MU-NLPC/Calc-aqua_rat huggingface dataset:
The dimensions of a rectangular solid are 4 inches, 5 inches, and 9 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?  Choose one
A) 2:5
B) 5:9
C) 5:16
D) 25:7
E) 32:25

Solution: Answer: 5:9.
Answer: B
Two trains are moving in the same direction at 108 kmph and 36 kmph. The faster train crosses the slower train in 17 seconds. Find the length of the faster train in meters.  Options.
A) 270 m B) 340 m C) 310 m D) 350 m E) 327 m

Solution: Relative speed = (108 - 36) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in 17 sec= 17 * 20= 
17 * 20 = 340
340 m.   The length of the faster train= 340 m.   Answer:340 m
Answer: B
Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same? Choose the correct choice from the following options
A) 10  B) 9  C) 11  D) 10.4  E) 20

Solution: Explanation :   Here's is the solution :   S.I. on Rs. (260 - 20) for a given time = Rs. 20.   S.I. on Rs. 240 for half the time = Rs. 10.   T.D. on Rs. 250 = Rs. 10.   Therefore True Discount on Rs. 260 = Rs. (10 / 250) * 260   = Rs. 10.40   Hence (D) is the correct answer.   Answer : 10.4
Answer: D
A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
Choose the correct answer
A) 2 mins 14 sec B) 2 mins 34 sec C) 150 sec D) 164 sec E) 2 mins 44 sec

Solution: D = 25 * 60 + 1000= 
25 * 60 + 1000 = 2_500
2500 m   T= 2500/60 * 18/5= 
2500/60 * 18/5 = 150
150 sec   ANSWER:150 sec
Answer: C
Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 15kmph. What time will they take to be 50km apart?	Choose the correct choice from the following answers
A) 1hr  B) 2hrs  C) 3hrs  D) 5hrs  E) 6hrs

Solution: To be (10+15) km apart, they take 1 hour   To be 50 km apart, they take   1/25 *50= 
  1/25 *50 = 2
2 hrs   Answer is 2hrs
Answer: B
If 2/z = 2/(z + 1) + 2/(z + 36) which of these integers could be the value of z?	Pick one
A) 0
B) 1
C) 2
D) 3
E) 6

Solution: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:   A. 2/0 = 2/1 +2/36 INCORRECT (Division by zero)   B. 2/1 = 2/2 +2/37 INCORRECT   C. 2/2 = 2/3 +2/38 INCORRECT   D. 2/3 = 2/4 +2/39 INCORRECT   E. 2/4 = 2/5 +2/40 CORRECT   The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: E
Square ABCD is the base of the cube while square EFGH is the cube's top face such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2? Choices
A) 1/sqrt2  B) 1  C) sqrt2  D) sqrt3  E) 2sqrt3

Solution: distance from mid point of AB to AD = sqrt [(1/sqrt2)^2+(1/sqrt2)^2] = 1   the distance between the midpoint of edge AB and the midpoint of edge EH = sqrt [1^2+(sqrt2)^2] = sqrt3.   ANSWER:sqrt3
Answer: D
A boy has nine trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
Choose the correct answer:
A) 88
B) 98
C) 126
D) 108
E) 111

Solution: Explanation:   The boy can select one trouser in nine ways.   The boy can select one shirt in 14 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 14= 
  9 * 14 = 126
126 ways   126)
Answer: C
If f is a function defined for all k by f(k) = k^(2/3)/16, what is f(64 k) in terms of f(k)?
Choose the correct choice
A) 1/8 f(k)	B) 5/8 f(k)	C) 2 f(k)	D) 16 f(k)	E) 32 f(k)

Solution: f(k) = k^(2/3)/16   f(64 k) = (64k)^(2/3)/16 = 16 * k^(2/3)/16 = 16 * (k^(2/3)/16) = 16 f(k).   So answer is 16 f(k).
Answer: D
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each. The radius of the sphere is Select the correct option:	A) 3 cm	B) 5 cm	C) 6 cm	D) 8 cm	E) None

Solution: Solution   4Î R2	= 2Î 5x10   â‡’ R2 = (5x10/2)   â‡’ 25   â‡’ R = 5 cm.   Answer 5 cm
Answer: B
A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
Select the correct option:
A) 6 ½ sec	B) 4 ½ sec	C) 9 ½ sec	D) 8 ½ sec	E) 2 ½ sec

Solution: 8 ½ sec = 170   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 170/20 = 8 ½ sec   Answer: 8 ½ sec
Answer: D
How much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m, moving at 36 kmph in the same direction?	Pick one:	A) 50	B) 80	C) 88	D) 76	E) 12

Solution: The distance to be covered = Sum of their lengths = 300 + 500= 
300 + 500 = 800
800 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 800/10= 
800/10 = 80
80 sec.   Answer:80
Answer: B
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is? Choose the correct answer.
A) 20% loss
B) 20% profit
C) 10% profit
D) 25% loss
E) None of these

Solution: Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit = 10/40 * 100= 
10/40 * 100 = 25
25%   ANSWNone of theseR:None of these
Answer: E
In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election? Pick one:	A) 901	B) 989	C) 990	D) 991	E) 1,001

Solution: James = (0.5/100)*2000= 
(0.5/100)*2000 = 10
10   Votes to win= (50/100)*Total Votes +1 = (50/100)*2000 +1= 
(50/100)*2000 +1 = 1_001
1001   Remaining Voted needed to win election= 1001 - 10= 
1001 - 10 = 991
991   Answer: option 991
Answer: D
If 2x-y=4 then 6x-3y=?  Options
A) 15
B) 12
C) 18
D) 10
E) 14

Solution: 6x-3y=3*(2x-y)   6 -3= 
6 -3 = 3
3*(2x-y)=3*4= 
3*4 = 12
12   ANSWER:12
Answer: B
An assembly line produces 20 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
Choose the correct choice from the following
A) 25	B) 30	C) 35	D) 40	E) 45

Solution: The time to produce the first 60 cogs is 60/20= 
60/20 = 3
3 hours.   The time to produce the next 60 cogs is 60/60= 
60/60 = 1
1 hour.   The average output is 120 cogs / 4 hours= 30 cogs per hour.   The answer is 30.
Answer: B
A dual sink has a right side and left side. Working alone, the right side can fill up in 5 hours. Working alone, the left side can empty in 15 hours. If it is desired that the sink should be filled, from empty, exactly 6 hours after the right side is turned on at 9:30am, then at what time should the left side also be turned on? Choose one:
A) 10:00am  B) 10:45am  C) 12:00pm  D) 12:30pm  E) 1:30pm

Solution: In 6 hours the right side will fill up with water equal to 6*1/5 = 6/5 of the sink. So, 1/5 more than necessary, which should be compensated by the left side of the sink. To pump out 1/5 of the water the left side needs  15/5= 
 15/5 = 3
3 hours.   Therefore, the left side of the sink should be turned on at 9:30am + 6 hours - 3 hours= 12:30pm.   Answer: 12:30pm.
Answer: D
Some persons can do a piece of work in 8 days. Two times the number of these people will do half of that work in?  Choose the correct choice from the following answers:	A) 2	B) 4	C) 5	D) 6	E) 8

Solution: 8/ (2 * 2)= 
8/ (2 * 2) = 2
2 days   2nswer:2
Answer: A
A number when divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:
Choose the correct choice:
A) 214
B) 476
C) 954
D) 1908
E) 1910

Solution: Z= 6*1 +4= 
6*1 +4 = 10
10.   Y= 5z+3= 53   X= 4y+2= 214.   214NSWER:214
Answer: A
After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?	Choose the correct option
A) 27 B) 28 C) 20 D) 24 E) 12

Solution: 1/3 ---- 6   1 -------? A = 18   R = 1/18 * 60/100 = 1/30   1 ----- 1/30   2/3 ----? => 20 days   Answer:20
Answer: C
A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
Pick one:	A) 20	B) 25	C) 30	D) 40	E) 50

Solution: Ans.(D)   Sol. Number of choices to go by ship = 8 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 8 x 5 = 40 ways
Answer: D
At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years.	Options:
A) 10%	B) 15%	C) 20%	D) 12%	E) 22%

Solution: Explanation:   principal P = 2400/-   Rate of interest R = ?   Time T = 5 years   10%ccumulated 10%mount 10% = Rs.10400/-   10% = P + I   10% = P + PTR/100   10% = P(1+ TR/100)   2400[ 1 + (5 x R)/100] = 3600   2[(20 + R)/20] = 3   20 + R = 30   R = 10%   10%nswer: Option 10%
Answer: A
Two-third of a positive number and 16/216 of its reciprocal are equal. Find the positive number.
Pick:	A) 4 /12	B) 4 /17	C) 4 /15	D) 4 /11	E) 4 /03

Solution: Explanation:   Let the positive number be x.   Then, 2/3 x = 16/216 * 1/x   x2 = 16/216 * 3/2   = 16/144   x = √16/144 =4 /12.   4 /12NSWER:4 /12
Answer: A
A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?	Choose the most appropriate option.
A) 24	B) 6	C) 5	D) 4	E) 3

Solution: As A and B can finish the work in 12 days time, hence   (A + B)’s one day’s work = 1/12;   similarly   (B + C)’s one day’s work = 1/16   Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1   A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1   Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1   i.e. 5/12 + 2/16 + C’s 11 days’ work = 1   or C’s 11 days’ work = 1 - (5/12 + 2/16)   or C’s 11 days’ work = 1 - 13/24   or C’s 11 days’ work = 11/24   or C’s 1 day’s work = 11/24 x 1/11 = 1/24   Therefore, C alone can finish the complete work in 24 days.   24NSWER:24
Answer: A
A, B and C completed a piece of work, A worked for 16 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
Choose the correct choice from the following.
A) Rs.80
B) Rs.120
C) Rs.71.15
D) Rs.51.15
E) Rs.180

Solution: 3x 4x 5x   16 9 4   48x + 36x + 20x = 1480   104x = 1480 => x = 14.23   5x = 71.15 Rs.   ANSWER:Rs.71.15
Answer: C
A 340-liter solution of Kola is made from 64% water, 9% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 8 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
Choose the correct option:
A) 6%. B) 7.5%. C) 9.2%. D) 10.5%. E) 26.5%.

Solution: Denominator:   340+8+3.2+6.8= 
340+8+3.2+6.8 = 358
358   Numerator:   340(1-.64-.09)+3.2   340(0.27)+3.2   91.8+3.2   95   Ratio:   95/358=0.265   Answer: 26.5%.
Answer: E
In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (5,5) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.  Answers: A) (-2,6) B) (0,4) C) (2,-6) D) (2,6) E) (4,0)

Solution: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).   (2,-6) and (2,6) are not on that line. If A is at (0,5) or (5,0), then the area is 1/2*5*5=25/2. Thus A must be at (2,6).   Answer: (2,6).
Answer: D
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
Select the correct option.
A) 87
B) 27
C) 90
D) 26
E) 29

Solution: 200*2= 
200*2 = 400
400   580   -----   180   1----2   ?----180= 90   Answer: 90
Answer: C
Which of the following CANNOT be the median R of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?	Select:
A) (w+x)/2 - 1  B) (w+z)/2  C) (x+y)/2  D) (y+z)/2 -1  E) (w+x+y+z)/4

Solution: Using the properties of consecutive positive integers we could right away eliminate B,C and E.   (B) - The average of first and last terms is the median   (C) - For even number of integers, the median is the average of middle terms   (E) - The average is equal to median if the integers are consecutive   Remaining answer choices are A and D.   For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median R.   (w+x)/2 - 1nswer ((w+x)/2 - 1)
Answer: A
A money lender lends Rs.1800 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit? Choose the correct answer:
A) 2205	B) 1984.5	C) 2834	D) 2827	E) 2781

Solution: A = 1800(21/20)2   = 1984.5   Answer: 1984.5
Answer: B
John has $1,600 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
Choose the correct answer:
A) $200  B) $400  C) $600  D) $800  E) $1,200

Solution: let the money spent be x   money he is left with after spending = x-800   total money --> x+(x-800) = 1600   solving for x will give x = 1200,   therefore the money he is left with = x-800   = 1200 - 800= 
1200 - 800 = 400
400   ANSWER:$400
Answer: B
The present ratio of students to teachers at a certain school is 35 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?  Choose the correct choice from the following answers
A) 5  B) 8  C) 10  D) 12  E) 15

Solution: We are given that the ratio of students to teacher is 35 to 1. We can rewrite this using variable multipliers.   students : teachers = 35x : x   We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:   Students/Teachers  25/1 = (35x + 50)/(x + 5)   If we cross multiply we have:   25(x + 5) = 35x + 50   25x + 125 = 35x + 50   7.5 = x   x~8   Since x is the present number of teachers, currently there are 8 teachers.   Answer 8.
Answer: B
Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
Options.
A) 12 days	B) 5 days	C) 9 3/8 days	D) 8 days	E) 6 days

Solution: Explanation:   1/15 + 1/25 = 8/75   75/8 = 9 3/8 days   Answer: 9 3/8 days
Answer: C
Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 6 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?  Choose the correct choice from the following choices:
A) 1/2  B) 1/3  C) 1/4  D) 2/3  E) 2/5

Solution: Tom paints 1/6 of the room in the first hour.   Tom and Peter paint 1/6+1/3 = 1/2 of the room in the next hour for a total of 4/6.   The three people then paint the remaining 2/6 in a time of (2/6) / (4/6) = 1/2 hours   Peter worked for 3/2 hours so he painted 3/2 * 1/3 = 1/2 of the room.   The answer is 1/2.
Answer: A
A material is purchased for Rs. 600. If one fourth of the material is sold at a loss of 20% and the remaining at a gain of 10%, Find out the overall gain or loss percentage Choose the most appropriate option:
A) 4 1/2 B) 3 1/2 C) 2 1/2 D) 1 1/2 E) None of these

Solution: Explanation:   We need to get the Total selling price to solve this question. Because after getting selling price we can get profit or loss, then we can calculate profit% or loss%   So lets solve this:   Price Received by selling one fourth of the material at a loss of 20% =   (1/4) * 600 * (80/100) = Rs. 120   Price Received by remaining material at a gain of 10% =   (3/4) * 600 * (110/100) = Rs. 495 [Note: 1-(1/4) = 3/4]   Total Selling Price = 120 + 465 = Rs. 615   Profit = 615 - 600= 
615 - 600 = 15
15   Profit%=(Gain/2 1/2ost∗100)%=(15/600∗100)%=5/2%=2 1/2%   Option 2 1/2
Answer: C
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choose the correct option.
A) 76 sec	B) 12 sec	C) 15 sec	D) 14 sec	E) 13 sec

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (120 + 120)/20= 
(120 + 120)/20 = 12
12 sec.   Answer: 12 sec
Answer: B
A train passes a platform in 18 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is	Options
A) 120 B) 250 C) 260 D) 230 E) 220

Solution: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s   Length of the train = speed × time taken to cross the man = 15×20 = 300 m   Let the length of the platform = L   Time taken to cross the platform = (300+L)/15   => (300+L)/15 = 18   => 300+L = 15×18 = 270   => L = 390-270= 
390-270 = 120
120 meter   120nswer is 120.
Answer: A
When m divided by 288, the remainder is 47. Find the remainder when the same m is divided by 24?	Choose the correct choice from the following choices
A) 20  B) 21  C) 22  D) 23  E) 26

Solution: 23   Option 23
Answer: D
Two good train each 650 m long, are running in opposite directions on parallel tracks. Their speeds are 45 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 most appropriate option:  A) 12.4 sec  B) 24.3 sec  C) 62.4 sec  D) 60.1 sec  E) None

Solution: Sol.   Relative Speed = (45 + 30) km / hr   = (75 x 5 / 18) m/sec   = (125/6) m/sec.   Distance covered = (650+ 650)= 
(650+ 650) = 1_300
1300 m.   Required time= (1300 x 6 / 125) sec = 62.4 sec.   Answer 62.4 sec
Answer: C
How many ways are there for 5 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? Pick.
A) 6  B) 12  C) 240  D) 100  E) 720

Solution: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 5 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 5! different ways, so total 2*5!=240.   Answer 240.
Answer: C
There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is  Choose the correct choice from the following answers:
A) 55
B) 21
C) 42
D) 51
E) 21

Solution: List down possibilities: From only 1 box all the way to all 6   If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.   If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.   If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.   If all 6 boxes have green balls, there is just 1 possibility.   Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21.   Ans: 21
Answer: E
In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?  Select the correct option:
A) 16.55	B) 16.59	C) 16.54	D) 16.5	E) 16.51

Solution: Let the quantities of A and B mixed be 3x kg and 7x kg.   Cost of 3x kg of A = 9(3x) = Rs. 27x   Cost of 7x kg of B = 15(7x) = Rs. 105x   Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x   Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66   Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50   Answer:16.5
Answer: D
19 times a number gives 342. The number is  Options
A) 18	B) 19	C) 16	D) None	E) Cannot be determined

Solution: Explanation:   Let the number be 'N'   19×N=342⇒N=18   Correct Option: 18
Answer: A
A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 5 days. How many more days are required to complete the remaining work if they work together? Select:
A) 3 (5/18)
B) 3 (5/16)
C) 3 (5/11)
D) 3 (5/13)
E) 5/11

Solution: A can do 1/10 of the work in a day.   B can do 1/12 of the work in a 1 day.   Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60   They take 60/11 days to complete the work together.   Given that they already worked for 5 days.   The number of days required to complete remaining work => 60/11 - 5 = 5/11 = 5/11 days.   Answer:5/11
Answer: E
If -1<x<0, what is the median N of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3 Choose the correct choice from the following answers:
A) 1/x	B) x^2	C) x^2(x+1)/2	D) N=x(x^2+1)/2	E) x^2/2x

Solution: My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:   -8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.   median will be between -0.5 and -0.125.   So, (x^3+x)/2 (N=x(x^2+1)/2).
Answer: D
The average of two numbers is P. If one number is Q, then the other number is  Choose the correct choice from the following answers.
A) 2Q	B) 2P	C) P - Q	D) 2P-Q	E) None of these

Solution: Explanation :   Let the other number be x,   According to the question,   => ( x + Q ) / 2 = P.   => x + Q = 2P.   => x = 2P - Q.   Hence, the required number is 2P - Q.   Answer : 2P-Q
Answer: D
The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 3. If p is any prime number then f(p)=  Choose the correct answer
A) p-1  B) p-2  C) (p+1)/2  D) (p-1)/2  E) 2

Solution: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.   Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).   If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.   Answer: (p-1)/2.
Answer: D