while oil B consists of 8% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
Choose the correct choice from the following
A) a.	A – 260	B) b.	B – 280	C) c. C – 290	D) d.	D – 300	E) e.	E – 420

Solution: 6%*x + 8% *(480-x)=30   8.4 = 2 %*x   x=420   e.	E – 420
Answer: E
The product of the digits of the four-digit number E is 36. No two digits of are identical. How many different numbers are possible values of E ?
Select the correct option:
A) 6
B) 12
C) 24
D) 36
E) 48

Solution: The main question here is how can you arrange 4 different digits E. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.   Therefore no of ways to arrange 4 diff. digits is 4! which is 24   hence 24
Answer: C
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is:  Choices
A) 48 runs
B) 50 runs
C) 70 runs
D) 75 runs
E) 80 runs

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 6   = 11x + 66 = 10x + 108   = x = 42.   New average = (x + 6) = 48 runs.   48 runsNSWER 48 runs
Answer: A
In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles as shown below, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?  Choose the correct choice.
A) 1/21
B) 1/7
C) 4/21
D) 10/21
E) 12/21

Solution: She choose a route which allows her to walk fewest number of blocks   there are 2 blocks she will cross towards east moves represented by E,E and there will be 5 blocks she will cross towards south represented by S,S,S,S,S   total number of ways 7!5!2!7!5!2!   there are 4 ways she can cross 2 blocks on av.1 as shown in attached image.   4/21 is Answer 4/21 .
Answer: C
At lovely gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?	Pick.
A) 20	B) 24	C) 36	D) 48	E) 96

Solution: We are given that at lovely gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:   G/8 = integer and G/12 = integer   This means that G is a multiple of both 8 and 12.   We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.   Starting with 8, we have: 8, 16, 24, 32   For 12, we have: 12, 24   For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.   Answer 24.
Answer: B
What is the perimeter of a square with area 9p^2/25 ?  Answers.
A) 3p/4
B) 3p^2/4
C) 12p/5
D) 3p^2
E) 4p/3

Solution: Area of square, (side)^2 = (3p/5)^2   Therefore side of the square = 3p/5   Perimeter of square = 4*side = 4* (3p/5) = 12p/5   Answer is 12p/5.
Answer: C
A certain no. when divided by 35leaves aremainder 25, what is the remainder if the same no.be divided by 15?
Choose the correct choice from the following options.
A) 1
B) 3
C) 4
D) 6
E) 8

Solution: Explanation:   35 + 25= 
35 + 25 = 60
60/15= 
60/15 = 4
4 (Remainder)   4
Answer: C
Ritesh and Co. generated revenue of Rs. 2,500 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?  Choices.
A) 12.5%
B) 20%
C) 25%
D) 50%
E) None of these

Solution: Explanation :   Given, Ritesh and Co. generated revenue of Rs. 2,500 in 2006 and that this was 12.5% of the gross revenue.   Hence, if 2500 is 12.5% of the revenue, then 100% (gross revenue) is:   =>(100/12.5)×2500.   =>20,000.   Hence, the total revenue by end of 2007 is Rs. 10,000. In 2006, revenue grew by Rs. 2500. This is a growth of:   =>(2500/20000)×100.   =>12.5%.   12.5%nswer : 12.5%
Answer: A
Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 37 years, then how old is Chris ?  Choose the correct choice from the following.
A) 7 years	B) 10 years	C) 12 years	D) 13 years	E) 14 years

Solution: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.   (2x + 2) + 2x + x = 37   5x = 35   x = 7   Hence, Chris's age =7 years.   7 yearsnswer : 7 years
Answer: A
A clock shows the time as 12 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? Choices:
A) 45 minutes
B) 55 minutes
C) 35 minutes
D) 30 minutes
E) 40 minutes

Solution: there are 6 hours in between 12 a.m. to 6 p.m.   6*5= 
6*5 = 30
30 minutes.   ANSWER:30 minutes
Answer: D
The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?  Choose the correct choice from the following answers
A) 1288 B) 1299 C) 1000 D) 10000 E) 2887

Solution: 100 * 100= 
100 * 100 = 10_000
10000   125 * 80= 
125 * 80 = 10_000
10000   Answer: 10000
Answer: D
How many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number?
Choose one.
A) 4
B) 9
C) 11
D) 12
E) 15

Solution: The Question basically asks how many positive odd integers less than 90 are odd multiples of 5   So we have 5,15,25,35,45,55,65,75,85   = 9   Ans 9
Answer: B
If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many T digits does this integer consists of? Choose the most appropriate option:
A) 150
B) 339
C) 342
D) 359
E) 362

Solution: Number of single digit integers = 9   Number of 2 digit integers = 99 - 10 + 1= 
99 - 10 + 1 = 90
90   Number of 3 digit integers= 150 - 100 + 1= 
150 - 100 + 1 = 51
51   Number of digits in the integer T= 1*9 + 2*90 + 3*51 = 9 + 180 + 153= 
9 + 180 + 153 = 342
342   Answer: 342
Answer: C
What is the smallest integer y for which 27^y> 3^24?  Choose the correct choice from the following
A) 7
B) 8
C) 9
D) 10
E) 12

Solution: 27^y> 3^24   9onverting into the same bases:   27^y> 27^8   Therefore for the equation to hold true, y> 8 or y= 9   Option 9
Answer: C
A tradesman by means of his false balance defrauds to the extent of 50%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Select the correct option:	A) 120%	B) 125%	C) 150%	D) 100%	E) 115%

Solution: g% = 50 + 50 + (50*50)/100= 
50 + 50 + (50*50)/100 = 125
125%   ANSWER:125%
Answer: B
The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?	Pick one:	A) 10	B) 87	C) 20	D) 72	E) 74

Solution: Let the two numbers be 5x and 6x.   Let the number added to both so that their ratio becomes 7:8 be k.   (5x + k)/(6x + k) = 7/8   42x = 7k => k = 2x.   6x - 5x = 10 => x = 10   k = 2x = 20.   Answer:20
Answer: C
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?  Pick one.
A) 11	B) 16	C) 77	D) 88	E) 99

Solution: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4   Suppose Tanya takes x days to do the work.   5:4 :: 20:x => x= 16 days.   Hence, Tanya takes 16 days to complete the work.   Answer: 16
Answer: B
If the charge of staying in a student youth hostel $18.00/day for the first week, and $15.00/day for each additional week, How much does it cost to stay for 23 days?
Select the correct option.
A) $336  B) $289  C) $282  D) $274  E) $286

Solution: Total number of days of stay = 23   Charge of staying in first week = 18*7= 
18*7 = 126
126 $   Charge of staying for additional days=(23-7)*15 = 16*15= 
16*15 = 240
240 $   Total charge=126 +240= 
126 +240 = 366
366$   $336nswer $336
Answer: A
A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make ? Pick:	A) 40	B) 54	C) 45	D) 39	E) None

Solution: Answer   Let number of toys be N.   More hours, More toys (Direct proportion)   2 : 80 : : 1 : N   ⇒ N = 80/2= 
80/2 = 40
40 toys   Correct Option: 40
Answer: A
In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Select:
A) 120  B) 125  C) 153  D) 200  E) 250

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 â€“ 82= 18%    850 * 18/100= 
 850 * 18/100 = 153
153   120NSWER 120
Answer: A
When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5? Select the correct option:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?   Putting a value say x = 24 we get remainder as 24 when divided by 61.   When 24 divided by 5 we get 4 as remainder.   4 is the answer.
Answer: C
If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 11), what is the value of x? Select.
A) 9 B) 11 C) 13 D) 15 E) 17

Solution: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 11)   2^x - 2^(x-2) = 3. 2^11   Hence x = 13.   Answer is 13
Answer: C
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?  Answers
A) 2 2 1/8 kmph B) 2 3 1/2 kmph C) 4 2 1/2 kmph D) 2 2 1/2 kmph E) 2 2 4/2 kmph

Solution: 100 --- 10 2 2 1/2 kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 1/2 kmph   Answer:2 2 1/2 kmph
Answer: D
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?	Choose one:
A) 6400 B) 2777 C) 2666 D) 2888 E) 1671

Solution: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,   (x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508   28x - 22x = 350800 - (13900 * 22)   6x = 45000 => x = 7500   So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.   6400nswer: 6400
Answer: A
Three cannons are firing at a target. If their individual probabilities to hit the target are 0.9, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94  Choose the correct choice from the following answers.
A) 0.06	B) 0.12	C) 0.21	D) 0.29	E) 0.94

Solution: The probability that eachdoesn'thit is: 0.1, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:   .9*.7*.8 = 0.06.   Option: 0.06
Answer: A
A can finish a piece of work in 5 days. B can do it in 10 days. They work together for 1 day and then A goes away. In how many days will B finish the work? Choose the correct choice from the following answers: A) 8 days B) 5 days C) 6 days D) 7 days E) 9 days

Solution: 1/5 + (1 + x)/10 = 1 => x = 7 days   Answer: 7 days
Answer: D
How many two letter words are formed using the letters of the word MICKY?
Choose one:	A) 28	B) 21	C) 26	D) 20	E) 29

Solution: The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is 5P2   = 5 * 4= 
5 * 4 = 20
20.   Answer: 20
Answer: D
A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
Choose the correct option:
A) 70 B) 560 C) 630 D) 1,260 E) 1,980

Solution: Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 7 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor)   = 17C3 - 10C3 = 680 - 120= 
680 - 120 = 560
560   ANSWER:560
Answer: B
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 402 to 500 inclusive? Pick
A) 14,550  B) 18,550  C) 22,550  D) 26,550  E) 30,550

Solution: 2 + 4 + 6 + 8 +...+ 100 = 2550   402 + 404 + ... + 500 = 50(400) + (2+4+...+100) = 20,000 + 2550 = 22,550   The answer is 22,550.
Answer: C