MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?  Choose the correct choice from the following choices
A) 32 sec
B) 17 sec
C) 12 sec
D) 46 sec
E) 15 sec

Solution: D = 250 m + 250 m = 500 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 500 * 3/125= 
500 * 3/125 = 12
12 sec   Answer:12 sec
Answer: C
The contents of a certain box consist of 72 apples and 30 oranges. How many oranges must be added to the box so that exactly 30% of the pieces of fruit in the box will be apples?
Choose the most appropriate option.
A) 68 B) 78 C) 88 D) 138 E) 108

Solution: apple = (apple + orange + x)*0.3   72 = (30 + 72 + x)*0.3   x = 138   Answer: 138
Answer: D
From given equation find the value of x: 2x² + 9x − 5  Choose the correct choice from the following:
A) 1/2
B) 1
C) 1 1/2
D) 2/3
E) 3/5

Solution: That quadratic is factored as follows:   2x² + 9x − 5 = (2x − 1)(x + 5).   Lesson 17.   Now, it is easy to see that the second factor will be 0 when x = −5.   As for the value of x that will make   2x − 1 = 0,   we must solve that little equation. (Lesson 9.)   We have:   2x = 1   x = 1   2   The solutions are:   x = 1/2 or −5   1/2
Answer: A
A bulk pack consists of 7 primary parts and 4 secondary parts. If a bundle is created with 4 primary parts and 2 secondary parts, in how many ways can the bundles be formed?  Choose the correct choice from the following:	A) 6	B) 36	C) 45	D) 210	E) 235

Solution: Choose 4 primary parts from 7 primary parts and choose 2 secondary parts from 4 secondary parts:   4C7 * 2C4 = 35*6= 
35*6 = 210
210   Ans: 210
Answer: D
At a dinner party, 9 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?  Select the correct option:
A) 5 B) 10 C) 40320 D) 3200 E) 12000

Solution: Has to be C.   Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle   hence (9-1)= 
(9-1) = 8
8!= 40320
Answer: C
if jacob sold a watch costing rs.400 to john at 15% profit and john sold the same to sudhir at 15% profit, what is the price paid by sudhir? Choose the correct choice from the following options:
A) 460
B) 510
C) 529
D) 560
E) 575

Solution: John cp=1.15*400= 
1.15*400 = 460
460   sp of john=1.15*460= 
1.15*460 = 529
529   ANSWER:529
Answer: C
A restaurant meal cost $60 and there was no tax. If the tip was more than 20 percent but less than 30 percent of the cost of the meal, then total amount paid must have been between:
Choose the correct answer:
A) $70 and $76  B) $73 and $78  C) $71 and $79  D) $68 and $75  E) $60 and $71

Solution: let tip=t   meal cost=60   range of tip = from 20% of 60 to 30% of 60 = 12 to 18   hence range of amount paid= 60+T= 72 to 78 i.e. $71 and $79
Answer: C
Complete the below series
5,6,7,8,10,11,14, ?	Choose the correct answer:
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: when we separate odd and even places the we get   5,7,10,14 and 6,8,11   difference between the first series is   2,3,4   difference between the second series is   2,3 so next number should be addition of 4 ie( 11+4=15)   the answer is 15   ANSWER:15
Answer: D
3-3*7+2= Select:  A) A)2  B) B)-13  C) C)-18  D) D)-16  E) of the above

Solution: 3-3*7+2 = 5-21 = -16...   so the answer is -13... -16
Answer: D
Martha's Hair Saloon has recently lowered the prices of haircuts. If the decrease in the price of a haircut is 20% of the new price of a haircut, what is the approximate percent decrease in the price of a haircut at Martha's ?
Pick one:
A) 15%  B) 16.7%  C) 20%  D) 25%  E) 87.5%

Solution: Assume new price to be x.   decrease = 20% of the new price of a haircut = 0.2x   Hence, Old price = 1.2x   %decrease = 0.2x/1.2x = 1/6 = 16.67%   Answer :Option 16.7%
Answer: B
In how many ways the letters of the word RAIXBON be arranged?  Choose the correct option:
A) 4367
B) 5657
C) 8756
D) 5040
E) 4345

Solution: Total ways of arranging the letters = 7! = 5040 ways.   5040)
Answer: D
A round table conference to be held between 43 delegates of 43 countries. In how many ways can they seated if two particular delegates are always to sit together? Choose the correct choice from the following answers
A) 27!*3!  B) 32!*7!  C) 45!*1!  D) 39!*5!  E) 41!*2!

Solution: Regarding two particular delegates who are to sit together as on one person, we have only   41+1= 
  41+1 = 42
42 persons.these 42 persons can be seated at the round table in 42! ways.   But two particular persons can be arranged among themselves in 2! ways.   Required number=41!*2!   Answer is 41!*2!
Answer: E
In an examination, 47% failed in English and 54% failed in Mathematics. Find the pass percentage in both the subjects if 31% failed in both the subjects?
Choose the most appropriate option
A) 900	B) 277	C) 287	D) 255	E) 121

Solution: X * 4/5 * 80/100 = 576   X = 14400/16= 
14400/16 = 900
900   900nswer: 900
Answer: A
A restaurant meal cost $33.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:	Choose the correct choice from the following options
A) $40 and $42 B) $39 and $41 C) $38 and 40 D) $37 and $39 E) $36 and $37

Solution: let tip=t   meal cost=33.50   range of tip = from 10% of 33.5 to 15% of 33.5 = 3.55 to 5.325   hence range of amount paid= 33.5+T= 37.05 to 38.825   ANSWER:$37 and $39
Answer: D
The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a 10?	Pick:
A) 1/52	B) 1/26	C) 1/4	D) 1/13	E) 5/13

Solution: The question should ask about the probability not the odds.   There are 13 spades, the probability that the spade we already have is a 10 is therefore 1/13.   Answer: 1/13.
Answer: D
The purchase price of an article is $48. In order to include 20% of cost for overhead and to provide $12 of net profit, the markup should be
Choose the correct choice:
A) 15%
B) 25%
C) 35%
D) 40%
E) 45%

Solution: Cost price of article = 48$   % of overhead cost = 20   Net profit = 12 $   We need to calculate % markup   Net profit as % of cost price = (12/48)*100= 
(12/48)*100 = 25
25%   Total markup should be= 25 + 20= 
25 + 20 = 45
45%   Answer 45%
Answer: E
Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?	Choose the most appropriate option:
A) 90	B) 88	C) 66	D) 55	E) 11

Solution: Let the length of each train be x m.   (x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)= 
(750 * 18) / (30 * 5) = 90
90 sec.   90nswer: 90
Answer: A
There are 40 students in a certain geometry class. If one half of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? Choices:  A) 6  B) 12  C) 15  D) 24  E) 27

Solution: Total Students = 40   One half of the students are boys = 1/2*40= 
1/2*40 = 20
20   Three fourths of the boys are under six feet tall= 3/4*20= 
3/4*20 = 15
15 ...   Therefore Number of boys in the class under six feet tall= 15 ... Answer C....   Alternatively... Number of boys in the class under six feet tall = 3/4 of 1/2 of Total Students = 3/4*1/2*40 = 15...   Answer 15
Answer: C
In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?  Choices.
A) 170 B) 180 C) 200 D) 30 E) 220

Solution: Option '30'   6p2 = 6 x 5 = 30
Answer: D
A class consists of 100 students, 30 of them are girls and 70 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is  Pick one.
A) 3/125 B) 1/59 C) 1/56 D) 1/54 E) 1/53

Solution: The probability of selecting girl is: 30/100 = 3/10   The probability of selecting rich is: 20/100 = 1/5   The probability of selecting fair complexioned is: 40/100 = 2/5   Three are independent;probability of rich and fair complexioned girl is:   (3/10) Ã—(1/5) Ã— (2/5) = 3/125   3/125nswer: 3/125
Answer: A
For how many integers n is 1^n+5 = (n+5)^1?
Pick one:  A) 1  B) 2  C) None of these  D) 3  E) 4

Solution: If n=0   1^0+5= (0+5)^1   1^5 = 1 ; 5^1 =5 not ok   If n=1   1^1+5 =1 ; (1+5)^1=6^1=6 not OK   So, Answer : None of these
Answer: C
Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 10 meters. What distance is she from the starting point and in which direction? Pick one.
A) 35 m East
B) 35 m North
C) 30 m West
D) 45 m West
E) 30 m East

Solution: The net distance is 20 + 10= 
20 + 10 = 30
30 meters to the east.   The answer is 30 m East.
Answer: E
A train passes a station platform in 50 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Choose the correct choice from the following options
A) 180 m B) 200 m C) 240 m D) 320 m E) 450 m

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 50= 15 ⇔ x + 300 = 750 ⇔ x = 450 m.   Answer 450 m
Answer: E
The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:30 am, in the same direction from the same station, with a speed of 75 km/hr. What time will the second train catch the first train?  Choose one.
A) 11:30 am
B) 12:30 pm
C) 1:30 pm
D) 2:30 pm
E) 3:30 pm

Solution: In ninety minutes, the first train travels 90 km.   The second train catches the first train with a relative speed of 15 km/h.   The second train will catch the first train in 6 hours.   The second train will catch the first train at 1:30 pm.   The answer is 1:30 pm.
Answer: C
A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?	Choose one: A) A)1km B) B)500m C) C)600m D) D)750m E) E)800m

Solution: Relative speed of the policeman = 20-15= 
20-15 = 5
5 km/hr   time taken by policeman to cover 200m= (200/1000)*(1/5) = 1/25 hr   In 1/25 hr the thief covers a distance of 15/25 km = 3/5 km = 600m   Answer is 600m
Answer: C
Seven years ago Anoop was P times as old as Kiran was. If Anoop is now 17 years old, how old is Kiran now in terms of P ?	Choose one.
A) 10/P + 7  B) P/11 +7  C) 17 - P/7  D) 17/P  E) 11.5P

Solution: let's call Kiran's age seven years ago is x   so seven years ago 10/P + 7noop was:  17-7= 
 17-7 = 10
10 years old   and seven years ago 10/P + 7noop was P times as old as Kiran was=> 10/x = P   => x = 10/P   => Now Kiran's age will be : x+7 = 10/P+7   => the answer is 10/P + 7
Answer: A
The surface of a cube is 24sq cm. Find its volume?
Select:
A) 8
B) 7
C) 6
D) 5
E) 4

Solution: 6a2 = 24   a = 2 => a3 = 8cc   8nswer: 8
Answer: A
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
Answers:	A) 5:15	B) 5:17	C) 5:12	D) 5:13	E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128 = 5:16   Answer: 5:16
Answer: E
A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 15 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?  Choose the correct choice from the following answers:
A) 2 hours, 225 miles B) 3 hours, 350 miles C) 4 hours, 450 miles D) 2.75 hours, 325 miles E) 6 hours, 650 miles

Solution: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.   Equation 1 - x= 100 (t+.25) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.   Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.   Now equating 12 we get 100(t+.25)=120(t-.25)   => 10t +2.5 = 12t - 3   => 2t=5.5 => t= 2.75 hrs.   Hence x= 100(2.75+.5) =>100 X 3.25 => 325 miles.   Hence correct answer 2.75 hours, 325 miles
Answer: D
The ratio of the number of females to males at a party was 1:2 but when 6 females and 6 males left, the ratio became 1:3. How many people were at the party originally?
Choose the correct choice from the following choices:
A) 24
B) 28
C) 32
D) 36
E) 40

Solution: The total number of people are x females + 2x males.   3*(x-6) = 2x - 6   x = 12   There were 3x = 36 people at the party originally.   The answer is 36.
Answer: D
If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A^B is also a prime number.
Choose the correct choice from the following answers
A) 1 only.  B) 2 only.  C) 3 only.  D) 2 and 3 only.  E) 1, 2 and 3.

Solution: Answer is D : 2 and 3 only   (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true   (2) A x B is also a prime number. : Beats the property of primes, so false   (3) A^B is also a prime number. : Beats the property of primes, so false   1 only.ns :1 only.
Answer: A
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?	Select the correct option.
A) Rs.2400  B) Rs.3600  C) Rs.2850  D) Rs.2000  E) Rs.3000

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400   Rs.2400NSWER:Rs.2400
Answer: A
When 19 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?  Choices
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: This means that 16 must be a multiple of k.   The factors of 16 are 1, 2, 4, 8, and 16.   Out of these, k can be 4, 8, and 16.   The answer is 3.
Answer: C
In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?  Choose the correct choice from the following options:
A) 2 years
B) 3 years
C) 4 years
D) 5 years
E) 6 years

Solution: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,   [ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3   n = 3 years.   ANSWER 3 years 3 years
Answer: B
A person traveled from P to Q at a speed of 40km/hr and return by increasing his speed by 50km/hr. What is his average speed for both the trips?  Choose the correct choice from the following:
A) 30km/hr B) 50km/hr C) 55km/hr D) 48km/hr E) 60km/hr

Solution: Speed on return trip = 150% of 40 = 60kmph   Average = 2*40*60/(40+60) = 4800/100= 
4800/100 = 48
48km/hr   Answer is 48km/hr
Answer: D
We had $2800 left after spending 30% of the money that we took for shopping. How much money did we start with?
Pick one.
A) $3700  B) $4000  C) $4300  D) $4600  E) $4900

Solution: Let x be the amount of money we started with.   0.7x = 2800   x = 4000   The answer is $4000.
Answer: B
You are renting an apartment and you need √841 for each side, how many feet are you looking to measure?
Choose the correct choice from the following options:	A) 21	B) 22	C) 23	D) 27	E) 29

Solution: Try filling the numbers into the answer y x y =   Find the closest to 841.   Answer 29
Answer: E
What approximate value should come in place of the question mark (?) in the following equation ?
6⁄7 of 1596 + 3015 = ? – 2150	Choose the correct choice from the following options
A) 7200  B) 48000  C) 6530  D) 58000  E) 6300

Solution: ? ≈ 6 × 230 + 3000 + 2150   = 1380 + 3000 + 2150= 
1380 + 3000 + 2150 = 6_530
6530   Answer 6530
Answer: C
When x is divided by 5, the quotient is y and the remainder is 1. When x is divided by 8, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?  Choices:	A) 4z/7 + 5	B) (7z + 5) / 6	C) (6z + 7) / 4	D) (8z + 5) / 5	E) (4z + 6) / 7

Solution: When x is divided by 5, the quotient is y and the remainder is 1: x = 5y + 1.   When x is divided by 8, the quotient is z and the remainder is 6: x = 8z + 6.   Equate those two:   5y + 1 = 8z + 6;   y = (8z + 5)/5.   Answer: (8z + 5) / 5.
Answer: D
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.5 km?
Choose the most appropriate option:
A) 375 m  B) 200 m  C) 300 m  D) 400 m  E) 100 m

Solution: 375 m   375 m   Distance covered by 375 mmar = 18/4.8 (1.5km) = 3/8(1500) = 375 m
Answer: A
Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 2.5%.  Select:  A) 237  B) 270  C) 177  D) 166  E) 111

Solution: Explanation:   177ost of each share = (20 + 2.5% of 20) = Rs.20.5   Therefore, number of shares = 8200/20.5= 
8200/20.5 = 400
400   ANSWER:177
Answer: C
If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. The slope of L is negative
2. Line L does pass the origin.
3. Line L must passes through the first quadrant  Choose the correct option:
A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: Slope of the given line= 3-n/n-3   Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.   1) n<3 (n=2)   3-2/2-3= -1   2) n<3 (n= 0)   3-0/0-3= -1   3) n<3 (n=-3)   3+3/ -3-3= -2/3   4) n>3   3-4/4-3= -1   I onlynswer I only
Answer: A
The price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2 reductions together are equal to a single reduction of Select the correct option.
A) 30	B) 40	C) 60	D) 80	E) 90

Solution: Let the original price of the cycle be 100. After the first reduction the price will be 75.   This new price is then reduced by 20% = 0.8 x 75 = 60   60 represents a reduction of 40 percent on the original.   60
Answer: C
Marco rode his dirt bike at 45 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride? Choose the correct choice
A) 14 mph  B) 20 mph  C) 70/3 mph  D) 80/3 mph  E) 34 mph

Solution: Average speed for first two hours, S1 = 45 mph   Distance travelled in these two hours, D1 = 90 miles   Average speed for the entire 5 hour ride, S = 30 mph   Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.   Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 90= 
150 - 90 = 60
60   Average speed for the latter 3 hour period S2= D2/3 = 60/3= 
60/3 = 20
20   Hence, the correct answer is 20 mph
Answer: B
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in z hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of z?  Choose the correct choice from the following:
A) 3/4
B) 1[1/5]
C) 1[2/5]
D) 1[3/4]
E) 2

Solution: Rate*Time=Work   Let Painter W's rate be W and Painter X's rate be X   R*T = Work   W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2   X * z = 1 => X = 1/z   When they both work together then their rates get added up   Combined Rate = (W+X)   R*T = Work   (W+X) * 3/4 = 1   => W+X = 4/3   => 1/2 + 1/z = 4/3   => 1/z = (8-3)/6 = 5/6   => z = 6/5 = 1[1/5]   Answer 1[1/5]
Answer: B
A can do a job in 15 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Choose the correct choice from the following answers.
A) 14 days	B) 16 days	C) 20 days	D) 11 days	E) 19 days

Solution: 20 days   1/15 + 1/30 = 1/10   10*2= 
10*2 = 20
20 days
Answer: C
How many 7 in between 1 to 100? Choose the correct choice from the following choices.
A) 18
B) 20
C) 22
D) 23
E) 24

Solution: 7,17,27,37,47,57,67,   70,71,72,73,74,75,76,77(two 7's),78,79,87,97   20 7's between 1 to 100   ANSWER:20
Answer: B
(1/5)^w * (1/4)^18 = 1/(2(10)^35). What is w?  Choose one.
A) 17  B) 18  C) 34  D) 35  E) 36

Solution: We need to arrive at a common base. -->   (5)^(-w) * 2^(-36) = 2^(-36)*5^(-35)   5^(-w)=5^(-35)   -w=-35   w=35=35
Answer: D
A and B can finish a piece of work in 12 days and 18 days respectively. A begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in  Select.
A) 14 1/3 days  B) 15 2/3 days  C) 16 1/3 days  D) 18 2/3 days  E) None of these

Solution: Explanation:   Both of them together can finish the work (daily working) in 12 × 18/30 days = 36/5   = 7 1/5 days.   By working in alternate days, their 2 day’s work = 5/36   Their, 14 day’s work (because they take more than double of 7 days) = 5/36 × 7   = 35/36   Remaining work = 1 – 35/36 = 1/36   Because A started the work, the remaining work is finished by A   A’s 1 day’s work = 1/12   Therefore, the No. of days taken by A to finish 1/36 work = 1/36/1/12 = 1/3 days.   Therefore, the total work is completed in 14 + 1/3 = 14 1/3 days.   14 1/3 daysnswer: Option 14 1/3 days
Answer: A
if n>0 and x is n percent of y, then, in terms of n, y is what percent of x?	Choose one:
A) a)100n	B) b)1/100n	C) c)1/n	D) d)10^4/n	E) e)10,00/n

Solution: Given (n*y)/100=x   to find (y/x)*100   Rearranging first equation   y/x*100 = 100*100/n   =10000/n   Answer d)10^4/n
Answer: D
Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of two rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again? Choose the correct choice from the following options
A) 30	B) 45	C) 60	D) 75	E) 90

Solution: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.   The relative speed of Sandy and Molly is   2 - 1= 
  2 - 1 = 1
1 round per hour.   The time required to complete one round at this speed 60 minutes.   The answer is 60.
Answer: C
When x is divided by y, the quotient is z with remainder s. Which of the following is equal to s?
Choose the correct answer
A) yz – x	B) y/x−z	C) x – y – z	D) x – yz	E) zx – y

Solution: (x/y)=z(+s)   (18/8)=2(+2)   x-yz   which is   18-(8*2)= 
  18-(8*2) = 2
2   Answer is x – yz
Answer: D