MU-NLPC/Calc-aqua_rat huggingface dataset:
BIRLA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Choose one.
A) 16	B) 64	C) 256	D) 576	E) 4096

Solution: MAGOOSHOFFICIAL SOLUTION:   BIRLA company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.   N = 4*4*4*4 = 16*16= 
16*16 = 256
256   Answer= (256)
Answer: C
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder  Choose the correct option
A) 1235 B) 1345 C) 1450 D) 1567 E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that y > x or x > 0?	Choose the most appropriate option:
A) 7/8	B) 5/6	C) 3/8	D) 1/2	E) 3/4

Solution: The line y=x divides the circle into two equal areas.   All the points above the line y=x satisfy the condition that y > x.   All the points to the right of the y-axis satisfy the condition that x > 0.   The union of these two areas is 7/8 of the circle.   The answer is 7/8.
Answer: A
11 is subtracted from 40% of a number and results is 23. What is the number? Choose the most appropriate option:
A) 160 B) 92 C) 88 D) 85 E) 34

Solution: (40/100) * X â€“ 11 = 23   4X = 340   X = 85   Answer:85
Answer: D
22
a2
+ 3b
____
80
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ?  Choose the most appropriate option.
A) 2	B) 7	C) 9	D) 11	E) 14

Solution: Adding the digits in unit's place , 2+ 2 + b = 10 (Since a and b are positive single digits )   => b = 6   Now adding the digits in ten's place , 2+a + 3 + 1= 8 (1 has been carried over from unit's place addition)   => a= 2   a +2= 
 +2 = 2
2+2*6= 
2+2*6 = 14
14   Answer 14
Answer: E
The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?  Choose the correct choice from the following choices:
A) 24  B) 26  C) 27  D) 29  E) 30

Solution: 5:3:4   Total parts = 12   12 parts --> 108   1 part ---->9   The second number of the three numbers is = 3   3 parts ----> 27   27
Answer: C
96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part? Pick one
A) 42 B) 56 C) 74 D) 36 E) 55

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 96= 
7/16 * 96 = 42
42   42NSWER 42
Answer: A
A sum of Rs.5000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.	Pick.
A) 2888
B) 3120
C) 2877
D) 2999
E) 3250

Solution: Let A be the amount received at the end of the three years.   A = 5000[1 + 10/100][1 + 20/100][1 + 25/100]   A = (5000 * 11 * 6 * 5)/(10 * 5 * 4)   A = Rs.8250   So the interest = 8250 - 5000 = Rs.3250   Answer: 3250
Answer: E
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 30%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?	Choose the correct choice from the following answers
A) 100% decrease  B) 60% decrease  C) 40% decrease  D) 40% increase  E) 50% increase

Solution: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 30%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer 60% decrease.
Answer: B
In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 5 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?	Choose the correct choice from the following answers:	A) 168.	B) 80.	C) 56.	D) 48.	E) 64.

Solution: Bed = Select 1 out of 4 = 4C1 = 4   Shelf = Select 1 out of 2 = 2C1= 2   Chair (5)+ Closet (3) = Total 8 = Select 1 out of 8 = 8C1   Possible combinations to chooseB64.D*SH64.LF*(CHAIR+CLOS64.T)=4*2*8= 
4*2*8 = 64
64 ways   ANSW64.R IS 64.
Answer: E
For a,e,d are the positive integers, and d|a means that “a is divisible by d”, if d|ae, which of the following must be true?  Choose the most appropriate option:
A) d|a  B) d|e  C) d|2ae  D) d|(a+e)  E) d|(a-e)

Solution: d/a means a is divisible by d   d/ae means ae divisible by d.   all are integers so ,   if ae is divisible by d,   1 a can be divisible by d   or   2 e can be divisble by d.   so the question stem asks must true.   so option a and b are could but not must.   option c is 2ae divisible by d. if ab is divisible by d then 2ae is divisible by d.   option d and e we can't predict.   so option d|2ae is correct.
Answer: C
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8600 for a computer table, then what was the cost price of the computer table?
Answers.
A) Rs.6289	B) Rs.6298	C) Rs.6290	D) Rs.7166	E) Rs.7708

Solution: CP = SP * (100/(100 + profit%))   = 8600(100/120) = Rs.7166.   Answer: Rs.7166
Answer: D
How many two-digit numbers yield a remainder of 2 when divided by both 5 and 16?	Choose the correct choice from the following:	A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Easier to start with numbers that are of the form 16p+2 ---> 18,34,50,66,82,96.   Out of these,there is only one number (82) is also of the form 5q+2. Thus 1 is the answer. 1 is the correct answer.
Answer: B
A committee has 5 men and 6 boys. What are the number of ways of selecting 2 men and 3 boys from the given committee?	Select:
A) A)165 B) B)178 C) C)180 D) D)200 E) E)210

Solution: Explanation:   The number of ways to select two men and three boys = âµCâ‚‚ * â¶Câ‚ƒ   = (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)= 
(5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 200
200   200)
Answer: D
Two taps A and B can fill a cistern in 12 minutes and 18 minutes respectively. They are turned on at the same time. If the tap A is turned off after 4 minutes, how long will tap B take to fill the rest of the cistern ?
Answers.
A) 8 min.  B) 9 min.  C) 10 min.  D) 7 min.  E) None of these

Solution: In one min, (A + B) fill the cistern = 1⁄12 + 1⁄18 = 5⁄36th   In 4 min, (A + B) fill the cistern = 5⁄36 × 4 = 5⁄9th   Rest part = 1 - 5⁄9 = 4⁄9th   ∵ 1⁄18th part is filled by B in one min.   ∴ 4⁄9th part is filled by B in 18 × 4⁄9 = 8 min   8 min.nswer 8 min.
Answer: A
Two trains 160 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Choose the correct choice from the following answers.
A) 10.52 sec B) 18.8 sec C) 14.52 sec D) 10.8 sec E) 11.52 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 160 + 160= 
160 + 160 = 320
320 m.   Required time= 320 * 9/250 = 288/25= 
288/25 = 288/25 = around 11.52
11.52 sec.   Answer: 11.52 sec
Answer: E
What is the maximum number of points that 10 circles of different radii intersect?
Choose the correct choice.
A) 24	B) 26	C) 33	D) 90	E) 100

Solution: the maximum number of points that two circles intersect is two.   therefore, each of these 10 circles intersect two point with each of the other 9 circles.   as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.   2∗(10!)/(2!∗10!)=90   Answer: 90
Answer: D
A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 700,000? Choose the correct option.
A) 60  B) 100  C) 180  D) 240  E) 300

Solution: The first digit and last digit are the same so the only possibility is 8.   The second and third digits can be any number from 0 to 9.   The total number of palindromic integers is   1*10*10= 
  1*10*10 = 100
100   The answer is 100.
Answer: B
Which of the following is the full form of the term SLR as used in the banking sector?  Select: A) Social Lending Ratio B) Statutory Liquidity Ratio C) Scheduled Liquidity Rate D) Separate Lending Rate E) None of these

Solution: Answer:Statutory Liquidity Ratio
Answer: B
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 36 minutes. The waste pipe can empty the full cistern in?  Select the correct option
A) 8.2
B) 7.2
C) 6.2
D) 9.2
E) 5.2

Solution: 1/10 + 1/15 - 1/x = 1/36   x = 7.2   Answer:7.2
Answer: B
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Choose the correct answer
A) 300	B) 340	C) 350	D) 320	E) 310

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.   Answer: Option 350
Answer: C
If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 5 m of the same rod? Choose the correct choice from the following choices:
A) 22.8 kg B) 25.6 kg C) 19 kg D) 26.5 kg E) None of these

Solution: Explanation :   Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)   => 11.25 : 5 :: 42.75 : x   => 11.25 x x = 5 x 42.75   => x = (5 x 42.75) / 11.25   => x = 19   Answer : 19 kg
Answer: C
It takes 80 identical printing machines 5 hours to print 200,000 posters. How long would it take 50 of these machines to print the same total? Choices:
A) 6 hr, 40 min	B) 7 hr	C) 7 hr, 30 min	D) 8 hr	E) 10 hr

Solution: 50% of 80 = 40% or 0.40   5 hr x 60 min = 300 min   300 min x 0.40 = 120 min   120 min + 5 hr = 2 hr + 5 hr = 7 hr total   It will take 50 machines 7 hours to print the same amount of posters.   Answer is 7 hr
Answer: B
How many words with or without meaning, can be formed by using all the letters of the word, â€˜MOUSEâ€™, using each letter exactly once?  Choose the correct choice from the following answers:
A) 120	B) 140	C) 160	D) 720	E) 820

Solution: The word â€˜MOUSEâ€™ contains 5 different letters.   Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time   =5P5   = 5!   = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   120NSWER:120
Answer: A
Find the angle between the hour hand and the minute hand of a clock when
3.25.
Choose the correct choice from the following answers:  A) 47.5  B) 46.5  C) 45.5  D) 48.5  E) 44.5

Solution: angle=30(hours)-(11/2)(minutes)   =30*3-(5.5*25) (hour=3 and minutes=25)   =90-137.5   =47.5   47.5NSWER:47.5
Answer: A
x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median Q of x, y, and z?
I. 9
II. 10
III. 11	Choose the correct choice from the following choices.
A) I only
B) II only
C) III only
D) I and II only
E) I and III only

Solution: Average gives us an idea that 3 nos. are close to 10.   so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.   Let us see options.   If 9 has to be median.   1st term has to less than 9 or equal to 9. (also maintain z-x = 3)   9 9 12 --> satisfies all conditions so 9 can be a median value.   If 11 has to be a median   3rd term has to be 11 or more than 11. (also maintain z-x = 3)   8 11 11 -->satisfies all conditions so 9 can be a median value.   Now for 10 to be median Q.   z+ x = 20 and z-x = 3, we wont have integer values of z.   10 cannot be a median   I and III only is the answer.
Answer: E
The price of a laptop . set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Answers.
A) A)19009  B) B)19074  C) C)19008  D) D)19000  E) E)19002

Solution: Explanation:   Money paid in cash = R . 1000   Balance payment = (20000 - 1000) = Rs. 19000   Answer: Option 19000
Answer: D
Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then  Select the correct option:
A) XB < YD B) XB < YD C) AX > XB D) AX < XB E) CY < AB

Solution: A------X--B   C--Y------D   CY < AB.   Answer: CY < AB.
Answer: E
In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the each share of profit?  Choose the correct choice
A) 7800	B) 8000	C) 8200	D) 8400	E) 8600

Solution: Given 7800=45000 B=30000 C=22500   7800:B:C= 450:300:225   7800s 7800 withdrew its half of capital after 4 months,it can withdraw 22500 rupees   But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost  9+4= 
 9+4 = 13
13 months.For that 9 months, the capital for 7800 is half of its original capital,   So 7800= 450*4+ 225*9= 1800+2025= 
1800+2025 = 3_825
3825   Similarly, B= 300*13= 
300*13 = 3_900
3900   Similarly,C= 225*13= 
225*13 = 2_925
2925   Therefore, ratio of 7800:B:C= 3825: 3900 : 2925= 51:52:39   C's share=39/142(28400)=7800   7800NSWER:7800
Answer: A
A, B and C rents a pasture for Rs.638. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? Choose the correct choice from the following choices:	A) 270	B) 198	C) 676	D) 156	E) 122

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 638= 
9/29 * 638 = 198
198   Answer: 198
Answer: B
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 55, what is the compound interest on the same sum at the rate and for the same time?  Choose the correct choice from the following.
A) s. 56.37 B) s. 53.22 C) s. 56.219 D) s. 51.18 E) s. 51.11

Solution: Explanation:   Sum = (55 * 100) / (2 * 5) = Rs. 550   Amount = [550 * (1 + 5/100)2] = Rs. 606.375   C.I. = (606.375 - 550) = Rs. 56.37   s. 56.37nswer:s. 56.37
Answer: A
If an amount of Rs 41,800 is distributed equally
amongst 22 persons, how much amount would each
person get? Choose the correct choice from the following choices
A) Rs 1900  B) Rs 2000  C) Rs 745  D) Rs 765  E) None

Solution: Required amount =41800/22= 
41800/22 = 1_900
Rs 1900   Rs 1900nswer Rs 1900
Answer: A
The simple interest on a sum of money will be Rs.800 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Choose the correct choice from the following answers: A) 8981 B) 3799 C) 1200 D) 1600 E) 1732

Solution: P --- 10 ---- 800   P --- 5 ----- 400   3P --- 5 ----- 1200   ------   => 1600   Answer: 1600
Answer: D
Find the simple interest on Rs.620 for 10 months at 10 paisa per month?
Pick one: A) 277 B) 620 C) 640 D) 678 E) 121

Solution: I = (620*10*10)/100= 
(620*10*10)/100 = 620
620   Answer: 620
Answer: B
You collect coins. Suppose you start out with 18. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?  Choose the correct choice from the following answers
A) 2
B) 3
C) 4
D) 5
E) 11

Solution: Solution   Start with 18 coins.   Sharon takes 3 coins from you:   18 - 3= 
  18 - 3 = 15
15 coins.   Steven takes 4 coins from you:   15 - 4= 
  15 - 4 = 11
11 coins.   So you have 11 at the end.   Correct answer : 11
Answer: E
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec. What is the length of the platform?	Pick
A) 287 m  B) 350 m  C) 1267 m  D) 1287 m  E) 1162.5 m

Solution: Speed = 300/8 = 75/2 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 75/2   => x = 1162.5 m.   Answer:1162.5 m
Answer: E
A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
Select the correct option
A) 100/17% loss B) 100/17% gain C) 20/3% loss D) None of these E) Cannot be determined

Solution: Explanation :   Let the cost price of 1st transistor be Rs. x and the cost price of 2nd transistor be Rs. y   S.P. of 1st transistor at 20% profit = Rs. 840   => (x + 20% of x) = 840   => x*(120/100) = 840   => x = 700   S.P. of 2nd transistor at 4% loss = Rs. 960   => (y - 4% of y) = 960   => y*(96/100) = 960   => y = 1000   So, total C.P. = (x + y) = Rs. 1700   Total S.P. = 840 + 960= 
840 + 960 = 1_800
1800   Profit= (S.P. - C.P.) = (1800 - 1700) = Rs. 100   % Profit = (100/1700∗100)% = 100/17 %   Answer : 100/17% gain
Answer: B
If the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum.
Choose the correct answer:
A) 0.6%
B) 0.5%
C) 0.1%
D) 0.2%
E) 0.7%

Solution: Applying the above formula, we have   20=1500*r*2/100   r=20*100/1500*2=0.7%.   Answer is 0.7%
Answer: E
A train 175 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice.
A) 22 sec B) 16 sec C) 17 sec D) 88 sec E) 10 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 175 * 2/35= 
175 * 2/35 = 10
10 sec   Answer:10 sec
Answer: E
A sum of Rs. 1870 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
Select:
A) Rs. 120	B) Rs. 160	C) Rs. 240	D) Rs. 330	E) None

Solution: EXPLANATION   Let C’s share = Rs. x   Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6   =x/6 + x/4 + x = 1870   => 17x/12 = 1870   => 1870 x 12/ 17 = Rs.1320   Hence, B’s share = Rs. (1320/4) = Rs. 330.   Answer Rs. 330
Answer: D
A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 3 specified cars. In how many ways cars can be arranged? Options
A) 720
B) 650
C) 1500
D) 1640
E) 1440

Solution: we arranged 3 specified cars in 3 slots = 3!   remaining 5 cars in 5 slots = 5!   number of ways = 3!*5! = 720   correct option is 720
Answer: A
3/4 of 1/2 of 2/5 of 5060 = ?	Pick:
A) 392
B) 759
C) 753
D) 493
E) 540

Solution: 759   759   ? = 5060 * (2/5) * (1/2) * (3/4)= 
5060 * (2/5) * (1/2) * (3/4) = 759
759
Answer: B
A rectangular grass field is 85 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?	Choices
A) 1450	B) 1971	C) 9676	D) 1679	E) 2691

Solution: 1450rea = (l + b +2d) 2d   = (85 + 55 +2.5 * 2) 2*2.5 => 725   725 * 2 = Rs.1450   1450nswer:1450
Answer: A
At a certain conference, 42% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 40% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
Choose the correct option:
A) 18.0%
B) 62.0%
C) 79.2%
D) 70.0%
E) 82.0%

Solution: Refer to the table in the attachment:   Let x= No. of members who have paid in Full   40 % members paid in full and did not register in advance = 0.4x   42 % registerd in advance and paid in full.   So if total No. of members = 100, then 42 members paid Full and registered in advance.   Hence total members who paid full amount = 0.4x + 42 =x   0.6x =42   Hence x = 70   i.e. 80 out of 100 or 70 %   Ans. 70.0%
Answer: D
2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?
Select:
A) 10  B) 20  C) 30  D) 34  E) 36

Solution: 1/x + 1/(x + 10) = 1/12   x = 20   20
Answer: B
The percentage profit earned by selling an article for Rs. 1820 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?  Choose the correct option
A) 3000	B) 1230	C) 2000	D) 5600	E) 1937.5

Solution: C.P. be Rs. x.   Then, (1820 - x)/x * 100 = (x - 1280)/x * 100   1820 - x = x - 1280   2x = 3100 => x = 1550   Required S.P. = 125 % of Rs. 1550 = 125/100 * 1550 = Rs. 1937.5.   ANSW1937.5R 1937.5
Answer: E
If a*b*c=130, b*c*d = 65, c*d*e=500 and d*e*f=250 the (a*f)/(c*d) = ?
Choose one.
A) 1/2 B) 1/4 C) 3/4 D) 2/3 E) 1

Solution: 1xplanation :   aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2   dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/500 => f/c = 1/2   a/d* f/c = 2 * 1/2= 
2 * 1/2 = 1
1   Answer : 1
Answer: E
Average weight of 10 people increased by 0.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is	Choose the correct choice from the following.
A) 50 B) 55 C) 60 D) 65 E) 70

Solution: Explanation:   Total weight increased is 0.5 * 10= 
0.5 * 10 = 5
5.   So weight of new person is 45+5= 
45+5 = 50
50   50nswer: Option 50
Answer: A
A coin is tossed 4 times. What is the probability of getting exactly 3 heads?  Choose the correct choice
A) 1/2  B) 1/4  C) 1/8  D) 1/16  E) 3/16

Solution: The number of possible outcomes is 2^4 = 16   There are 4 ways to get exactly 3 heads.   P(exactly 3 heads) = 4/16 = 1/4   The answer is 1/4.
Answer: B
Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations Y of classes are available? Choose the correct choice from the following answers:	A) 3	B) 6	C) Y=7	D) Y=9	E) Y=12

Solution: I think it should be E only.   No where it is given that he attends different classes on each day.   Experts please provide your views.   --- EDITED my Response. It was a typo. I meant 12 is the answer.   If only Y=9ay 1 : 3 options   If Y=9ay 1 and Y=9ay 2 : 3*3= 
3*3 = 9
9 Options   So, Total= 3+9= 
3+9 = 12
12.
Answer: D
If 20 men can build a water fountain 56 metres long in 3 days, what length of a similar water fountain can be built by 35 men in 3 days? Choose the correct choice from the following answers
A) 40 m
B) 64 m
C) 77 m
D) 89 m
E) 98 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 3: 3 : : 56 : x   Therefore (20 x 3 x x)=(35 x 3 x 56)   x=(35 x 3 x 56)/60=98   Hence, the required length is 98 m.   Answer : 98 m
Answer: E
What is the sum of all possible solutions to |x - 5|^2 + |x - 5| = 20 ?	Select:
A) -1	B) 6	C) 7	D) 10	E) 14

Solution: Denote |x - 5| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 5|, so it's an absolute value and thus cannot be negative.   y = |x - 5| = 4 --> x = 9 or x = -1. The sum =10   Answer: 10.
Answer: D