MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following points is symmetric with y=x at (1,2)?  Choose the correct answer:
A) (-2,-1)
B) (-2,1)
C) (2,1)
D) (-1,-2)
E) (-1,2)

Solution: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.   (1,2) would become (2,1).   Answer ((2,1)).
Answer: C
A machine puts c caps on bottles in m minutes. How many seconds will it take to put caps on b bottles?
Choose the correct choice from the following answers.
A) 60bm/c  B) bm/60c  C) bc/60m  D) 60b/cm  E) b/60cm

Solution: A machine puts c caps on bottles in m minutes.   So, the machine puts 1 cap in m/c minutes   To put caps on b bottles, the machine will take bm/c minutes   In order to calculate the no. of hours taken , multiply the product by 60.   So, our answer is bm60/c   60bm/cnswer : 60bm/c
Answer: A
Oak trees line both sides of a street for a length of 6/8 of a kilometer. If there is 12 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?  Choose the correct choice from the following choices:
A) a)	59 B) b)	23 C) c)	24 D) d)	44 E) e)	46

Solution: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.   6/8 of 1 km = 750 m   Lets assume that x trees are planted So equation is   x*1 +(x-1)*12 = 750   Solve for x and we get x = 59, answer is a)	59
Answer: A
A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately? Choose the correct choice from the following choices:
A) 2 days	B) 8 days	C) 6 days	D) 8 days	E) 9 days

Solution: A + 8 days = 1/20 + 1/15 = 7/60   A + C = 1/20 + 1/12 = 8/60   7/60 + 8/60 = 15/60 = 1/4   4 days * 2 = 8 days   Answer: 8 days
Answer: B
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers T are there between 6* + 2 and 6* + 6, inclusive? Options
A) None  B) One  C) Two  D) Three  E) Four

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.   Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes T in this range.   Nonenswer: None.
Answer: A
The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class?	Choose the correct answer:
A) 218  B) 226  C) 234  D) 242  E) 250

Solution: 1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20   The number of degrees is  13/20 * 360= 
 13/20 * 360 = 234
234 degrees   The answer is 234.
Answer: C
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?  Choices
A) 33 1/8% B) 33 1/9% C) 33 1/3% D) 33 8/3% E) 33 2/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer: 33 1/3%
Answer: C
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7, 8, 9}(repetition of digits is not allowed)?	Pick one
A) 840  B) 697  C) 278  D) 279  E) 274

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is   7Pâ‚„ =7* 6 * 5 * 4= 
7* 6 * 5 * 4 = 840
840.   840nswer: 840
Answer: A
(1^2+2^2+3^2+.....+12^2)=?
Choose one: A) 330 B) 345 C) 365 D) 385 E) 650

Solution: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)   n=12   =(1/6x12x13x25)   =650   Answer is 650.
Answer: E
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Choose the correct choice from the following:	A) 286 m	B) 278 m	C) 278 m	D) 150 m	E) 276 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150 m
Answer: D
Two friends want to buy a snack. They combine their money and find they have $3.10, consisting of quarters, dimes, and nickels. If they have 28 coins and the number of quarters is half the number of nickels, how many quarters do they have?	Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let x be the number of quarters. Then 2x is the number of nickels.   (1) 25x + 10x + 10D = 310. Then 7x + 2D = 62   (2) 3x + D = 28. Then 6x + 2D = 56   Let's subtract equation (2) from equation (1).   x = 6   The answer is 6.
Answer: D
Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is  Answers:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set   1NSWER:1
Answer: A
John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month?
Choose the correct choice: A) $1,248 B) $1,300 C) $1,331 D) $1,410 E) $1,463

Solution: 1,000 + 100 (10%) = 1,100   1,100 + 110 (10%) = 1,210   1,210 + 121 (10%) = 1,331   Answer: $1,331
Answer: C
The radius of a semi circle is 6.3 cm then its perimeter is?	Choose the correct choice from the following answers:
A) 32.5 B) 32.4 C) 32.1 D) 32.9 E) 32.3

Solution: 36/7 r = 6.3 = 32.4   Answer:32.4
Answer: B
In a survey about potential presidential candidates A and B, 39% of the public like A and 57% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?  Options:
A) 28%
B) 35%
C) 43%
D) 22%
E) 61%

Solution: Let x be the percentage of people who like both.   Then the percentage of people who like only 1 but not both is 2x.   39% + 57% = 2x + 2(x) because the percentage who like both are counted twice.   Then x = 24% and 2x = 48%   100% = 24% + 48% + Neither   Neither = 28%   The answer is 28%.
Answer: A
A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?
Choose the correct choice from the following answers.
A) 5%  B) 70%  C) 25%  D) 40%  E) 55%

Solution: The complete round trip consists of driving to the service center and then back home again.   So, once the technician drives to the service center he/she has already competed 50% of the entire trip.   Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%   so  0.5+0.5*0.4= 
 0.5+0.5*0.4 = 0.7
0.70   Answer:   70%
Answer: B
What is the square root of 261,121? Answers.
A) 476 B) 489 C) 497 D) 511 E) 524

Solution: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.   2) B = 489^2 and D = 511^2   B = (500-11)^2 and D = (500 + 11)^2   Since we need the answer less than 250000 => B is out.   Thus we have 511 as the ans.
Answer: D
14 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work? Choose the most appropriate option:
A) 27.5 days  B) 15.5 days  C) 17.5 days  D) 16.5 days  E) 18.5 days

Solution: 14 * 25 = 20 * x => x = 17.5 days   ANSWER:17.5 days
Answer: C
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?  Choose the correct choice from the following options
A) 29.42 B) 29.22 C) 29.25 D) 23.25 E) 29.28

Solution: Average of 9 = x   9x = 8 * 3 + x * 2 x = 3.25   Total = 9 * 3.25= 
9 * 3.25 = 29.25
29.25   Answer:29.25
Answer: C
The average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added. If average weight of the whole group after including the additional 30 members is 40 kg, what is the average weight of the additional friends?	Choices
A) 50 kg	B) 60 kg	C) 61 kg	D) 62 kg	E) 91 kg

Solution: let a=avg. wt. of additional 30 friends   original total weight=(30 friends)(30 kg avge)=900kg   (900+30a)/(30+30)=40 kg avge   a=50 kg   50 kgnswer - 50 kg
Answer: A
If p^2 – 13p + 40 = h, and p is a positive integer between 1 and 10, inclusive, what is the probability that h < 0?  Choose the correct choice from the following choices:
A) 1/10 B) 1/5 C) 2/5 D) 3/5 E) 3/10

Solution: p2 – 13p + 40 = h   so (p – 8)(p – 5) = h   For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.   The correct answer is 1/5.
Answer: B
A man walks at a rate of 10 mph. After every ten miles, he rests for 5 minutes. How much time does he take to walk 50 miles? Choose the correct choice from the following answers:
A) 300 B) 318 C) 320 D) 324 E) 330

Solution: To cover 50 miles the man needs (time) = (distance)/(rate) = 50/10= 
50/10 = 5
5 hours= 300 minutes. He will also rest 4 times (after 10, 20, 30 and 40 miles), so total resting time = 4*5= 
4*5 = 20
20 minutes.   Total time= 300 + 20= 
300 + 20 = 320
320 minutes.   Answer: 320.
Answer: C
A cyclist bikes x distance at 12 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?	Choose the correct choice from the following answers
A) 8.1	B) 8.3	C) 9.6	D) 8.9	E) 9.0

Solution: Distance = d1 = x miles   Speed = s1 = 12 miles per hour   Time = t1 = Distance/ Speed = x/12   2. Going from B to A   Distance = d2 = x miles   Speed = s2 = 8 miles per hour   Time = t2 = Distance/ Speed = x/8   3. Average Speed = Total Distance/Total Time   Total Distance = x + x = 2x   Total Time = x/12 + x/8 = x (1/12 + 1/8) = =5x/24   Speed = 2x/(5x/24) = 48/5= 
48/5 = 48/5 = around 9.6
9.6   Answer : 9.6
Answer: C
There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls. A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.	Pick:
A) 7/120 B) 17/120 C) 27/120 D) 37/120 E) 47/120

Solution: P(Getting a red ball from the first bag): (1/2)*(5/12)   P(Getting a red ball from the 2nd bag): (1/2)*(3/15)   P(37/120rawing a red ball):   (1/2)*(5/12)+(1/2)*(3/15)= 37/120   ANSWER:37/120
Answer: D
The triplicate ratio of 1:3 is?  Select:
A) 1:0  B) 1:8  C) 1:27  D) 1:2  E) 1:1

Solution: 13: 33 = 1:27   Answer: 1:27
Answer: C
A man two flats for $675958 each. On one he gains 12% while on the other he loses 12%. How much does he gain or lose in the whole transaction? Select the correct option:	A) 1.44%	B) 2.56%	C) 3.12%	D) 4.65%	E) 5.12%

Solution: In such a case there is always a loss   Loss% = (12/10)^2 = 36/25= 
36/25 = 36/25 = around 1.44
1.44%   1.44%nswer is 1.44%
Answer: A
Which is the middle even number between 4 and 12?
Choose the correct choice from the following:  A) 9  B) 12  C) 14  D) 8  E) 22

Solution: 4+x = 12-x   2 x = 8   X = 4   Now 4+x = 8   ANSWER:8
Answer: D
It takes John 20 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?  Choose the most appropriate option.
A) 7:50 B) 7:45 C) 6 D) 5 E) 4

Solution: The time it takes John to get to work: time to walk to car park + time to drive   20 + 45 = 70 minutes = 1 hour and 10 minutes   John needs to get out of the house 1 hour and 10 minutes before 9:00 am at   9:00 - 1:10 = 7:45 a.m.   7:45
Answer: B
The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Choose the correct answer:	A) 245	B) 777	C) 282	D) 266	E) 215

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (160 + x)/30 = 25/2 => 2(160 + x) = 750 => x = 215 m.   Answer: 215
Answer: E
A cyclist rides a bicycle 9 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 9 km/hr. What is the average speed for the entire trip? Pick one:
A) 9.5 B) 9.8 C) 10.1 D) 10.6 E) 11.2

Solution: distance = 21 km   time = 9/12 + 12/9 = (81 + 144) / 108 = 225 / 108 = 25/12 hours   average speed = (21 * 12) / 25 = 10.1 km/h   The answer is 10.1.
Answer: C
A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Select: A) 229 B) 277 C) 600 D) 275 E) 221

Solution: D = 30 * 5= 
30 * 5 = 150
150   RS= 40 – 30 = 10   T = 150/10= 
150/10 = 15
15   D= 40 * 15= 
40 * 15 = 600
600 km.,Answer: 600
Answer: C
For how many values of B, is |||B - 5| -10| -5| = 2?
(Those ls are mods)
Choose the correct choice from the following choices
A) 0  B) 2  C) 4  D) 8  E) More than 8

Solution: I think its 8   |||B-5|-10|-5| =2   let |B-5| = a which makes above   ||a-10|-5| =2   let |a-10| = b which makes   |b-5| = 2   now for the above b can take 3, 7   for every b =3 a can have 13, 7   and for b = 7 a can have 17 and 3   so 'a' has four solutions 13, 7, 17 and 3   for a = 13; x has 18 or -8 thus has 2 for every combination hence 4x2 = 8   answer 8
Answer: D
A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be the member chosen to be the secretary ? Choose the most appropriate option
A) 1/720  B) 1/80  C) 1/10  D) 1/9  E) 1/5

Solution: This question is much easier than it appears.   Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 .   Answer: 1/10
Answer: C
Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers? Choose the correct answer:	A) 9,375	B) 9,750	C) 9,975	D) 9,984	E) 10,736

Solution: 1st number= 10,000   2nd number = 20% of 10,000= 2000   3rd number= 20% of 2000= 400   4th number = 20% of 400= 80   5th number= 20% of 80= 16   Range = 10,000-16= 9984   9,984 is the answer
Answer: D
A, B and C rents a pasture for Rs.870. 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?	Pick:
A) 270	B) 289	C) 267	D) 255	E) 552

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 870= 
9/29 * 870 = 270
270   270nswer: 270
Answer: A
A club with a total membership of 40 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees? Select the correct option
A) 5  B) 7  C) 8  D) 10  E) 20

Solution: As no member of committee M is on either of the other 2 committees then 40-M=40-8= 
40-8 = 32
32 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees   General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 32-12= 
32-12 = 20
20 is the greatest possible number of members in the club who are on none of the committees.   Answer: 20.
Answer: E
In a school with 640 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is Pick one.
A) 160
B) 200
C) 250
D) 350
E) None

Solution: Sol.   Let the number of grils be x.   Then, number of boys = (640 - x).   Then, (11 3/4 × 640)   ⇔ 11x + 12(640 - x) ⇔ x = 7680 - 7520 ⇔ 160.   160nswer 160
Answer: A
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).  Choose the correct choice from the following.
A) 8, 20, 28 B) 16, 28, 36 C) 20, 35, 45 D) None of these E) cannot be determined

Solution: EXPLANATION   Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x – 8) + (7x – 8) + (9x – 8) = 56   20x = 80   x = 4.   Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.   Answer 16, 28, 36
Answer: B
Tap ‘A’ can fill a water tank in 25 minutes, tap ‘B’ can fill the same tank in 40 minutes and tap ‘C’ can empty that tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied? Choose the correct answer:
A) 3 2⁄13  B) 15 5⁄13  C) 8 2⁄13  D) 31 11⁄19  E) None of these

Solution: Tank filled in 1 minute = 1⁄25 + 1⁄40 - 1⁄30 part   = 24+15−20/600=19/600 part   ∴ tank will be filled complete in minutes   = 600⁄19 = 3111⁄19   Answer 31 11⁄19
Answer: D
A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work? Choose the correct choice.
A) 12  B) 10  C) 27  D) 24  E) 92

Solution: A can do the work in 30/2 i.e., 15 days.   A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10   So A and B together can do the work in 10 days.   Answer:10
Answer: B
If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 3, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
Choose the correct choice from the following.
A) 3 B) 4 C) 5 D) 6 E) 8

Solution: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 3, and 3x – 2 are ALLintegers   For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.   Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers   When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 3, and 3(3) – 2.   When we evaluate these terms we get: 4, 6, 3, 6 and 7   Rearrange to get: 3, 4, 6, 6, 7. So, when x = 3, we getconsecutive integers.   In this case, the ME6IAN = 5   Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)   Answer:   6
Answer: D
Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for v dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?	Choose one:
A) (x – s)v – sd
B) xv – (xd – sd)
C) xd – sv
D) (x – s)d – xv
E) (s – v)d – xv

Solution: Answer D:   The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time v, so the profit is (x-s)d-xv.
Answer: D
From below option 50 is divisible by which one? Options.
A) 3
B) 2
C) 7
D) 8
E) 9

Solution: 50/2= 
50/2 = 25
25   2
Answer: B
The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit U on the height of vehicles that are allowed to use the tunnel?	Choose the most appropriate option:  A) 5½ ft  B) 7½ ft  C) 8 ½ ft  D) 9½ ft  E) 10 ft

Solution: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.   We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.   Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).   Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).   Finally: AB=8, so the correct answer U is 8 - .5 = 7.5... choose (7½ ft)!   From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.7½ ft
Answer: B
Which of the following is closest to 10^180 – 10^10 ? Choose the most appropriate option
A) 10^210  B) 10^90  C) 10^150  D) 10^180  E) 10^6

Solution: 10^180 – 10^10   10^10 * (10^170 – 1)   as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^170 – 1) would remain as 10^170.   and 10^10 * 10^170 = 10^180. Answer is 10^180.
Answer: D
If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?	Choose the correct answer:
A) 289
B) 334
C) 364
D) 356
E) 346

Solution: A particular players is never chosen, it means that 11 players are selected out of 14 players.   => Required number of ways = 1436411   = 14!/11!x3! = 364   364
Answer: C
Sasha likes to go biking on the weekends. One Saturday, she leaves home and heads east at 10 AM. She travels 12 miles per hour for three hours, then 18 miles per hour for the next two hours. She turns around to head home after a short water break, how fast does Sasha need to ride, in miles per hour, to get home at 5 PM?	Choose the correct choice:  A) 17  B) 18  C) 19  D) 20  E) 21

Solution: She travels 12*2 + 18*2= 
12*2 + 18*2 = 60
60 miles east in 4 hours, taking a short rest at 2 PM   She needs to travel at (60 miles) / (5 PM - 2PM)= 60 miles / 3 hours = 20 miles per hour   Correct answer: 20
Answer: D
The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it? Choose the correct option:	A) 8729	B) 8721	C) 2772	D) 9927	E) 2388

Solution: Actual price = 95% of 90% of 85% of Rs. 12000   = 95/100 * 90/100 * 85/100 * 12000   = Rs. 8721.   Answer: 8721
Answer: B
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?	Choose the correct choice from the following:
A) 1  B) 7  C) 3  D) 8  E) 5

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 64   ? --- 12=> Rs.3   Answer: 8
Answer: D