MU-NLPC/Calc-aqua_rat huggingface dataset:
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using ten colors?
Choose the correct choice from the following:  A) 21  B) 35  C) 105  D) 120  E) 210

Solution: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.   As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:   ABC   ACB   BAC   BCA   CAB   CBA   By extension, the first part of your calculation would be the number of possible substances that could be identified with 10 colors: 10c3 = 120 possible substances   120
Answer: D
Find the simple interest on Rs.450 for 8 months at 5 paisa per month?	Pick.
A) 277  B) 270  C) 180  D) 266  E) 121

Solution: I = (450*8*5)/100= 
(450*8*5)/100 = 180
180   Answer: 180
Answer: C
A solution of 66 litres contains milk and water in the ratio 7:x. If four litres of water is added to the solution, the ratio becomes 3:2, find the value of x?	Select:	A) 8	B) 5	C) 3	D) 4	E) 6

Solution: Total new quantity = original sol + water =66+4= 
66+4 = 70
70   New ratio= 3:2, New quantity of milk =3/5*70= 
3/5*70 = 42
42 Lit,   New quantity of water= 2/5*70= 
2/5*70 = 28
28 Lit   Water present initially= (28-4)= 
(28-4) = 24
24 Lit   Ratio= 42/24 =7/4 There for x = 4   ANSWER:4
Answer: D
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?	Choose the correct choice:  A) 11  B) 28  C) 156  D) 44  E) 148

Solution: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28   Answer: 28
Answer: B
On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 44 centimeters assuming that 1-inch is 2.54 centimeters?  Options:
A) 174.2  B) 277  C) 288.1  D) 296  E) 282.4

Solution: 1.5 inch = 2.54*1.5 cm.   So, 2.54*1.5 represents 24 miles.   So for 44 cm.:   44/(2.54*1.5) = x / 24 ---> x = 24*44/(3.81) = 277   Answer will be 277.
Answer: B
A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. Choose the correct choice.
A) 71/9
B) 7/15
C) 7/18
D) 4/17
E) 2/17

Solution: let S be the sample space   Then n(S)=no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
10c2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   Let E=event of getting both balls of same colour   Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)   =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=n(E)/n(S)=21/45=7/15   Option 7/15
Answer: B
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Select:
A) 5	B) 8	C) 9	D) 2	E) 3

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer: 8
Answer: B
Find the value of m from (12)^3 x 6^4 ÷ 432 = m?
Pick one: A) 2346 B) 3546 C) 4566 D) 3455 E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 130 marks, the no of questions he attempts correctly is :	Choose the correct answer
A) A)35
B) B)38
C) C)90
D) D)88
E) E)42

Solution: Let the number of correct answers be X.   Number of incorrect answers = (60 – X).   4x – (80 – x) = 130   => 5x = 210   => x = 42   Answer:42
Answer: E
find the number, difference between number and its 3/5 is 60.  Choose one: A) 150 B) 153 C) 154 D) 155 E) 156

Solution: Explanation:   Let the number = x,   Then, x-(3/5)x = 60,   => (2/5)x = 60 => 2x = 60*5,   => x = 150   150nswer: Option 150
Answer: A
Albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born. What is the difference between the ages of her parents?
Choose the correct choice from the following answers
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Mother's age when Albert's brother was born = 46years   Father's age when Albert's brother was born = 48+2= 
48+2 = 50
50years   Required difference= 50-46= 
50-46 = 4
4 years   Answer is 4
Answer: B
A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 4% dividend at the end of the year,then how much does he get ?  Select the correct option
A) Rs. 500
B) Rs. 600
C) Rs. 650
D) Rs. 720
E) None

Solution: Solution   Number of shares = (14400/120)= 
(14400/120) = 120
120.   Face value= Rs. (100x120 ) = Rs. 12000.   Annual income = Rs.(4/100x12000) = Rs. 480.   Answer None
Answer: E
The contents of a certain box consist of 20 apples and 30 oranges. How many oranges must be added to the box so that exactly 20% of the pieces of fruit in the box will be apples?  Choose the correct option.
A) 50
B) 55
C) 75
D) 85
E) 100

Solution: apple = (apple + orange + x)*0.2   20 = (30 + 20 + x)*0.2   x = 50   50nswer: 50
Answer: A
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?	Choose one:
A) 8%	B) 5%	C) 2%	D) 3%	E) 1%

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%   Answer: 5%
Answer: B
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?
Choices:
A) 22
B) 38
C) 62
D) 122
E) 672

Solution: Same logic but with application of factorials.   2*4*6*8*...*n = 2(1*2*3*4*...n/2) = 2*(n/2)!   Now we have: 2*(n/2)!/2013=2*(n/2)!/(3×11×61)   For the expression 2*(n/2)! To be divisible by 2013 min value of n/2 should be 61.   So n/2=61 => n=122   Answer 122.
Answer: D
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.650 in 2 years?
Choose the correct choice
A) 221	B) 287	C) 400	D) 589	E) 171

Solution: Explanation:   650 = P(21/20)2   P = 589.56   Answer:589
Answer: D
A basket contains 8 blue, 8 red and 8 yellow marbles. If 8 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Choose the correct choice from the following answers
A) 2/21  B) 3/25  C) 1/6  D) 9/28  E) 64/253

Solution: 24/24*16/23*8/22 = 64/253   the answer is (64/253)
Answer: E
In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 90π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?  Choose one:
A) 360π
B) 400π
C) 450π
D) 500π
E) 600π

Solution: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.   4(90π) = 360π   The answer is 360π.
Answer: A
Given that 0.0010010 x 10^q > 10^3, and q is an integer, which of the following is the smallest possible value of q? Choose the correct choice from the following choices
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 0.0010010 x 10^q > 10^3, and q is an integer   This will be true only when LHS will be 1001   so the smallest possible value of q to make LHS > 10^3 is q=6   ANSWER:6
Answer: D
The area of a triangle will be when a = 1m, b = 2m, c = 7m, a, b, c being lengths of respective sides?  Select the correct option.
A) 3  B) 6  C) 5  D) 9  E) 1

Solution: S = (1 + 2 + 7)/2= 
(1 + 2 + 7)/2 = 5
5 Answer:5
Answer: C
0.6 of a number equals 0.09 of another number. The ratio of the number is: Choose one:
A) 2:3
B) 1:15
C) 20:3
D) 3:20
E) None of these

Solution: Explanation :   Let 0.6 of x be equal to 0.09 of y:   i.e. 0.6x = 0.09y   => x/y = 0.09/0.6 = 3/20   Answer : 3:20
Answer: D
If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4, then the first part is: Choose the correct choice from the following:
A) 202	B) 203	C) 204	D) 205	E) 206

Solution: (1/2+2/3+3/4)x=782   x=782*12/23= 
782*12/23 = 408
408   fist part is: (1/2)x=408/2= 
408/2 = 204
204   ANSWER:205
Answer: D
The average marks of a class of 24 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Answers: A) 52.2 B) 59.5 C) 52.8 D) 53.5 E) 52.1

Solution: Sum of the marks for the class of 24 students = 24 * 40= 
24 * 40 = 960
960   Sum of the marks for the class of 50 students= 50 * 60= 
50 * 60 = 3_000
3000   Sum of the marks for the class of 74 students=   960 + 3000= 
960 + 3000 = 3_960
3960   Average marks of all the students= 3960/74   = 53.5   Answer:53.5
Answer: D
If in a certain sequence of consecutive multiples of 50, the median is 725, and the greatest term is 950, how many terms that are smaller than 725 are there in the sequence?	Pick one: A) 6 B) 5 C) 8 D) 12 E) 13

Solution: Since the median is 725 we know there must be a even number of integers because 50 is not a multiple of 725.   So the list around 725 must go. 600 650 700(725) 750 800 850 900 950   Since we know there are 5 numbers greater than 725 then there must be 5 numbers less then 725.   answer:5
Answer: B
What will be the day of the week 15th August, 2010?
Choose the correct choice from the following answers:
A) Tuesday
B) Saturday
C) Monday
D) Sunday
E) Friday

Solution: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)   Odd days in 1600 years = 0   Odd days in 400 years = 0   9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.   Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.   (31 + 28 + 31 + 30 + 31 + 30 + 31 + 15)= 
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227
227 days   227 days= (32 weeks + 3 days) 3 odd days.   Total number of odd days = (0 + 0 + 4 + 3)= 
(0 + 0 + 4 + 3) = 7
7= 0 odd days.   Given day is Sunday   Answer is Sunday.
Answer: D
Find the area of the square, one of whose diagonals is 3.8 m long ?
Choose the correct option
A) 7.22m^2  B) 3.86m^2  C) 8.96m^2  D) 2.68m^2  E) 7.89m^2

Solution: 7.22m^2rea of the square= 1/2(diagonal)^2   =(1/2*3.8*3.8)m^2   = 7.22m^2   7.22m^2nswer (7.22m^2)
Answer: A
If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 5
III. 7
Choose the correct choice from the following choices:
A) I only  B) II only  C) III only  D) I,III only  E) II,III only

Solution: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....   Let's TEST VALUES....   IF we use the 6 consecutive integers: 5, 6, 7,8,9 and 10, then the sum = 45.   45 is divisible by 5   45 is NOT divisible by 6   45 is NOT divisible by 7   There's only one answer that 'fits' with these facts. Answer : II only
Answer: B
Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3647	Pick one
A) 3647  B) 9654  C) 5945  D) 7963  E) 8216

Solution: The product of first two digits in a number equals the last two digits, except in 3647. Hence, it is the odd one.   The answer is 3647.   3647NSWER:3647
Answer: A
A train 490 m long, running with a speed of 63 km/hr will pass a tree in?	Choose the correct answer.
A) 25  B) 26  C) 27  D) 28  E) 29

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 490 * 2/35= 
490 * 2/35 = 28
28 sec   Answer: Option 28
Answer: D
In a race of length Lmetres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)	Choose the correct choice.
A) L(L-N) / L-M
B) (N-M)*L/(L-M)
C) L-N
D) M-N
E) M+

Solution: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:   L = 100   M = 10   N =20.   So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..   looking the the opion C to E, one can make out that they are incorrect   Out of which, i choose (N-M)*L/(L-M).
Answer: B
Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 38 years. What is Deepak present age?	Answers: A) 22 B) 24 C) 77 D) 266 E) 182

Solution: Present age is 4x and 3x,   => 4x + 6 = 38 => x = 8   So Deepak age is = 3(8) = 24   Answer: 24
Answer: B
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Choose the most appropriate option:
A) s.4529
B) s.4586
C) s.4597
D) s.6342
E) s.4528

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 7   =Rs.6342   Answer: s.6342
Answer: D
A man is 27 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?  Pick one
A) 11	B) 25	C) 27	D) 22	E) 91

Solution: Let the son's present age be x years.   Then, man's present age = (x + 27) years.   (x + 27) + 2 = 2(x + 2) x + 29 = 2x + 4 => x = 25.   Answer: 25
Answer: B
In how many different ways can the letters of the word â€˜EVERâ€™ be arranged?  Choices
A) 12	B) 280	C) 300	D) 310	E) 360

Solution: Number of ways = 4!/2! = 4X3X2X1/2X1 = 12   12
Answer: A
The average of numbers 0.54204, 0.54203, 0.54202 and 0.54201 is ? Pick one
A) 0.54202 B) 0.54204 C) 0.542022 D) 0.542025 E) None

Solution: Answer   Average = (0.54204 + 0.54203 + 0.54202 + 0.54201)/ 4   =2.1681/ 4= 
2.1681/ 4 = 0.542025
0.542025   Correct Option: 0.542025
Answer: D
Jill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 18 songs, what are the chances that the third song he hears will be his favorite?	Choose the correct choice from the following answers.
A) 1/18  B) 1/12  C) 1/11  D) 3/14  E) 1/3

Solution: The player plays the songs on the album at random, so there are 18 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.   Total outcomes ==> 18   Total positive outcomes ==> 1   Correct answer is 1/18) 1/18
Answer: A
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 4 cups of tea are prepared, 2 in one way and 2 in other. Find the different possible ways of presenting these 4 cups to the expert.  Choose the correct choice from the following answers.
A) 25  B) 24  C) 30  D) 34  E) None

Solution: Solution:   Since, there are 2 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,   [4!/(2!x2!)]= 24   Answer: Option 24
Answer: B
A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be A's share in the total profit of Rs.26,000 earned at the end of 2 years from the starting of the business? Choose the correct choice from the following options
A) Rs.7500 B) Rs.9000 C) Rs.9500 D) Rs.10,400 E) None

Solution: Solution   A : B : C	=(20000×24):(15000×24):(20000×18)   =4 :3 :3   A's share	=Rs.(26000×4/10)   = Rs.10400.   Answer Rs.10,400
Answer: D
What is the probability of rolling a nine with two, fair, six-sided dice?  Answers:	A) 1/6	B) 1/9	C) 2/13	D) 1/12	E) 5/36

Solution: There are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9. 1/9
Answer: B
Three race cars driven by James, Myles and Samantha start moving around a circular race track of length 1500m from the same point simultaneously in the same direction at speeds of 15 m/s, 25 m/s and 45 m/s respectively. When will they meet for the first time after they started moving?  Answers:
A) 540 seconds  B) 240 seconds  C) 200 seconds  D) 300 seconds  E) 150 seconds

Solution: If they all meet after T seconds, it means they covered the distances 15T, 25T, and 45T respectively.   Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 1500m. So, 10T, 20T, and 30T must all be multiples of 1500. 10T multiple of 1500 means T multiple of 150. The smallest T with this property is 150 and is on the list of answers.   Answer 150 seconds.
Answer: E
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike? Choose one.
A) 54.3 kg  B) 55.5 kg  C) 66.5 kg  D) 67.8 kg  E) 69 kg

Solution: Let Mike's weight be X kg.   According to Mike, 65 < X < 72.   According to Mike's brother, 60 < X < 70.   According to Mike's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   67.8 kg
Answer: D
If a + b + c = 13, then find the ab + bc + ca :	Select the correct option.
A) 22  B) 99  C) 50  D) 29  E) 11

Solution: Answer: 50) 50
Answer: C
In order to complete a reading assignment on time, Terry planned to read 100 pages per day. However, she read only 75 pages per day at first, leaving 625 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?	Choose the correct choice from the following options:
A) 8
B) 7
C) 9
D) 10
E) 11

Solution: D=100*X - according to the plan, assignment to be completed on time reading 100 pages per day for next X days. 7ut, Terry's plans changed so she read as follow:   75 pages for first Y days and 625 pages for last 6 days, we get these equations:   75*Y+625=100*X   X-Y=6 --------->>X planned number of days, Y - actually used reading 75 pages per day and 6 leftover days used to complete a lump 625 pages   From above we find that X=Y+6 and 75Y+625=100Y+600 or 25Y=25 --->>>>> Y=1, hence X=7   Answer : 7
Answer: B
If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ? Choose the correct choice from the following answers
A) 1/2
B) 1/4
C) 3/4
D) 2/3
E) None of these

Solution: Explanation :   a∗b∗c/b∗c∗d= 130/65 => a/d = 2   d∗e∗f/c∗d∗e= 250/1000 => f/c = 14   a/d* f/c = 2 * 1/4 = 1/2   1/2nswer : 1/2
Answer: A
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 12 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
Choices.
A) 18/79  B) 16/900  C) 1/25  D) 1/50  E) 1/900

Solution: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.   AA   BB   CC   AB, AC, BC, BA, CA, CB.   Thus; total government vehicles = (10)^2*(3)^2 = 100*9= 
100*9 = 900
900   Vehicles inspected within 3 hours= 60*3/12 = 16   P = 16/900   Ans:16/900
Answer: B
Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas? Pick one
A) 236
B) 354
C) 432
D) 512
E) 670

Solution: 54/4= 
54/4 = 27/2 = around 13.5
13.5 gallons     13.5*32= 
  13.5*32 = 432
432 miles   The answer is 432.
Answer: C
Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector?	Choose the correct choice from the following.
A) 50
B) 43
C) 45
D) 55
E) 60

Solution: Widgets inspected by Lauren: ((95-5)/5)+1=18+1= 
18+1 = 19
19   Widgets inspected by Steven:   ((93-3)/3)+1= 
  ((93-3)/3)+1 = 31
31+1= 
31+1 = 32
32   Widgets inspected by both: ((90/15)+1=6   Total :   19+32 -6= 
  19+32 -6 = 45
45   hence, widgets not inspected: 95-45= 
95-45 = 50
50   Option 50
Answer: A
A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 30% less than the price each head sold for on the day before. What was the total gross profit on this shipment. Pick:
A) $100 B) b $115 C) c $125 D) d $130 E) e $75

Solution: Purchase cost = 600/1500= 
600/1500 = 2/5 = around 0.4
$ 0.4   25% above the cost per head= (125/100)*0.4= 
(125/100)*0.4 = 0.5
$ 0.5   2/3 of the heads were sold means 2/3*1500= 
2/3*1500 = 1_000
1000 ,Selling amount for 1000 cabbage= 1000 * 0.5= 
1000 * 0.5 = 500
$ 500   Remaining were sold at a price equal to 30% less than the price each head sold for on the day before i.e , (70/100)*0.5= $ 0.35   Hence selling cost for the remaining cabbage = 500 * 0.35= 
500 * 0.35 = 175
$ 175   Total selling cost= 500 + 175= 
500 + 175 = 675
$ 675   Gross profit= $ 675 - $ 600 = $ 75   Hence Answer is e $75.
Answer: E
Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?	Choose the correct choice from the following answers.
A) (a + y) / t B) 2(a + t) / ay C) 2ayt / (a + y) D) 2(a + y + t) / ay E) x(y + t) + y(x + t)

Solution: If we choose for d (distance): 10 miles, for a 10 and for y 5.   t would be 90 minutes or 1,5 hours.   If I try this for answer choice 2ayt / (a + y) it fits.
Answer: C
A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 2 days, B can complete the job in 5 days and C can complete the job in 7 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
Choose the correct choice from the following:
A) 71/59 days  B) 70/59 days  C) 3 days  D) 12days  E) 14 days

Solution: Let the total number of cans to be prepared be 70.   The number of cans prepared by A in 1 day = 35.   The number of cans prepared by B in 1 day = 14.   The number of cans prepared by C in 1 day = 10.   Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 59.   Therefore, the number of days taken to complete the whole work = 70/59 days.   ANSWER:70/59 days
Answer: B
An error 4% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
Choose the correct choice from the following answers.
A) 4.05% B) 4.02% C) 8.16% D) 3% E) 2%

Solution: Percentage error in calculated area   =(4+4+(4Ã—4)/100)%   =8.16%   ANSWER:8.16%
Answer: C
The average of five numbers is 60. If one number is excluded, the average becomes 65. The excluded number is?  Pick:  A) 40  B) 6  C) 58  D) 35  E) 96

Solution: Excluded number   = (60 * 5) - (65 * 4)   = 300 - 260= 
300 - 260 = 40
40   40nswer:40
Answer: A