MU-NLPC/Calc-aqua_rat huggingface dataset:
36 men can complete a piece of work in 18 days. in how many days will 27 men complete the same work ?	Choose the correct choice from the following answers:
A) 12 B) 18 C) 22 D) 24 E) 26

Solution: Solution   Let the required number of days be x.   Then, Less men, More days   ∴ 27 : 36 :: 18 : x ⇔ 27 × x = 36 × 18 ⇔ x =36x18/27x = 24. Answer 24
Answer: D
A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 5 minutes?
Choose the correct answer
A) 36
B) 54
C) 108
D) 270
E) 324

Solution: ONE Veggiematik machine can chop 36 carrots in 4 minutes   So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes   In other words, ONE Veggiematik machine can chop 54 carrots in5minutes   So,SIXVeggiematik machines can chop (5)(54) carrots in5minutes   In other words, SIX Veggiematik machines can chop 270 carrots in5minutes   Answer 270
Answer: D
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the most appropriate option:
A) 565
B) 444
C) 676
D) 420
E) 663

Solution: 1h ----- 3   ? ------ 60   12 h   RS = 16 + 19= 
16 + 19 = 35
35   T= 12   420 = 35 * 12= 
35 * 12 = 420
420   Answer: 420
Answer: D
A cubical tank is filled with water to a level of 2 feet. If the water in the tank occupies 32 cubic feet, to what fraction of its capacity is the tank filled with water?  Pick one:
A) 1/2  B) 1/3  C) 2/3  D) 1/4  E) 3/4

Solution: The volume of water in the tank is H*L*B = 32 cubic feet.   Since H = 2, then L*B = 16 and L = B = 4.   Since the tank is cubical, the capacity of the tank is   4*4*4= 
  4*4*4 = 64
64.   The ratio of the water in the tank to the capacity is 32/64= 1/2   The answer is 1/2.
Answer: A
A rower can row 7 km/h in still water. When the river is running at 2 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
Choose the most appropriate option:
A) 2.92
B) 3.04
C) 3.12
D) 3.21
E) 3.35

Solution: Let x be the distance to Big Rock.   time = x/5 + x/9 = 1   x = 45/14 = 3.21 km   The answer is 3.21.
Answer: D
A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.  Choose the correct choice from the following options:
A) 65 B) 85 C) 48 D) 12 E) 25

Solution: Explanation :   Work done by A in 1 hour = 1/4   Work done by B and C in 1 hour = 1/3   Work done by A and C in 1 hour = 1/2   Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12   Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours   ANSWER:12
Answer: D
The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s? Choices
A) 30%	B) 25 1/13 %	C) 23 1/13 %	D) 22 1/13 %	E) 22 2/13 %

Solution: y=100	x=130   130---------30   100---------? => 23 1/3%   ANSWER:23 1/13 %
Answer: C
Two vehicles each 900 m long are running in opposite directions on parallel paths. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Choose the correct choice.
A) 77 sec
B) 66 sec
C) 48 sec
D) 81 sec
E) 45 sec

Solution: Relative speed = 50 + 30= 
50 + 30 = 80
80 km/hr.   80 * 5/18= 200/9 m/sec.   Distance covered = 900 + 900 = 180 m.   Required time = 1800 * 9/200= 
1800 * 9/200 = 81
81 sec.   Answer: 81 sec
Answer: D
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be Choose the correct choice from the following choices:
A) (1.5)^4	B) 4(1.5)	C) (1.05)^5	D) 1 + (0.05)^4	E) 1 + 4(0.05)

Solution: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be   1(1.05)^5   1.05^5   C. (1.05)^5
Answer: C
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 3 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?	Choose the most appropriate option.
A) 5729  B) 5760  C) 2889  D) 2870  E) 4320

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 3= 
 24 * 60 * 3 = 4_320
4320.Answer: 4320
Answer: E
Of 600 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B? Choose the most appropriate option: A) 20 B) 25 C) 30 D) 35 E) 75

Solution: Say the number of students who read book A is A and the number of students who read book B is B.   Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.   Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 600=1.25B+B-0.25B --> B=300, A=1.25B= 375 and {Both}=0.25B=75.   The number of students who read only book A is {A}-{Both}=375-75= 
375-75 = 300
300;   The number of students who read only book B is {B}-{Both}=300-75= 
300-75 = 225
225;   The difference is  300-225= 
 300-225 = 75
75.   Answer: 75.
Answer: E
If a fisherman rows upstream at 7kmph, and downstream at 10kmph, what is the speed of the stream?  Choose the correct choice from the following choices:
A) 1.7 kmph	B) 1.5 kmph	C) 2.5 kmph	D) 1.9 kmph	E) 3.5 kmph

Solution: Sol.   Speed of stream = 1/2(10 -7) kmph = 1.5 kmph.   Answer 1.5 kmph
Answer: B
The youngest of 4 children has siblings who are 4, 5, and 7 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?
Choose the correct option:
A) 14
B) 15
C) 16
D) 17
E) 18

Solution: x + (x+4) + (x+5) + (x+7) = 84   4x + 16 = 84   4x = 68   x = 17   The answer is 17.
Answer: D
The edge of a cube is 4a cm. Find its surface?
Answers:
A) 24a8	B) 24a4	C) 96a2	D) 24a2	E) 24a7

Solution: 6a2 = 6 * 4a * 4a = 96a2   Answer:96a26 * 4  * 4= 
6 * 4  * 4 = 96
96a2   Answer:96a2
Answer: C
A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Select the correct option:  A) 15 days  B) 14 days  C) 13 days  D) 11 days  E) 12 days

Solution: Explanation:   x/24 + x/30 + x/40 = 1   x = 11 days   ANSWER IS 11 days
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?  Select the correct option:
A) 1000	B) 1288	C) 2778	D) 2682	E) 1021

Solution: 1120 = P [1 + (5*12/5)/100]   P= 1000   1000nswer: 1000
Answer: A
The ratio of pens to pencils is 5 to 6. There are 4 more pencils than pens. How many pencils are there?	Choose the correct choice from the following:
A) 12 B) 16 C) 20 D) 24 E) 28

Solution: Let the number of pens be 5x and the number of pencils be 6x.   6x - 5x = 4   x = 4   The number of pencils is 24.   The answer is 24.
Answer: D
Two dice are tossed. The probability that the total score is a prime number is Choose one:
A) 3/8  B) 4/9  C) 5/12  D) 4/7  E) 3/5

Solution: n(S)=36   E= {(1,1),(1,2), (1,4),….(6,5)}   n(E)=15   P(E)=15/36   =5/12   Ans: 5/12
Answer: C
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18300. A's share is?  Select the correct option:
A) 8876	B) 2765	C) 6000	D) 1298	E) 6100

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18300= 
1/3 * 18300 = 6_100
6100   Answer:6100
Answer: E
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of the interest. If she paid Rs. 432 as interest at the end of the period,what was the rate of interest ?
Pick one:  A) 3.6  B) 6  C) 18  D) Cannot be determined  E) None

Solution: Solution   Let rate = R% and time = R years.Then,   (1200xRxR/100)= 432 = 12R2= 432 = R2=36 =R = 6   Answer 6
Answer: B
A and B together have Sterling 1240. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Pick:
A) Sterling 496
B) Sterling 484
C) Sterling 550
D) Sterling 664
E) None

Solution: Explanation: 4/15A = 2/5B   A = (2/5 x 15/4)B   A = 3/2 B   A/B = 3/2   A : B = 3 : 2.   B's share = Sterling (1240 x 2/5) = Sterling 496.   Sterling 496nswer: Option Sterling 496
Answer: A
If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area?
Answers
A) 120 cm2	B) 765 cm2	C) 216 cm2	D) 270 cm2	E) 275 cm2

Solution: The triangle with sides 39 cm, 36 cm and 15 cm is right angled, where the hypotenuse is 39 cm.   Area of the triangle   = 1/2 * 36 * 15= 
1/2 * 36 * 15 = 270
270 cm2   Answer: 270 cm2
Answer: D
What is the average of xx, 2x2x, and 66? Choose the correct choice from the following
A) 2x+2
B) x+2x
C) x+2x+2
D) x+2
E) x

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or Option x+2x+2
Answer: C
A 6% stock yields 8% . The market value of the stock is?
Choose the correct option: A) Rs.11 B) Rs.75 C) Rs.17 D) Rs.16 E) Rs.22

Solution: For an income of Rs. 8, investment = Rs. 100.   For an income of Rs 6, investment =Rs. \inline \left ( \frac{100}{8} \times 6\right ) = Rs. 75   Market value of Rs. 100 stock = Rs. 75.   Answer: Rs.75
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet? Choose the correct answer:  A) 20/7  B) 20/5  C) 20/9  D) 20/5  E) 20/1

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 100/35 = 20/7 sec.   20/7nswer:20/7
Answer: A
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
Choose the correct choice
A) 3:4 B) 7:6 C) 1:4 D) 5:4 E) 2:4

Solution: A   3:4   Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)   3:4nd, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)   Solving (i) and (ii), we get x = 60 and y = 80   Ratio of speeds = 60:80 = 3:4
Answer: A
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 5 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 correct choice from the following choices
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 = 5 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 5 and 2 = 10   If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 22:00 hours   Answer 22:00.
Answer: D
If (4x + 3)(x - 2) = 4x^2 + x, what is a possible value of x?
Choose the correct choice:
A) 5 B) -6 C) -1 D) 1 E) 6

Solution: Rearranging the given expression:   (4x + 3)(x - 2) = 4x^2 + x   i.e. 4x^2 - 5x - 6 = 4x^2 + x   i.e. -6x = 6   i.e. x = 6/-6 = -1   Answer: Option -1   Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: C
If 2 dice are rolled, what is the probability of the total score being a even number?
Choose the most appropriate option: A) 1/4 B) 1/3 C) 5/12 D) 1/2 E) 7/12

Solution: Using the rules of probability, the likelihood of rolling a even number would be 1/2, as half the numbers from 1-12 are even numbers. Answer: 1/2
Answer: D
A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4. If the total value of all the coins in the bag is Rs.400, find the number of coins of each kind?  Choose the correct answer.
A) 800
B) 277
C) 266
D) 288
E) 1221

Solution: 50*2k + 20*3k + 10*4k = 40000   200k = 40000 => k = 200   50p coins = 2k = 2*200= 
2*200 = 400
400   20p coins= 3k = 3*200= 
3*200 = 600
600   10p coins= 4k = 4*200= 
4*200 = 800
800   800nswer: 800
Answer: A
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?  Choose the correct answer:
A) 57%  B) 63%  C) 73%  D) 90%  E) 58%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400.   Required percentage=(11628/20400	)x 100% = 57%.   57%nswer:57%
Answer: A
An empty pool being filled with water at a constant rate takes 7 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
Choices:
A) 5 hr 30 min
B) 5 hr 20 min
C) 4 hr 40 min
D) 3 hr 12 min
E) 2 hr 40 min

Solution: (3/5) of a pool/ 7 hours = 3/35 (the rate)   (3 pools/35 hours) = (2/5* pool)/ x hours   4 hr 40 minross multiply 3x = (2/5) 35   x = 4 2/3   2/3 of an hour = 40 minutes   4 hr 40 min
Answer: C
In a village of 100 households, 75 have at least one DVD player, 85 have at least one cell phone, and 70 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:	Choices:
A) 65
B) 55
C) 40
D) 35
E) 25

Solution: Am I missing something here??? it seems straightforward......   The obvious maximum that have all 3 is 70, because you are limited by the SMALLEST number.   The minimum is simply the sum of the max of each people who DONT have the product, so:    100-85= 
 100-85 = 15
15 don't have Cell    100-75= 
 100-75 = 25
25 don't have DVD   and  100-70= 
 100-70 = 30
30 don't have MP3   SO a total of   15+25+30= 
  15+25+30 = 70
70 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get  100-70= 
 100-70 = 30
30.   70-30= 
70-30 = 40
40   40
Answer: C
The average age of husband, wife and their child 3 years ago was 28 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is  Choose the correct choice from the following answers:	A) 22	B) 40	C) 33	D) 21	E) 11

Solution: Explanation:   Sum of the present ages of husband, wife and child = (28 x 3 + 3 x 3) years = 93 years.   Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (93 - 50) years = 33 years.   Answer: 33
Answer: C
What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?	Select:
A) 28800
B) 24800
C) 24400
D) 20000
E) None

Solution: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800   Amount = P + I = 18000 + 10800 = Rs. 28800   28800NSWER 28800
Answer: A
A electronics shop has a sale of Rs. 16000, Rs. 25000, Rs. 65000 for 3 consecutive months. How much sale must he have in the fourth month so that he gets an average sale of Rs. 40000?
Choose the correct choice from the following options
A) s. 499110	B) s. 165000	C) s. 114000	D) s. 250000	E) s. 116000

Solution: Total sale for 3 months = Rs. (16000 + 25000 + 65000) = Rs. 106000.   Required sale = Rs. [ (55000 x 4) - 106000]   = Rs. 220000 - 106000)   = Rs. 114000.   Option s. 114000
Answer: C
A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?	Select:  A) 27 km/hr  B) 28 km/hr  C) 48 km/hr  D) 19 km/hr  E) 10 km/hr

Solution: Speed on return trip = 150% of 40   = 60 km/hr.   Average speed = (2 * 40 * 60)/(40 + 60)= 
(2 * 40 * 60)/(40 + 60) = 48
48 km/hr.   Answer:48 km/hr
Answer: C
A 9-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point? Choices:
A) 1/5 B) 2/7 C) 2/9 D) 3/10 E) 4/11

Solution: The longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end. The probability of this is 2/9.   The answer is 2/9.
Answer: C
A 1500 m long train crosses a tree in 120 sec, how much time will it take to pass a platform 500m long?  Select the correct option
A) 288
B) 160
C) 188
D) 188
E) 12

Solution: L = S*T   S= 1500/120= 
1500/120 = 25/2 = around 12.5
12.5m/Sec.   Total length (D)= 2000 m   T = D/S   T = 2000/12.5= 
2000/12.5 = 160
160 Sec   Answer:160
Answer: B
How many seconds will a 600 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Choose the correct choice.
A) 48	B) 36	C) 26	D) 11	E) 18

Solution: Explanation:   Here distance d = 600 mts   speed s = 63 - 3= 
63 - 3 = 60
60 kmph= 60 x 5/18 m/s   time t = = 36 sec.   Answer: 36
Answer: B
A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?  Options
A) Rs. 2000	B) Rs. 2010	C) Rs. 2100	D) Rs. 2200	E) Rs. 2300

Solution: Total expenditure for the first 3 months = 3 × 1600 = 4800   Total expenditure for 4 months = 4 × 1550 = 6200   Total expenditure for 5 months = 5 × 1800 = 9000   Total expenditure and saving (which is income for one year)   = 4800 + 6200 + 9000 + 5200 = Rs. 25200   So, Average monthly income = 25200/12 = Rs. 2100   Rs. 2100
Answer: C
10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.110000, find the cost of a camel?
Choose the correct answer:  A) s.9800  B) s.3800  C) s.9800  D) s.4400  E) s.6880

Solution: Cost of the camel = P   10 camels = 24 horses   16 horses = 4 oxen   6 oxen = 4 elephants   10 elephants = Rs.110000   P = Rs.[(24 * 4 * 4 * 110000)/(10 * 16 * 6 * 10)]   P = Rs.(42240000/9600) => P = Rs.4400   Answer:s.4400
Answer: D
The product of all the prime numbers less than 10 is closest to which of the following powers of 10? Choose the most appropriate option.
A) 10^9
B) 10^2
C) 10^7
D) 10^6
E) 10^5

Solution: Quickly approximate   2, 3, 5, 7, = 210 =2.1x10^2   10^2
Answer: B
The difference between the costs of two brands is 20 Rs. Ten years ago, the costlier one was thrice as costly as the cheaper one. The present price of the costlier brand is Pick one
A) 30	B) 20	C) 10	D) 40	E) 50

Solution: Let their costs of x Rs and (x + 20) Rs respectively.   Then, (x + 20) - 10 = 3(x - 10)   ⇔ x +10= 3x - 30   ⇔ 2x = 40   ∴ Present cost of the costlier person = (20 + 10)= 
(20 + 10) = 30
30Rs.   30nswer :Rs.30
Answer: A
Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 90 grams of water?  Choose the correct option
A) 16	B) 90	C) 112	D) 128	E) 142

Solution: Solution:   We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 90 grams of water.   2x + 16x = 90   18x = 90   x = 5   Since x is 5, we know that there are 16 x 5 = 80 grams of oxygen in 90 grams of water.   Answer 90.
Answer: B
How many three letter words are formed using the letters of the word TIME?	Select the correct option.
A) 27 B) 20 C) 28 D) 24 E) 21

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 ⁴P₃   = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   Answer: 24
Answer: D
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?	Choose the correct choice from the following answers.
A) 59 B) 11! / (2!*2!*2!) C) 56 D) 23 E) 11! / (3!*2!*2!*2!)

Solution: Explanatory Answer   Select 2 letters and rearrange them   MEDITERRANEAN is 13-letter word.   We have to make 4 letter words that start with an 'E' and end with 'R'.   Therefore, we have to find two more letters from the remaining 11 letters.   Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.   The second and third positions can either have two different letters or can have both as same letters.   Case 1: When the two letters are different   One has to choose two different letters from the 8 available different choices.   This can be done in   8 * 7= 
  8 * 7 = 56
56 ways.   Case 2: When the two letters are same   There are 3 options - the two letters can be Ns or Es or As. Therefore, 3 ways.   Total number of posssibilities= 56 + 3= 
56 + 3 = 59
59   Choice 59
Answer: A
Sachin's age after 15 years will be 5 times his age 5 years back. Find out the present age of Sachin? Pick:	A) 5	B) 10	C) 8	D) 9	E) 12

Solution: Let present age of Sachin =x. Then,   (x+15)=5(x−5)⇒4x=40⇒x=10   Answer is 10.
Answer: B
A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
.	Choose the most appropriate option.
A) 2/16 B) 1/4 C) 7/24 D) 5/16 E) 15/32

Solution: Brunnel explained it in detail. I would just count the number of possibilities and divide it by 2^n   HHHHH   HHHTT   HHHHT   THHHT   TTHHH   HHHTH   THHHH   HTHHH   8/(2)^5 ==> 8/32 ==> 1/4   Answer: 1/4
Answer: B
If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 3 = ?
Select.
A) 2  B) 4  C) 8  D) 16  E) 32

Solution: 4 Ø 2 = 2^4/2^2 = 4   4 Ø 3 = 2^4/2^3 = 2   The answer is 2.
Answer: A
A person saved $10 in buying an item on sale. If he spent $600 for the item, approximately how much percent he saved in the transaction?  Options.
A) 8% B) 1.6% C) 2% D) 5% E) 6%

Solution: Actual price = 600+10= 
600+10 = 610
$610   Saving= 10/610 * 100 = 100/61 = 1.6% approximately   Answer is 1.6%
Answer: B
A right angled cone has its height 'h'. The cone is being cut parallel to its base at h/5 distance from its vertex. What will be the ratio of the cone and the cutting portion
Choose the correct choice from the following.
A) 1:124  B) 1:125  C) 1:25  D) 1:26  E) 1:24

Solution: let radius of smaller cone=R   radius of bigger cone=r   height of smaller cone=h/5   height of bigger cone=h   volume of smaller cone=1/3*pi*R^2*h   volume of reamaining portion=volume of bigger cone - volume of smaller cone   i.e 1/3*pi*r^2h-1/3*pi*R^2(h/5)   from the similarity of triangle   r/R=5:1   equating value   we get 1:124   1:124NSWER:1:124
Answer: A
A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Sale price of the article
II. Number of articles sold
Choose the correct choice from the following options.
A) Only I is necessary
B) Only II is necessary
C) Either I or II is necessary
D) Both I and II are necessary
E) None of these

Solution: EXPLANATION   Gain = 25% of C.P.   In order to find gain, we must know the sale price of each article and the number of articles sold.   answer is (Both I and II are necessary).
Answer: D