MU-NLPC/Calc-aqua_rat huggingface dataset:
Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?	Select:
A) 450 m
B) 680 m
C) 700 m
D) 900 m
E) 1000 m

Solution: Explanation:   When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race   ANSWER 700 m
Answer: C
A man loses 1/3rd of his money, then wins Rs. 10 loses 1/3rd of what he has and wins Rs. 20 and finds that he has exactly what be had at the beginning. What was the amount he originally bad ?  Pick:
A) 25
B) 36
C) 10
D) 48
E) 45

Solution: let x be that amount   so accordind to question , eqn will be like:   (((x-x/3)+10)-(((x-x/3)+10)/3))+20=x   => ((2x/3+10)-((2x/3+10)/3))+20=x   =>3x-4x/3=80   =>x=48   ANSWER:48
Answer: D
A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? Choose one.
A) 33  B) 77  C) 265  D) 21  E) 88

Solution: WC = 2:1   2x + x = 1/14 => x = 1/42   2x = 1/21   A can do the work in 21 days.   Answer: 21
Answer: D
A train travels 210 km in 3 hours and 270 km in 4 hours.find the average speed of train.	Choose the correct choice from the following answers
A) 80 kmph
B) 69 kmph
C) 70 kmph
D) 90 kmph
E) None of these

Solution: As we know that Speed = Distance / Time   for average speed = Total Distance / Total Time Taken   Thus, Total Distance = 210 + 270= 
210 + 270 = 480
480 km   Thus, Total Speed= 7hrs   or,Average Speed = 480/7   or, 69kmph.   ANSWER:69 kmph
Answer: B
A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(9)?	Choose the correct answer:	A) 53/32	B) 55/34	C) 57/36	D) 59/38	E) 61/40

Solution: A(n+1)=1+(1/A(n))   A(1) ( +1)= 
( +1) = 1
1+(1/A(n))   A(1)= 1   A(2) = 2   A(3) = 3/2   A(4) = 5/3   A(5) = 8/5   A(6) = 13/8   A(7) = 21/13   A(8) = 34/21   A(9) = 55/34   The answer is 55/34.
Answer: B
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Choose the correct choice from the following choices: A) 502 m B) 298 m C) 500 m D) 189 m E) 171 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (800 + x)/60 = 65/3   x = 500 m.   Answer:500 m
Answer: C
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 15. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?  Pick:
A) 1  B) 11  C) 15  D) 19  E) 47

Solution: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (11)
Answer: B
. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?	Select.
A) 10 a.m B) 10.30 a.m C) 11 a.m D) 11.30 a.m E) 11.15 a.m

Solution: Suppose they meet x hrs after 8 a.m. Then,   (Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330   60x + 75(x - 1) = 330 => x = 3   So, they meet at (8 + 3) i.e., 11 a.m.   ANSWER:11 a.m
Answer: C
In how many ways can you seat 5 people on a bench if one of them does not want to sit on the middle seat or at either end?	Choose one:
A) 40  B) 44  C) 48  D) 52  E) 56

Solution: One person can choose 2 possible chairs to sit. The remaining 4 people can sit in 4! ways.   The number of arrangements is 2*4! = 48.   The answer is 48.
Answer: C
A racng car travels k kilometres in n hours. How many miles will it travel in x hours at the same rate?	Pick:  A) knx  B) k⁄n  C) kn⁄x  D) kx  E) kx⁄n

Solution: Given Speed = k/n   To Find distance in x hours with same speed   Distance = speed * time   Distance = k/n*x = kx/n   Answer kx⁄n
Answer: E
Of 30 applicants for a job, 16 had at least 4 years' experience, 21 had degrees, and 5 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?  Options
A) 12	B) 10	C) 9	D) 7	E) 5

Solution: set 12 : people with more than 4 years exp   set B : people with degree   12UB = total - (less than 4 exp and no degree)   12UB = 30-5= 
30-5 = 25
25   12UB= 12 + B - 12iB   12iB = 21+16-25= 
21+16-25 = 12
12   12nswer 12
Answer: A
Six balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done? Choose the most appropriate option:	A) 60	B) 90	C) 210	D) 150	E) 180

Solution: Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box.   For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box.   Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.   For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.   For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.   Total of 120 + 90= 
120 + 90 = 210
210 possibilities.   Answer 210.
Answer: C
Subtract the absolute value from the local value of 4 in 564823 Choose the correct choice from the following answers:
A) 196	B) 1996	C) 2996	D) 3996	E) 6000

Solution: Explanation:   Place value = Local value   Face value = Absolute value   The place value of 4 in 564823 is 4 x 1000 = 4000   The face value of 4 in 564823 is nothing but 4.   => 4000 - 4 = 3,996   Answer: Option 3996
Answer: D
Find the simple interest on Rs 4000 at 20% per annum for the period from 2nd March 2016 to 4th May 2016.  Choose the correct choice.
A) Rs. 133.1
B) Rs. 228.1
C) Rs. 131.1
D) Rs. 128.1
E) Rs. 138.1

Solution: Explanation:   One thing which is tricky in this question is to calculate the number of days.   Always remember that the day on which money is deposited is not counted while the day on which   money is withdrawn is counted.   So lets calculate the number of days now,   Time = (29+30+4)= 
(29+30+4) = 63
63/365 years= 1/5 years   P = 4000   R = 20%   S.I. = =4000Ã—20Ã—0.17260273972/100=138.1   Answer: Rs. 138.1
Answer: E
P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? Select:	A) 3/5	B) 4/5	C) 8/15	D) 7/11	E) 3/41

Solution: Amount of work P can do in 1 day = 1/15   Amount of work Q can do in 1 day = 1/20   Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   Fraction of work left = 1 – 7/15= 8/15   8/15
Answer: C
Jeni has 7 flavors of cake in his bakery. How many options are there for Sheera to pick a one-flavor, two-flavor,three-flavor, four-flavor, five-flavor, six-flavor or seven-flavor order?  Options:  A) 423  B) 325  C) 142  D) 171  E) 127

Solution: 7C1 + 7C2+ 7C3+7C4+7C5+7C6+7C7 =127 .   Answer: 127
Answer: E
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next? Choose the correct choice from the following:
A) 14
B) 15
C) 16
D) 17
E) 18

Solution: 15   15   In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
Answer: B
A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal? Choose one: A) 1/3 B) 2/3 C) 1/4 D) 1/8 E) 1/9

Solution: Wine containing 40%spirit Wine containing 16% spirit   Wine containing 24% spirit   8 16   They must be mixed in the ratio of =1:2.   Thus 1/3 of the butt of sherry was left   hence the butler drew out 2/3 of the butt.   ANSWER 2/3
Answer: B
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?	Choose the correct choice from the following options.
A) 27	B) 50	C) 98	D) 77	E) 51

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.Answer: 50
Answer: B
In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled a quarter that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour? Pick one
A) d	B) 1/3*d	C) 1/2*d	D) 5/8*d	E) 3/2*d

Solution: Solution:   Lets look at the information given in the question...   Total time travelled = 2 hrs   Distance travelled first hour = d   Distance travelled second hour = d/4   The question is asking for the avg speed at which the car travels for 2 hrs   We know that avg speed = total distance/total time   Lets place the information given in the question to the formula above = (d+d/4)/2   = 5/8*d   We find that option D is the answer as it gives the same expression as found in our calculation above. Answer option 5/8*d.
Answer: D
How many integers from 10 to 180, inclusive, are divisible by 3 but not divisible by 7? Choose the correct choice from the following options:
A) 45
B) 49
C) 50
D) 52
E) 56

Solution: We should find # of integers divisible by 3 but not by 3*7= 
3*7 = 21
21.   # of multiples of 21 in the range from 10 to 180, inclusive is   (168-21)/21+1= 
  (168-21)/21+1 = 8
8;    57-8= 
 57-8 = 49
49.   Answer: 49.
Answer: B
Five kids were walking down the street. At a shop, they saw three brands of chocolates viz. Cadbury, Nestle and Ferrero being displayed. The shopkeeper has three chocolates which are of three different flavors of each brand. The kids bought all the chocolates available and decided to play a game. The chocolates will be distributed only to the winners of that game. Also they have decided that any winner cannot have all three brands of chocolates as his prize. Find the number of ways in which the chocolates can be distributed when there are four winners of the game and the best of them gets at least 4 chocolates?
Choose the correct choice.
A) 12312
B) 22536
C) 4320
D) 11268
E) 45072

Solution: Since, one child cannot have more than two brands of chocolates, therefore, one child can get a maximum of six chocolates.   When there are four winners, the winners can have the chocolates in the following possible way   Case I   One of them gets six chocolates and the other three get one each.   The one who gets six chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.   The three chocolates of the same brand will be distributed among the other three in 3! ways.   Hence, the total number of ways = 4 × 3 × 6 = 72   Case II   One of them gets 5 chocolates, one of them gets 2 chocolates and the other two get 1 each.   Kid with 5 chocolates:   The one who gets five chocolates can be selected in 4C1 ways and he will get any two brands out of three in 3C2 ways.   After choosing the two brands (say AB), he can get all three chocolates of one brand in 2 ways (i.e. either A or B). The other two chocolates can be chosen from the second brand in 3 ways. Thus, there are 4 × 3 × 2 × 3 = 36 ways   Kid with 2 chocolates:   This person can be chosen in 3 ways. Now, he can either get two chocolates from the same brand or from two different brands.   Thus, there are 6 × 3 = 18 ways   Kids with 1 chocolate each   The remaining chocolates can be distributed between the two remaining winners in 2 ways.   Therefore, total number of ways = 36 × 18 × 2 = 1296 ways.   Case III   Similarly for four chocolates the following combinations are possible:   a) 4 3 1 1   The number of ways = 4 × 3 × [{6 × 3(1 + ( 6 + 3))} + {1 × 9 × 3 (1 + 6)}] × 2 = 8856   b) 4 2 2 1   The number of ways = 4 × 3 × [{6 × 3(2 × 6 × 3 + (3 + 9))} + {9 × (9 + 9)}] = 12312   Since, the best of them can’t have less than 4 chocolates the above are the only cases applicable.   Hence, the total number of ways = 72 + 1296 + (8856 + 12312)= 
72 + 1296 + (8856 + 12312) = 22_536
22536.   Option 22536
Answer: B
On dividing 122 by a number, the quotient is 6 and the remainder is 2. Find the divisor?	Choose the correct choice from the following answers:
A) 14	B) 16	C) 18	D) 20	E) 22

Solution: d = (20-R)/Q   = (122 - 2)/6   = 122/6 = 20   20)
Answer: D
A farmer needs 2400 ounces of corn to feed his pigs. How many pounds should he buy?
Choose the correct choice from the following choices
A) 120	B) 130	C) 140	D) 150	E) 160

Solution: 1 pound = 16 ounces.   2400 ounces / 16 = 150 pounds.   Answer: 150.
Answer: D
How many minutes does it take John to type z words if he types at the rate of y words per minute?	Answers
A) z/y  B) y/x  C) xy  D) 60x/y  E) y/(60x)

Solution: time*rate=job --> time*y=z --> time=z/y.   z/ynswer: z/y.
Answer: A
Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?	Choose the correct choice from the following choices
A) Rs.29.25
B) Rs.39.25
C) Rs.29.29
D) Rs.23.25
E) Rs.29.45

Solution: Rs.29.25verage of 9 = x   9x = 8 * 3 + x * 2 x = 3.25   Total = 9 * 3.25= 
9 * 3.25 = 29.25
29.25   Rs.29.25nswer:Rs.29.25
Answer: A
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Choose the correct choice from the following: A) 17 1/7 B) 17 1/9 C) 17 8/7 D) 17 8/8 E) 17 2/7

Solution: 1/20 + 1/30 - 1/40   = 7/120   120/7   = 17 1/7   Answer:17 8/7
Answer: C
How long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length? Choose the correct choice from the following answers:
A) 15.8 sec B) 14.9 sec C) 12.4 sec D) 10.8 sec E) 11.8 sec

Solution: 10.8 sec   16.8 sec   10.8 sec = 100 + 80= 
100 + 80 = 180
180 m   S= 60 * 5/18 = 50/3   T = 180 * 3/50= 
180 * 3/50 = 54/5 = around 10.8
10.8 sec
Answer: D
Take number 1000 and then add 20 to it. Now add 1000 one more time. Now add 30. Now add 1000 one more time. Now add 40. Now add 1000 one more time. Now add 10. What is the total?	Choose the correct answer
A) 4100	B) 3590	C) 2800	D) 3700	E) 3600

Solution: 4100   4100
Answer: A
Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to	Choose the most appropriate option
A) 50°F B) 76°F C) 95°F D) 110°F E) 120°F

Solution: Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.   Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.   95°F
Answer: C
Three consecutive traffic signals each show either red or green. How many different arrangements of the three signals are possible? (Note: “Red-redgreen” is different from “green-red-red.”) Choose the correct choice from the following options:
A) 10 B) 9 C) 8 D) 7 E) 6

Solution: The best way to do this Q would be to find the ways separately for each type of arrangements..   all three of same colour= 1*2(for green and red)= 2..   two of one colour and third different colour= 3!/2!=3..   total= 1*2+3*2= 
1*2+3*2 = 8
8   ANSWER:8
Answer: C
A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 84 km downstream  Answers:
A) 3 hours
B) 4 hours
C) 5 hours
D) 6 hours
E) 7 hours

Solution: Explanation:   Speed of the boat in still water = 24 km/hr   speed of the stream = 4 km/hr   Speed downstream = (22+5) = 28 km/hr   Distance travelled downstream = 84 km   Time taken = distance/speed = 84/28= 
84/28 = 3
3 hours   3 hoursnswer: Option 3 hours
Answer: A
The average of first six prime numbers greater than 65 is?	Choose the correct choice from the following:
A) 55	B) 77	C) 56	D) 67	E) 98

Solution: 67 + 71 + 73 + 79 + 83 + 89= 
67 + 71 + 73 + 79 + 83 + 89 = 462
462/6= 
462/6 = 77
77   Answer: 77
Answer: B
The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Select:
A) 766 m  B) 156 m  C) 245 m  D) 225 m  E) 156 m

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2   ==> 2(150 + X) = 750 ==> X   = 225 m.   Answer: 225 m
Answer: D
A can do a piece of work in 12 days and B alone can do it in 14 days. How much time will both take to finish the work ?	Choose the correct choice from the following choices:
A) A)3.2222  B) B)5  C) C)6.46  D) D)8.3333  E) E)9

Solution: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.   Time taken to finish the job = XY / (X + Y)   = 12 x 14 / (12 + 14)   = 150 / 25   = 6.46 days   Answer: 6.46
Answer: C
The mean salary in ICM ltd. was Rs 1500, and the standard deviation was Rs 400. A year later each employee got a Rs 100 raise. After another year each employee's salary was increased by 20%. The standard deviation of the current salary is?	Choose the correct choice from the following choices
A) Rs 400
B) Rs 480
C) Rs 600
D) Rs 700
E) Rs 800

Solution: Mean salary was Rs 1500   Standard deviation = Rs 400   After 1 year all the employees got a uniform rise of Rs 100.   So, there will be no change in standard deviation.   After another year, every employee's salary was increased by 20%.   So, standard deviation will be increased by 20%.   Standard deviation=400×   120   100   = Rs 480   Answer Rs 480
Answer: B
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.240 in 2 years?  Choose the correct choice from the following answers:	A) 217	B) 287	C) 400	D) 288	E) 171

Solution: Explanation:   240 = P(21/20)2   P = 217   217nswer:217
Answer: A
If k is a non-negative integer and 15^k is a divisor of 823,435 then 5^k - k^5 =  Choose the most appropriate option:
A) 0  B) 1  C) 35  D) 120  E) 245

Solution: 8+2+3+4+3+5= 
8+2+3+4+3+5 = 25
25, so this number is not divisible by 3 and thus not divisible by 15.   Therefore, k=0   5^k - k^5 =1-0= 
1-0 = 1
1   The answer is 1.
Answer: B
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?	Choose the correct option.
A) 111.12  B) 111.13  C) 111.22  D) 111.0  E) 111.12

Solution: A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9   = 888.88 m.   B can give C = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12m.   111.12nswer:111.12
Answer: A
The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65, then how long is the base of isosceles triangle? Choose the correct choice from the following answers:
A) 10 B) 15 C) 20 D) 25 E) 30

Solution: The base of the isosceles triangle is 65-20-20= 
65-20-20 = 25
25 units   The answer is 25.
Answer: D
A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 295 meters long  Pick one:
A) 6 ½ sec	B) 7 ½ sec	C) 8 sec	D) 13 ½ sec	E) 9 sec

Solution: Explanation:   Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.   Distance covered in passing the platform = (200 + 295)= 
(200 + 295) = 495
495 m.   Time taken=495 ×(3/110) sec =27/2 sec = 13 ½ sec   Answer: Option 13 ½ sec
Answer: D
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 225 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Answers: A) 220 B) 200 C) 210 D) 225 E) 230

Solution: 200   225 * T = 1 km => T = 1/225 km/h   V*(T+2/3600) = 1   V (1/225 + 2/3600) = 1 => V = 200 km/h
Answer: B
Q is not equal to zero and k = (Q x n - s)/2.What is n?	Choose the most appropriate option.
A) (2 x k + s)/Q
B) (2 x s x k)/Q
C) (2 x k - s)/Q
D) (2 x k + s x Q)/Q
E) (k + s)/Q

Solution: k=(Q*n-s)/2   => (2k+s)/Q = n   (2 x k + s)/QNSWER:(2 x k + s)/Q
Answer: A
What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 19 units?
Select: A) 2.8 units B) 6 units C) 3 units D) 5 units E) 12 units

Solution: Sides are 8, 15 and 19...thus it is right angle triangle Since 19^2 = 8^2 + 15^2   therefore, area = 1/2 * 15 * 8= 
1/2 * 15 * 8 = 60
60   We have to find in-radius   Therefore, area of triangle= S*r ....where S=semi-perimeter and r= in-radius   Now S=semi-perimeter = 19+15+8 /2 = 21   Thus , 60 =21*r   and hence r=in-radius= 2.8   Option 2.8 units
Answer: A
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%? Choose the correct choice from the following answers.
A) 228 B) 299 C) 266 D) 600 E) 188

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84   5x/100 + 90 â€“ 6x/100 = 84   x/100 = 6   => x = 600   Answer:600
Answer: D
A woman complete a journey in 10 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.  Answers.
A) 334 km.
B) 216 km.
C) 314 km.
D) 224 km.
E) 544 km.

Solution: D   224 km.   0.5x/21 + 0.5x/24 = 10   --> x/21 + x/24 = 20   --> 15x = 168 x 20   --> x = (168 x 20)/15 = 224 km.
Answer: D
Pat and Cathy begin running at the same time and they start at the same place on a straight path. Pat runs at 9 miles per hour, and Cathy runs at 8 miles per hour. After 30 minutes, Pat stops to stretch. If it takes Pat 15 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pat to catch up to Cathy? Choose one
A) 50	B) 60	C) 70	D) 80	E) 90

Solution: In 30 minutes, Pat runs 4.5 miles.   In 45 minutes, Cathy runs 6 miles.   Pat can catch Cathy at a rate of 1 mile per hour.   Since Cathy is ahead by 1.5 miles, it will take Pat 1.5 / 1= 
1.5 / 1 = 1.5
1.5 hours= 90 minutes to catch Cathy.   the answer is 90.
Answer: E
An employer has 8 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
Choose the correct option.
A) a) 1,490 B) b) 132 C) c) 336 D) d) 60 E) e) 23

Solution: 8C3 * 4C2 = 336. Answer c) 336.
Answer: C
The calendar of the year 2060 can be used again in the year? Choose the correct choice from the following answers
A) 2081  B) 2083  C) 2088  D) 1971  E) 1973

Solution: Explanation:   Given year 2060 when divided by 4, leaves a remainder 0.   NOTE: When remainder is 0, 28 is added to the given year to get the result.   So, 2060 + 28 = 2088   Answer: 2088
Answer: C