MU-NLPC/Calc-aqua_rat huggingface dataset:
If a,b,c,d,e is an arithmetic sequence which of the following is also an arithmetic sequence?
I. 5a, 5b, 5c, 5d, 5e
II. a-6, b-6, c-6, d-6, e-6
III. a^8, b^8, c^8, d^8, e^8	Choose the most appropriate option
A) I and II B) II only C) II and III D) III only E) I only

Solution: lets look at the three choices...   I. 5a, 5b, 5c, 5d, 5e   since the difference is constant, it is an arithmetic sequence...   II. a-6, b-6, c-6, d-6, e-6   since the difference is constant, it is an arithmetic sequence   III. a^8, b^8, c^8, d^8, e^8   since the difference is not constant it is not be an arithmetic sequence...   only l and ll.. ans I and II....
Answer: A
Sonika bought a V.C.R. at the list price of 18,500. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
Choices:
A) 19,980  B) 19,780  C) 19,680  D) 19,380  E) None of these

Solution: Sol. List price of V.C.R. =18,500   Rate of sales tax = 8%   ∴ Sales tax = 8% of 18,500   = 8⁄100 × 18500 = 1480   So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,500 + 1480   = 19,980. 19,980nswer 19,980
Answer: A
The two lines y=x and x=-6 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
Choose one:
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: The point of intersection is (-6,-6).   The triangle has a base of length 6 and a height of 6.   area = (1/2)*base*height = (1/2)*6*6= 
(1/2)*6*6 = 18
18   The answer is 18.
Answer: D
Find the simple interest on $10000 at 4% per annum for 12 months? Choose the most appropriate option
A) $400 B) $500 C) $650 D) $710 E) $1000

Solution: P = $10000   R = 4%   T = 12/12= 
12/12 = 1
1 YEAR   S.I.= P*R*T/100 = 10000*4*1/100= 
10000*4*1/100 = 400
$400   $400nswer is $400
Answer: A
In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females? Choose the correct choice:	A) 16%	B) 25%	C) 30%	D) 40%	E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 45 are employed males, hence 19% are employed females.   (employed females)/(total employed people)=19/64=30%   Answer: 30%.
Answer: C
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?	Select the correct option:  A) 40 sec  B) 29 sec  C) 26 sec  D) 27 sec  E) 34 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secnswer: 40 sec
Answer: A
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10)
II. P(P(10))
III. P(P(P(10)))
Choose the correct answer:
A) I only	B) I and II only	C) I and III only	D) II and III only	E) I, II, and III

Solution: 2 is the only even prime number. Now, the sum of first 10 prime numbers = 9*odd + 2 = odd. Thus P(10) = odd.   Again, the sum of the first n -odd primes = (n-1)*odd+2 = even.Thus, p(P(10)) = even.   Similarly, the sum of the first m - even primes = (m-1)*odd+2 = odd.   I and III.   ANSWER:I and III only
Answer: C
A beekeeper has 900,000 bees living in ten beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have? Choose the correct option:
A) 18000
B) 109756
C) 46700
D) 657587
E) 4645747

Solution: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+9*(0.8)*x = 900,000 => 8.2x = 900,000 => x = 109756.   109756 is the answer.
Answer: B
Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -9 then by what factors will the Mean,Variance and Standard Deviation respectively change ? Choices
A) -9,-9,-9	B) -9,9,9	C) 1,1,1	D) -9,81,9	E) 9,9,81

Solution: Mean: If all values are multiplied by -9 then their sum will also be multiplied by -9 so Mean will also get -9   Variance:   Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values   When we multiply all the values by -9 then the difference between the mean and the individual values also gets multiplied by -9 and the square of that difference becomes 81. So, the variance gets multiplied by a factor of 81   SD:   Standard Deviation is the square root of variance so sqrt(81)=9. So SD gets multiplied by a factor of 9.   So, answer will be -9,81,9.
Answer: D
The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?  Options
A) A)0.8321  B) B)0.7  C) C)0.895  D) D)0.7531  E) E)0.8213

Solution: Out of 100 matches:   Matt is plays in 80 and not plays in 20.   Out of 80 matches Matt plays in, team wins   0.75*80= 
  0.75*80 = 60
60.   Out of 20 matches Matt does not play in, team wins   0.35*20= 
  0.35*20 = 7
7.   So, out of 100 matches 60 + 7= 
60 + 7 = 67
67 are won.   It is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67= 0.895...   Answer: 0.895.
Answer: C
Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is Choose the most appropriate option.
A) Rs 200	B) Rs 300	C) Rs 400	D) Rs 500	E) Rs 600

Solution: Explanation:   Let C = x.   Then B = x/2   and A = x/4   A:B:C = 1:2:4.   Rs 400's share Rs.[(4/7)*700) = 400   Option Rs 400
Answer: C
A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average of 4375 items per month over the whole?	Choose one: A) 4500 B) 4600 C) 4680 D) 4710 E) None

Solution: Sol.   Required average = (4375 x 12) - (4000 x 3 ) / 9   ⇔ 52500 - 12000 / 9   ⇔   40500 / 9= 
  40500 / 9 = 4_500
4500.   4500nswer 4500
Answer: A
A number is increased by 30 % and then decreased by 30 %. Find the net increase or decrease per cent.  Answers:	A) 9%	B) 8%	C) 7%	D) 3%	E) 6%

Solution: Let the number be 100.   Increase in the number = 30 % = 30 % of 100   = (30/100 Ã— 100)   = 30   Therefore, increased number = 100 + 30= 
100 + 30 = 130
130   This number is decreased by 30 %   Therefore, decrease in number= 30 % of 130   = (30/100 Ã— 130)   = 3900/100= 
3900/100 = 39
39   Therefore, new number= 130 - 39= 
130 - 39 = 91
91   Thus, net decreases= 100 -91= 
100 -91 = 9
9   Hence, net percentage decrease= (9/100 Ã— 100) %   = (900/100)= 
(900/100) = 9
9 %   9%nswer:9%
Answer: A
Set M contains numbers that satisfy the condition that, if integer x is in the set then x+1 will also be in the set M. If 0 is one of the value in the set, which of the following numbers must also be present in the set M.
I. 1
II. 3
III. 2
Pick:
A) I only  B) II only  C) I and II only  D) II and III only  E) I, II and III

Solution: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.   Now, if 0 is in the set, then 0+1= 
0+1 = 1
1mustbe in the set. Since 1 is in the set then   1+1= 
  1+1 = 2
2mustbe in the set, also 3.   Answer: I, II and III.
Answer: E
Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:  A) 10 minutes  B) 20 minutes  C) 15 minutes  D) 12 minutes  E) 18 minutes

Solution: Part of the filled by all the three pipes in one minute   = 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10   So, the tank becomes full in 10 minutes.   10 minutesNSWER:10 minutes
Answer: A
The value of land increases by m% during June and decreases by n% during July. If the value of the land is the same at the end of July as at the beginning of June, what is n in terms of m?	Select:
A) 200m/(100+2m)
B) 100m/(100+m)
C) m(2+m)/(1+m)2
D) m(200+m)/10000
E) 2m/m+2m

Solution: The simplest pairing is a 25% increase will be offset by a 20% decrease.   Here's the proof:   Starting value = 100   25% increase = 100 + (.25)(100) = 125   20% decrease = 125 - (.2)(125) = 100   Ending value = 100   So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...   Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.   Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.   Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.   Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.   Answer E:  (50/25) + 50= 
 (50/25) + 50 = 52
52. ELIMINATE E.   100m/(100+m)
Answer: B
If a rectangular room measures 8 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
Choose the most appropriate option.
A) 24,000	B) 16,000,000	C) 2,400,000	D) 24,000,000	E) 240,000,000

Solution: B. 160,000,000   8*100*5*100*4*100 = 160,000,000
Answer: B
In 26 minutes, the minute hand gains over the hour hand by
Choose the correct option
A) 116° B) 125° C) 143° D) 158° E) 172°

Solution: In one hour, the hour hand moves 30°, which is 0.5° each minute.   In one hour, the minute hand moves 360°, which is 6° each minutes.   The minute hand gains 5.5° each minute.   In 26 minutes, the minute hand gains   26 * 5.5= 
  26 * 5.5 = 143
143°.   The answer is 143°.
Answer: C
The total of 342 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is  Choose the correct answer
A) 238 B) 290 C) 278 D) 200 E) 288

Solution: Explanation:   Let the number of 20 paise coins be x. Then the no of 25 paise coins = (342 - x).   0.20 * (x) + 0.25 (342 - x) = 71 => x = 290..   Answer: 290) 290
Answer: B
Ben earns $12,800 a year. About 15% is taken out for taxes.
How much is taken out for taxes? Choose the correct answer:
A) $19200	B) $11920	C) $1920	D) $19820	E) $10920

Solution: 15/100=x/12.800   Divide by the remaining number:   1920/192000   100   $1920   correct answer $1920
Answer: C
Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Choose the correct choice from the following answers.
A) 11 1/8%	B) 11 1/5%	C) 11 1/9%	D) 11 12%	E) 11 5/9%

Solution: 900 --- 100   100 --- ? => 11 1/9%   Answer: 11 1/9%
Answer: C
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 50%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged? Choose the most appropriate option
A) 100% decrease B) 50% decrease C) 40% decrease D) 40% increase E) 50% increase

Solution: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 50%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer 40% decrease.
Answer: C
By selling an Shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is: Choose the correct choice from the following options.
A) 9%  B) 2%  C) 8%  D) 5%  E) 6%

Solution: C   8%   Marked price = $300   C.P. = 100/120 * 300= 
100/120 * 300 = 250
$250   Sale price= 90% of $300 = $270   Required gain % = 20/250 * 100= 
20/250 * 100 = 8
8%.
Answer: C
A number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?	Choose the correct choice.
A) 120	B) 180	C) 200	D) 220	E) None

Solution: Answer   Let the number be N.   Then, (N/5) + 3 = (N/4) - 3   â‡’ (N/4) - (N/5) = 6   â‡’ (5N - 4N)/20 = 6   âˆ´ N = 120   Option: 120
Answer: A
One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 50 of the attendees are neither female nor students, what is the total number of attendees at the convention?  Options:  A) 600  B) 300  C) 400  D) 500  E) 700

Solution: Let no. of Attendee are A.   Now As per the condition of the problem stated above .   We have following population in the convention as Attendee.   Total no. of females = [2/3]*A   Total no. of females as student : [1/6]*A   Total no. of students = [1/3]*A   Total no. of male as student = [1/6]*A   Total no. of males = A - [2/3]*A = [1/3]A   No. of males which are not student = [1/3]A - [1/6]*A = 50   Hence A =300   Total no of males who are not student will be the answer as it states it should be neither female nor student   So Answer is 300
Answer: B
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 90 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?	Choose the most appropriate option.
A) 8%
B) 9%
C) 11%
D) 12.5%
E) 16.7%

Solution: Typical dosage is Dose : weight :: 2: 15.   Now if weight is 90 (Multiplying factor is 6: (90/15)) then typical dosage would be 2 *6= 
2 *6 = 12
12 cc.   Dosage= 18 cc. Dosage is greater by 2 cc.   % dosage is greater: (2 / 12)*100 = 16.67 %   16.7% is the answer.
Answer: E
Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3? Choose the correct choice from the following answers
A) 3/10	B) 3/20	C) 2/5	D) 1/2	E) 1/3

Solution: S={1,2,3,….20}   E={3, 6,9,12,15,18}   P(E)=6/20   =3/10   Option 3/10
Answer: A
A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 128 runs, thereby increasing his average by 6 runs. His new average is	Choose the correct choice:
A) 18 runs B) 28 runs C) 48 runs D) 42 runs E) 68 runs

Solution: Explanation:   Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 6 => 11x + 66 = 10x + 128 => x = 62.   New average = (x + 6) = 68 runs.   Answer: 68 runs
Answer: E
Twelve people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...? Options: A) 1/12 B) 1/8 C) 1/11 D) 12/11 E) 10/11

Solution: Let P = total cost of the rental van.   The original share per person is P/12.   The new share per person is P/11.   P/11 = P/12 * 12/11 = (1 + 1/11)*original share   The answer is 1/11.
Answer: C
In a trapezium ABCD, AB is parallel to DC, AB = 3*DC, and the diagonals of the trapezium intersect at O. The ratio of the area of ∆OCD to the area of ∆OAB is:	Choose the correct choice from the following answers
A) 1:9
B) 1:3
C) 3:1
D) 1:10
E) Cannot be determined

Solution: triangles are similar , so ratio will be 1:9   1:9
Answer: A
There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe Choose the correct choice from the following answers:
A) 1/9	B) 2/9	C) 5/9	D) 4/9	E) 2/3

Solution: total 9 from take one.   9c1=9   red 5 from one   5c1=5   5/9   ANSWER:5/9
Answer: C
The average (arithmetic mean) monthly income of four workers is $3,000. After one worker’s income increases by 20 percent the new average income is $3,300. What was the original income of the worker whose monthly income increased? Options
A) $6,500
B) $6,400
C) $6,000
D) $6,200
E) $6,600

Solution: Increase in total income was 300*4= 
300*4 = 1_200
$1200, we know that this increase was 20% (1/5th) of the workers original income, thus his/her original income was 1200*5=$6,000.   Answer: $6,000
Answer: C
Find the one which does not belong to that group ? Choose the correct choice from the following:
A) 36
B) 49
C) 64
D) 81
E) 100

Solution: Explanation:   36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.   36, 64, 81 and 100 are squares of composite numbers, but not 49.   ANSWER IS 49
Answer: B
A can give B 100 meters start and C 150 meters start in a kilometer race. How much start can B give C in a kilometer race?	Choose the correct choice from the following options:
A) 10.55 meters
B) 11.55 meters
C) 33.55 meters
D) 55.55 meters
E) None of these

Solution: Explanation:   A runs 1000 meters while B runs 900 meters and C runs 850 meters.   Therefore, B runs 900 meters while C runs 850 meters.   So, the number of meters that C runs when B runs 1000 meters = (1000 x 850)/900 = 944.44 meters   Thus, B can give C (1000 - 944.44) = 55.55 meters start   Answer:55.55 meters
Answer: D
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a.for the next five years and 13% p.a.for the period beyond eight years If the total interest paid by him at the end of eleven years is 8160, how much money did he borrow?
Choose the correct choice from the following options.
A) 8000  B) 10,000  C) 12,000  D) Data inadequate  E) None of these

Solution: Let the sum be x. Then,   (x×6×3/100)+(x×9×5/100)+(x×13×/)=8160   ⇒ 18x + 45x + 39x = (8160 × 100)   ⇒ 102x = 816000   ⇒ x = 8000.   8000nswer 8000
Answer: A
If w is 40 percent less than t, t is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w? Choose the correct choice
A) 4%  B) 18%  C) 36%  D) 40%  E) 50%

Solution: GIven w= 0.6t, t=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. 50% is the correct answer.
Answer: E
What percent of 5 letter combinations that can be made from the letters of the word FERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant? Choose the correct choice from the following choices:	A) 23.8%	B) 20%	C) 25%	D) 30.2%	E) 35%

Solution: a) noof combinations when all 5 letters are different = 7*6*5*4*3   b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3   b/a = 5/21= 0.238   23.8%
Answer: A
A childrens identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
Pick one:  A) 211  B) 216  C) 1075  D) 1080  E) 2160

Solution: A childrens identification code will be of the type -,-,-,-   first digit can be selected from any of the 5 vowels in 5C1 ways   now for the remaining three digit lets consider the following two cases   case 1: when the number is greater than 200 but less than 300   number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18   now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:   211   233   244   255   266   277   288   299   here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)   thus total possible cases are 18 + 8= 
18 + 8 = 26
26   case 2: number ranging from 300 to 999   here for first digit we have 7 cases (3,4,5,6,7,8,9)   now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)   if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)   hence total number of ways= 7(18+9) = 189   thus different number of codes = 5(189+26) = 1075   hence 1075
Answer: C
The length of the bridge, which a train 150 m long and traveling at 45 km/hr can cross in 30 sec is?
Choose the correct choice from the following choices
A) 377
B) 225
C) 237
D) 245
E) 267

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (150 + x)/30 = 25/2   x = 225 m.   Answer: 225
Answer: B
A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets W be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .	Pick.
A) (J - 50)/3
B) 3(J + 20)/x
C) (J + x - 50)/3
D) (J - x + 60)/3
E) (J + x - 20)/3

Solution: here it goes:   Oldest inhabitant = sum of age of triplets + X   J = 3L + X so L = (J - X)/3   After 20 years = L + 20   = (J - X)/3 + 20   W= (J - X + 60)/3=(J - x + 60)/3
Answer: D
If John takes 7 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
Options:
A) 420xz	B) 7z/x	C) 420z/x	D) 7xz	E) 420x/z

Solution: It will take (z/x)(7) minutes which is (z/x)(7)(60) seconds = 420z/x seconds.   The answer is 420z/x.
Answer: C
The average of first 25 natural numbers is?
Answers.
A) 14 B) 13 C) 15 D) 18 E) 12

Solution: Sum of 25 natural no.   = 650/2= 
650/2 = 325
325   Average= 325/25= 
325/25 = 13
13   Answer:13
Answer: B
The distance from Steve's house to work is 30 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?	Select the correct option: A) 5. B) 10. C) 14. D) 15 E) 20.

Solution: Time is in the ratio 2:1 :: to: fro office   Therefore, 2x+1x=6 hrs   Time take to come back - 2 hrs, distance travelled - 30 km => Speed = 15 kmph   ANSWER:15
Answer: D
Two men, Vikas and Vishal, working separately can mow a field in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vikas beginning at 8 a.m, when will the mowing be finished? Choose the correct choice from the following answers:
A) 232 B) 787 C) 2369 D) 277 E) 281

Solution: Answer:787
Answer: B
A man complete a journey in 10 hrs. He 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?  Pick one.
A) 334  B) 224  C) 667  D) 2678  E) 112

Solution: Let the total distance be x km.   Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10   15x = 168 * 20 => x = 224 km   Answer: 224
Answer: B
The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the width and the length of the garden.
Choices:
A) 80 B) 90 C) 100 D) 70 E) 110

Solution: Let L and W be the length and width of the garden. The statement "the length of a rectangular garden is 2 feet longer than 3 times its width" may be formulated by   L = 2 + 3 W   The formula for the perimeter is given by   P = 2 L + 2 W   Substitute P and L in the above equation by 100 and 2 + 3 W respectively to obtain   100 = 2(2 + 3 W) + 2 W   Solve for W and L   W = 12 and L = 2 + 3 W = 38.   100heck that the perimeter of the rectangular garden is 100   P = 2 L + 2 W = 76 + 24= 
76 + 24 = 100
100   Answer 100
Answer: C