MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?	Choose the correct choice: A) 32 B) 48 C) 64 D) 96 E) None

Solution: We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).   Required number of ways	= (3C1 x 6C2) + (3C2 x 6C1) + (3C3)   = 3 x((6 x 5)/(2x1))	+((3 x 2)/(2x1))x 6+ 1   = (45 + 18 + 1)= 
(45 + 18 + 1) = 64
64.   Option 64
Answer: C
In X game of billiards, X can give Y 10 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 100?  Choose the correct choice from the following:	A) 30	B) 20	C) 25	D) 40	E) 50

Solution: X scores 60 while Y score 50 and Z scores 30.   The number of points that Z scores when Y scores 100 = (100 * 30)/50= 
(100 * 30)/50 = 60
60.   In X game of 100 points, Y gives (100 - 60)= 
(100 - 60) = 40
40 points to C.   40
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 the correct choice:
A) Rs. 6400
B) Rs. 6500
C) Rs. 7200
D) Rs. 7500
E) Rs. 7800

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.   Rs. 6400NSWER:Rs. 6400
Answer: A
A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $300. The football management has decided to change the dimensions of field by increasing the breadth by 5% of its original value and reducing the length by 20% of its original value and fence the field again.. What will be the cost of the new fencing?  Choose the most appropriate option
A) $360
B) $265
C) $425
D) $405
E) $415

Solution: Let's take x to be the breadth. Then the length of the football field is 2x.   The perimeter of the old football field is x + 2x + x + 2x = 6x.   Now, for the new football field:   The new breadth = 1.05 times old breadth = 1.05x   The new length is 0.8 times old length = (.8)2x = 1.6x   So the new perimeter is 1.6x + 1.6x + 1.05x + 1.05x =5.3x.   for old perimeter rate is $300   For new perimeter  1.6  + 1.6  + 1.05  + 1.05= 
 1.6  + 1.6  + 1.05  + 1.05 = 5.3
5.3x.   for old perimeter rate is $300   For new perimeter= (300 * 5.3)/6= 
(300 * 5.3)/6 = 265
265   Ans - $265
Answer: B
When n is divided by 5 the remainder is 3. What is the remainder when n^2 is divided by 5? Choices:	A) 0	B) 1	C) 2	D) 3	E) 4

Solution: n = 5x+3, for some integer x   n^2=(5x+3)^2=5y+9, for some integer y   When we divide this by 5, the remainder is 4.   The answer is 4.
Answer: E
A watch was sold at a loss of 10%. If it was sold for Rs.210 more, there would have been a gain of 4%. What is the cost price?	Select the correct option:
A) s:1000
B) s:1500
C) s:1278
D) s:1028
E) s:1027

Solution: 90%   104%   --------   14% ---- 210   100% ---- ? =>   Rs:1500   Answer: s:1500
Answer: B
I gain 70 paise on Rs.70.My gain percent is : Choose the correct choice from the following:
A) 0.1% B) 1% C) 7% D) 10% E) Noneof these

Solution: Solution   11.1   Gain% = (0.70/70x100)% = 1%.   Answer 1%
Answer: B
Evaluate: 986 x 237 + 986 x 863 Choose the correct choice:	A) 956000	B) 996000	C) 986000	D) 976000	E) None of them

Solution: = 986 x 137 + 986 x 863   = 986 x (137 + 863)   = 986 x 1000 = 986000.   Answer is 986000.
Answer: C
Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 462?
Choose the correct choice from the following answers:
A) 25.6% B) 21% C) 20% D) 19% E) None of these

Solution: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621   SP = Rs. 462, Discount = 621 - 462= 
621 - 462 = 159
159   Discount %= 159/621 * 100 = 25.6%   25.6%NSWER:25.6%
Answer: A
Find the last digit of
1!+2!+3!+4!+...............100!
Select:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: 5! +6! .... = always unit digit o.   1!+2!+3!+4! = 33   so, 33 + *0 = *3   so the unit digit will be 3   ANSWER:3
Answer: D
Seven friends are living in 7 different flats of an apartment. Each of them was allotted a parking slot to park their cars in the ground floor. But they used to park their cars randomly in any of the seven slots. In how many ways can they park their cars so that exactly five persons park their cars in the slots allotted to them?  Choose the correct choice from the following answers.
A) 14	B) 21	C) 35	D) 42	E) 49

Solution: C57=21 : choosing which of the 7 persons will be on the slots allocates to them, the remaining 2 will be parked on each others slots.   Answer: 21.
Answer: B
Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum R of their ages will be 51, how old is Stephanie ?	Choose the correct choice from the following answers
A) 6	B) 10	C) 14	D) 20	E) 24

Solution: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,   so eliminate C,D,E   2) take B (10y.o.), R=meaning S=10,J=20, so  20+10+10= 
 20+10+10 = 40
40 and for K=10-4/3=2+9= 
2+9 = 11
11, finally 40+11= 
40+11 = 51
51. It is correct   10
Answer: B
One fourth of one third of two fifth of a number is 20. What will be40% of that number
Answers:
A) 240
B) 150
C) 180
D) 200
E) 250

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 20 then x = 20 * 30= 
20 * 30 = 600
600   40% of 600= 240   240nswer: Option 240
Answer: A
The area of a square garden is A square feet and the perimeter is p feet. If a=p+5, what is the perimeter of the garden, in feet?	Choose the correct choice from the following answers:
A) 28 B) 20 C) 40 D) 56 E) 64

Solution: Perimeter of square = P   Side of square = P/4   Area of Square = (P^2)/16 =A   Given that A = P + 5   (P^2)/16 = P + 5   P^2 = 16P + 80   P^2 -16P -80 = 0   P^2 -20P + 4P -80 = 0   P(P-20)+4(P+20) = 0   (P-20)(P+4) = 0   P = 20 o r- 4   Discarding negative value , P = 20   Answer is 20
Answer: B
A boy has eight trousers and 10 shirts. In how many different ways can he select a trouser and a shirt? Answers
A) 80 ways	B) 86 ways	C) 88 ways	D) 108 ways	E) 89 ways

Solution: The boy can select one trouser in eight ways.   The boy can select one shirt in 10 ways.   The number of ways in which he can select one trouser and one shirt is   8 * 10= 
  8 * 10 = 80
80 ways.   80 waysnswer:80 ways
Answer: A
Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Choose the most appropriate option.
A) 3:5  B) 2:7  C) 1:6  D) 1:4  E) 1:3

Solution: (10/100)3:5+(2/100)B = (5/100)(3:5+B)   53:5 =3B   => 3:5/B = 3/5   3:5nswer is 3:5.
Answer: A
The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group?  Choose the correct choice from the following choices:
A) s. 25.6  B) s. 25  C) s. 16.6  D) s. 26  E) s. 25.6

Solution: Total members in the group = 7   Average amount = Rs. 30   Total amount with them = 7 * 30 = Rs. 210   One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150   The average amount with them = 150/6 = Rs. 25   ANSWER:s. 25
Answer: B
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?  Select the correct option:
A) 270. B) 480 C) 920 D) 280 E) 290

Solution: Speed = 72 x 5/18 m/sec = 20 m/sec.   Time = 26 sec.   Let the length of the train be x metres.   Then, x + 250/26 = 20   x + 250 = 520   x = 270.   270.nswer: 270.
Answer: A
In how many ways can the letters of the word BCGOI be rearranged such that the consonants always appear together?
Choose one:
A) 12
B) 36
C) 48
D) 60
E) 24

Solution: BCGOI   BCG will come together as a group which can be arranged in 3!=6ways.   BCG,O,I can be arranged in 3!=6 ways.   total possible arrangements = 6*6= 
6*6 = 36
36 ways   ANSWER:36
Answer: B
The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference w would have been how much?	Choose the correct choice from the following answers:	A) 40/3	B) 40	C) 120	D) 360	E) 420

Solution: CASE 1:   Deposit = $x;   Rate of increase = r.   Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.   Interest yearned in 2 year = (x + xr)r.   The difference w= (x + xr)r - xr = xr^2 = 40.   CASE 2:   Deposit = $x;   Rate of increase = 3r.   Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.   Interest yearned in 2 year = (x + 3xr)3r.   The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40= 
9*40 = 360
360.   Answer: 360.
Answer: D
In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 8 boys when a boy gets any no. of prizes?  Options:  A) 4890  B) 5095  C) 4096  D) 4089  E) 4000

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the four prizes can be given in 8 ways, i.e. (8 x 8 x 8 x 8) ways = 84 ways = 4096 ways Or nr ways = 84 ways = 4096 ways
Answer: C
Sachin can cover a distance in 1hr 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. The total distance is?
Choose the correct option.
A) 6 km  B) 8 km  C) 9 km  D) 11 km  E) 12 km

Solution: Let total distance =D=D   Distance travelled at 4 kmph speed =(23)D=(23)D   Distance travelled at 5 kmph speed =(1−23)D=(13)D=(1−23)D=(13)D   Total time =1 hr 24 min = (60+24) min =8460=8460 hr =2115=2115 hr   We know,   Time=DistanceSpeedTime=DistanceSpeed   Total time   2115=2/34D+1/35D2115=2/34D+1/35D   2115=2D12+D152115=2D12+D15   84=14D84=14D   D=6 km   Option 6 km is correct
Answer: A
How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr?  Answers
A) 1 min B) 1 (1/5) min C) 2 min D) 3 min E) 4 min

Solution: Adityaâ€™s speed = 20 km/hr = {20 *5/18}min=50/9 m/s   Time taken to cover 400 m={ 400*9/50= 
400*9/50 = 72
72 sec=1 (1/5) min   ANSWER 1 (1/5) min
Answer: B
What is the difference between the largest number and the least number written with the digits 9, 3, 5, 7?  Answers:
A) 6084 B) 3788 C) 2077 D) 2721 E) 6174

Solution: 6174xplanation:   3579   9753   ------------   6174   Answer:6174
Answer: E
The average of nine numbers is 27. If one number is excluded, the average becomes 25. The excluded number is  Choose the correct choice from the following answers:
A) 25 B) 27 C) 30 D) 35 E) 43

Solution: Sol.   Therefore excluded number   = (27 × 9) - ( 25 × 8)   = 243 – 200   = 43.   Answer 43
Answer: E
A grocer stacked oranges in a pile. The bottom layer was rectangular with 4 rows of 6 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?	Choose the correct choice from the following answers:	A) 3	B) 5	C) 6	D) 8	E) 10

Solution: Bottom Layer = 6 x 4 = 24   IInd Layer = (6-1) x (4-1) = 15   IIIrd Layer = (5-1) x (3-1) = 8   Answer = 8 = 8
Answer: D
If shares of two persons in profits are Rs.700 and Rs. 300 then ratio of their capitals is	Choose the correct choice from the following: A) 3:4 B) 2:3 C) 7:3 D) 1:3 E) 1:5

Solution: total profit =1000   ratio=700/300   =7:3   ANSWER:7:3
Answer: C
A rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m × 2.5. The earth dug out is spread evenly over the remaining portion of a field. How much is the level of the field raised ?  Choose the correct choice from the following:
A) 4.0 m  B) 4.1 m  C) 4.2 m  D) 4.3 m  E) None of these

Solution: Area of the field = 13.5 × 2.5 = 33.75 m2   Area covered by the rectangular tank   = 5 × 4.5 = 22.50 m2   Area of the field on which the earth dug out is to be spread = 33.75 – 22.50 = 11.25 m2   Let the required height be h.   Then, 11.25 × h = 5 × 4.5 × 2.1   or h = 4.2 m   Answer 4.2 m
Answer: C
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
Choose the correct choice from the following:
A) 17%	B) 10%	C) 20%	D) 18%	E) 40%

Solution: 2420 --- 242   100 --- ? => 10%   Answer: 10%
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: Choose the correct choice from the following:
A) 8 years	B) 14 years	C) 4 years	D) 2 years	E) 8 years

Solution: Explanation:   Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   Answer: 14 years
Answer: B
A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?  Options:  A) 33 1/8 %  B) 33 7/3 %  C) 33 1/3 %  D) 25 %  E) 34 1/3 %

Solution: The total number of mangoes bought by the shopkeeper be 20.   If he buys 5 a rupee, his CP = 4   He selling at 4 a rupee, his SP = 5   Profit = SP - CP = 5 - 4= 
5 - 4 = 1
1   Profit Percent= 1/4 * 100= 
1/4 * 100 = 25
25 %   Answer: 25 %
Answer: D
If n is a positive integer such that n! / (n - 2)! = 342, find n.
Choose the correct choice:
A) 13 B) 17 C) 15 D) 11 E) 19

Solution: Let expand n as follows   n! = n*(n - 1)*(n - 2)!   n! / (n - 2)! = n*(n - 1)*(n - 2)! = n(n - 1) = 342   Solve the equation n(n - 1) = 342 and select the positive integer solution which is n = 19   correct answer 19
Answer: E
The average of 13 result is 20. Average of the first 8 of them is 20 and that of the last 8 is 40. Find the 8th result? Choose the correct choice from the following:  A) 35  B) 37  C) 46  D) 90  E) 100

Solution: Sum of all the 13 results = 13 * 20= 
13 * 20 = 260
260   Sum of the first 7 of them= 8 * 20= 
8 * 20 = 160
160   Sum of the last 7 of them= 8 * 40= 
8 * 40 = 320
320   So, the 8th number= 260 + 160 - 320= 
260 + 160 - 320 = 100
100.   100
Answer: E
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?  Choose the correct choice from the following answers.
A) 756  B) 700  C) 650  D) 640  E) 800

Solution: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).   Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)   = (525 + 210 + 21)= 
(525 + 210 + 21) = 756
756   756NSWER 756
Answer: A
At a round table, 7 knights are to be seated around a circular table. two seating arrangement are considered different only when the position of the people are different relative to each other. what is the total number of possible seating arrangement for the group?	Choose the correct option.
A) a.5
B) b.10
C) c.24
D) d.32
E) e.720

Solution: for 5 people seating arrangement around a circular table = (7-1)= 
(7-1) = 6
6!= 6*5*4*3*2*1= 
6*5*4*3*2*1 = 720
720 OA is e.720
Answer: E
A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in  Choose the correct choice from the following
A) 18 sec  B) 12 sec  C) 15 sec  D) 8.25 sec  E) None of these

Solution: Length of train = 12 Ã— 15 = 180 m.   Then, speed of train = 180â„9 = 20 m/s   Now, length of train = 11 Ã— 15 = 165m   âˆ´ Required time = 165â„20 = 8.25 sec.   Answer 8.25 sec
Answer: D
Sam taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?
Choose the correct option
A) 165	B) 220	C) 310	D) 185	E) 181

Solution: Loan amount : Rs.15000/- @ 11.5%   Interest per month = 15000/- * 11.5% =Rs.1725   Interest for one day = 1725/30= 
1725/30 = 115/2 = around 57.5
57.50   Interest for 7 days is= 57.50*7 =403   FD amount is = Rs.10000/- @ 9.5%   Interest per month = 10000 * 9.5% = 950/-   Interest for 7 days = 950/30*7 = 222   Interest amount to be paid by Sam = 403-222= 
403-222 = 181
181/- for 7 days   Answer is 181
Answer: E
Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 33 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
Choices
A) 16.5 minutes  B) 33 minutes  C) 49.5 minutes  D) 66 minutes  E) 99 minutes

Solution: Danny's time is 33 minutes. The time to reach halfway is 16.5 minutes.   Steve's time is 66 minutes. The time to reach halfway is 33 minutes.   The time difference is   33 - 16.5= 
  33 - 16.5 = 16.5
16.5 minutes   The answer is 16.5 minutes.
Answer: A
The average expenditure of a labourer for 8 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is	Select.
A) 80	B) 85	C) 75	D) 95	E) 100

Solution: Income of 8 months = (8 × 85) – debt   = 680 – debt   Income of the man for next 4 months   = 4 × 60 + debt + 30   = 270 + debt   ∴ Income of 10 months = 950   Average monthly income = 950 ÷ 10 = 95   Answer 95
Answer: D
The three competitors in a race have to be randomly chosen from a group of three men and five women. How many different such trios contain at least one woman?
Choose one.
A) 48	B) 55	C) 62	D) 69	E) 76

Solution: The total number of ways to choose three runners 8C3 = 56   The number of trios with only males is 3C3 = 1   The number of trios which include at least one woman is 55.   The answer is 55.
Answer: B
If the length of the longest chord of a certain circle is 10, what is the radius of that certain circle?  Options:
A) 2.5  B) 5  C) 10  D) 15  E) 20

Solution: Longest chord of a circle is the diameter of the circle   diameter = 2 * radius   If diameter of the circle is given as 10 = 2 * 5   so radius of the circle = 5   correct answer - 5
Answer: B
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?	Choose the correct choice from the following choices
A) 16 2/3% B) 25% C) 33 1/3 D) 50% E) 75%

Solution: In 1986- 200   In 1988- 150   Decrease of 50 over 200 between 86 and 88   So 25%   ANSWER:25%
Answer: B
The area of rectangular field is 460 square metres. If the length is 15 per cent more than the breadth ,what is the breadth of the rectangular field?	Choose the correct choice from the following answers
A) 15 metres B) 26 metres C) 34.5 metres D) Cannot be determined E) None of these

Solution: Let the breadth of the rectangular field be ‘x’ m. Then,length of the field will be   x+x×15/100=23x/20   Now, x×23x/20=460   or, 23x2 = 460 × 20   or, x2 = 20 × 20   or, x = 20 m   Answer None of these
Answer: E
In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 20 years replaced by a new boy. The age of the new boy is?	Choose the correct option:
A) 14 years 8 months B) 15 years C) 16 years 8 months D) 17 years 10 months E) 17 years

Solution: Total decrease = (20 x 2) months   = 3 years 4 months   Age of the new boy   = 20 years - 3 years 4 months.   = 16 years 8 months.   ANSWER:16 years 8 months
Answer: C
At a certain college, 40 percent of the total number of students are freshmen. If 50 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
Choose the correct choice from the following answers
A) 10%
B) 12%
C) 14%
D) 16%
E) 18%

Solution: Let's say there is a TOTAL of 100students at this college.   40 percent of the total number of students are freshmen.   # of freshmen = 40% of 100 =40   50 percent of the fresh-men are enrolled in the school of liberal arts...   Number of liberal arts freshmen = 50% of 40 = 20   ...and, of these, 50 percent are psychology majors...   Number of liberal arts freshmen who are psychology majors = 50% of 20=10   What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?   10/100= 10%   10%nswer:10%
Answer: A
A(7, w^3) is the (x, y) coordinate of point located on the parabola Y = X^2 + 15. What is the value of w? Choose the correct choice:	A) 3.	B) 4.	C) 5.	D) 6.	E) 9.

Solution: y=x^2 +15   w^3=7^2+15   w^3=64   W=4   Answer 4.
Answer: B
Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 24 in two years, at the same percent rate per annum? Choose the correct choice from the following: A) s. 50 B) s. 48 C) s. 42 D) s. 20 E) s. 60

Solution: Explanation:   SI in 2 years = Rs. 20, SI in 1 year = Rs. 10   CI in 2 years = Rs. 24   % rate per annum = [(CI – SI) / (SI in 1 year)] *100   = [(24 – 20) / 20] * 100   = 20 % p.a.   Let the principal be Rs. X   Time = T = 2 years   % rate = 20% p.a.   SI = (PRT/100)   20 = (X*20*2) / 100   X = Rs. 50   s. 50NSWER: s. 50
Answer: A
A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Choose the correct answer:	A) 96	B) 70	C) 50	D) 80	E) 60

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 512   16x = 512   x = 32.   Hence, total number of notes = 3x = 96.   96nswer is 96.
Answer: A
A man is 25 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? Choose the correct choice from the following options
A) 11
B) 23
C) 27
D) 22
E) 91

Solution: Let the son's present age be x years.   Then, man's present age = (x + 25) years.   (x + 25) + 2 = 2(x + 2) x + 27 = 2x + 4 => x = 23.   Answer: 23
Answer: B
If it is 5:22 in the evening on a certain day, what time in the morning was it exactly 2,880,695 minutes earlier? (Assume standard time in one location.) Choices
A) 5:30	B) 5:32	C) 5:47	D) 5:49	E) 5:54

Solution: 5:22 minus 2,880,695 must end with 7, the only answer choice which ends with 7 is C.   Answer: 5:47.
Answer: C
The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.6. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match? Choose the correct choice:
A) A)0.8333
B) B)0.7
C) C)0.8571
D) D)0.7531
E) E)0.8213

Solution: Out of 100 matches:   Matt is plays in 80 and not plays in 20.   Out of 80 matches Matt plays in, team wins   0.75*80= 
  0.75*80 = 60
60.   Out of 20 matches Matt does not play in, team wins   0.6*20= 
  0.6*20 = 12
12.   So, out of 100 matches 60 + 12= 
60 + 12 = 72
72 are won.   It is known that the team has won the last match. Out of 72 matches won, Matt is in 60: 60/72= 0.833...   0.8333nswer: 0.8333.
Answer: A