MU-NLPC/Calc-aqua_rat huggingface dataset:
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?	Choose the correct choice from the following answers
A) 8/5 B) 5/2 C) 3 D) 33/25 E) 4

Solution: Let monthly salary for each of the 11 months except 33/25ecember was x, then   11x*1/10 + Nx*1/3 = 1/8(11x + Nx);   11/10 + N/3 = 1/8(11 + N)   33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66   N = 66/50=33/25   Answer: 33/25.
Answer: D
The average of first nine prime numbers is?
Pick one
A) 10 B) 11.1 C) 12.5 D) 15.8 E) 13.6

Solution: Average = (2+3+5+7+11+13+17+19+23)/9= 100/9 = 11.1   Answer is 11.1
Answer: B
If an integer t is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that t(t + 1)(t + 2) will be divisible by 8?	Choose the correct choice from the following answers
A) 1/4	B) 3/8	C) 1/2	D) 5/8	E) 3/4

Solution: for t Total numbers 8*12   There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))   and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))   The answer 5/8 -> 5/8
Answer: D
If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. wb + b^2
II. (w+ b)^2
III. w + b
Select the correct option.
A) I only  B) II only  C) III only  D) I and II only  E) I, II, and III

Solution: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK;   II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK.   Answer: II only.
Answer: B
Find the invalid no.from the following series 3, 6, 15, 31, 63, 127, 255	Choose the most appropriate option:
A) 6
B) 7
C) 27
D) 63
E) 127

Solution: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 6 is wrong.   6
Answer: A
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions?  Pick one:
A) 420
B) 770
C) 840
D) 165
E) 315

Solution: 1 of 7 will be chosen for the math   3 of 10 will be chosen for the computer   None of the 4 chosen people can be in more than one departments.   We can choose any of the 7 candidates for the math dep., which gives as 7 selections.   We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections.   So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:   10! /3!*7!= 120   We are multiplying our individual selections:  7*120= 
 7*120 = 840
840   In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.   Ans 840
Answer: C
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
Choices:
A) 10 : 5 B) 15 : 2 C) 20 : 2 D) 25 : 2 E) 28 : 2

Solution: Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.   US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.   Now US : Indian = 25 : 10, and Indian : British = 10 : 2   Hence the two ratios can be combined and US : British = 25 : 2 Answer: 25 : 2
Answer: D
. A boy has five trousers and 11 shirts. In how many different ways can he select a trouser and a shirt?  Choose the correct answer.
A) 45  B) 55  C) 65  D) 75  E) 80

Solution: Explanation:   The boy can select one trouser in five ways.   The boy can select one shirt in 11 ways.   The number of ways in which he can select one trouser and one shirt is   5 * 11= 
  5 * 11 = 55
55 ways.   Answer: Option 55
Answer: B
Jim is able to sell a hand-carved statue for $540 which was a 35% profit over his cost. How much did the statue originally cost him?	Choose one
A) $400.00
B) $412.40
C) $455.40
D) $474.90
E) $488.20

Solution: 540 = 1.35*X   X = 540/1.35= 
540/1.35 = 400
400   $400, which is ($400.00).
Answer: A
What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
Choose the correct option.
A) 988
B) 500
C) 378
D) 373
E) 287

Solution: 70 = (P*4*7/2)/100   P = 500   Answer: 500
Answer: B
In a car wheel, ten spokes cover 60 degrees. Then for the entire car,how many spokes are there? Options:
A) 120
B) 140
C) 240
D) 320
E) 340

Solution: given, 10 spokes cover 60degrees,   so for 360 degrees.---->360*10/60=60..   so, for entire car, 4*60=240   ANSWER:240
Answer: C
If y = x^2 + cx + d, y is minimum when x is: Choose the correct choice from the following options
A) c/d	B) -c/d	C) -c/2	D) -d/2	E) d/c

Solution: We're given the equation Y = X^2 + cX + d.   IF.. we use a simple Classic Quadratic....   c = 2   d = 1   Y = X^2 + 2X + 1   We can then go about finding the answer that yields the MINIMUM result when X = ...   Answer A: c/d = 2/1= 
2/1 = 2
2 --> 4+4+1= +9   Answer B: -c/d = -2/1 = -2 --> 4-4+1 = +1   Answer -c/2: -c/2 = -2/2 = -1 --> 1-2+1 = 0   Answer D: -d/2 = -1/2 -->(1/4)-1+1 = +1/4   Answer E: d/c = 1/2 --> (1/4)+1+1 = +2 1/4   From these results, we can see the minimum result:   -c/2
Answer: C
If two sides of a triangle are 12 and 4, which of the following could be the area of triangle?
1. 35
2. 48
3. 56 Options.
A) a) 1 only
B) b) 1 and 2 only
C) c) 1 and 3 only
D) d) 2 and 3 only
E) e) 1, 2 and 3 only

Solution: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.   lets say base = 12 , height =8 (angle = 90)   maximum area = (1/2)*12*8= 
(1/2)*12*8 = 48
48 ( this is the same maximum area even when base is 8 and height is 12).   if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.   C,D and E are ruled out.   3 and 2 are possible areas as their areas are less than 48.   Hence the answer is d) 2 and 3 only.
Answer: D
How many bricks each measuring 22cm x 10.25cm x 8cm, will be needed to build a wall 9m x 7m x 10.5m
Select the correct option
A) 5600  B) 3066  C) 3055  D) 7200  E) None of these

Solution: Explanation:   no. of bricks= volume of the wall/volume of 1 brick = (900 x 700 x 10.5) / (22 x 10.25 x 8) = 3066   Answer: 3066
Answer: B
An association of mathematics teachers has 1,500 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 36 percent of the votes cast?	Pick one
A) 7.5%  B) 5.8%  C) 4.2%  D) 34.5%  E) 12.6%

Solution: Total umber of members = 1500   Number of members that cast votes = 525   Since , winning candidate received 36 percent of the votes cast   Number of votes for winning candidate = (36/100)*525= 
(36/100)*525 = 189
189   Percent of total membership that voted for winning candidate= (189/1260)*100 = 12.6%   Answer 12.6%
Answer: E
Today is Sunday. After 36 days, what day of the week will it be?	Select the correct option
A) Thursday
B) Monday
C) Tuesday
D) Saturday
E) Sunday

Solution: Each weekday is repeated every 7 days. 36 divided by 7 is 5 with a remainder of 1. So, after 35 days it will be a Sunday. After 36 days, it will be a Monday. Answer: Monday
Answer: B
The LCM and HCF of two numbers are 60 and 2 respectively. Find the larger of the two numbers if their sum is 22.	Choose the correct option:
A) 12 B) 2 C) 4 D) 54 E) 56

Solution: There are 2 approaches in solving this.   Methode 1.   HCF * LCM = The Actual Number.   60* 2= 
60* 2 = 120
120   So the answer which we are looking for has to be a factor of 120.   So among the options shortlist the answers by eliminating those numbers which is not divisible by 120. and then take the highest number as the answer as the question asks abt the highest number.   answer is 12
Answer: A
In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 4/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have?
Choose the correct choice from the following choices.
A) 30	B) 150	C) 60	D) 90	E) 135

Solution: We can start with the known quantity and then go on to find the others.   Shiny igneous ricks are 40. These are (4/5) of total igneous rocks.   (4/5)*Total igneous rocks = 40   Total igneous rocks = 40 * (5/4)= 
40 * (5/4) = 50
50   Total sedimentary rocks= 2*Total igneous rocks = 2*50= 
2*50 = 100
100   Total number of rocks= 50 + 100= 
50 + 100 = 150
150   Answer (150)
Answer: B
In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 10:6:5. If there are in all Rs.92, the number of 25 paisa coins is?	Choose the correct choice from the following answers:
A) 26
B) 46
C) 48
D) 42
E) 28

Solution: 10x 6x 5x   50 25 100   500x + 150x + 500x = 9200   1150x = 9200   x = 8 => 6x = 48   Answer: 48
Answer: C
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.45. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?	Choices:
A) 0.05  B) 0.15  C) 0.45  D) 0.5  E) 0.55

Solution: P(A or B) = P (A) + P(B) - p(a n b)   0.6= 0.4 + P(B) - 0.45   P(B) = 0.55   Ans : 0.55
Answer: E
1. Mrs. Ram got a weekly raise of $145. If he gets paid every other week, write an integer describing how the raise will affect her paycheck.  Choose the correct answer:
A) 145  B) 245  C) 100  D) 150  E) 345

Solution: Let the 1st paycheck be x (integer).   Mrs. Ram got a weekly raise of $ 145.   So after completing the 1st week he will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   145nswer :145
Answer: A
Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Choose the most appropriate option: A) Rs.1056 B) Rs.1001 C) Rs.2056 D) Rs.1026 E) Rs.1856

Solution: (900*3*3)/100= 
(900*3*3)/100 = 81
81   920 + 81= 
920 + 81 = 1_001
1001   ANSWER:Rs.1001
Answer: B
If x > y, x < 6, and y > -3, what is the largest prime number that could be equal to x + y?	Choose the correct choice.
A) 10	B) 11	C) 12	D) 14	E) 16

Solution: Primes: 2, 3, 5, 7, 11, 13, 17, etc   If X is less than 6 and y is less than X, then 6+6= 
6+6 = 12
12 would be impossible. We know 13 and all the primes > 13 are out. Let's try 11.   5.9 + 5.1= 
5.9 + 5.1 = 11
11   5.9 < 6   5.1 < 5.9   everything checks out   Answer 11   ANSWER:11
Answer: B
In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten? Pick:
A) 15 B) 18 C) 21 D) 23 E) 29

Solution: There are two conditions:   1. Angel got at least one score of each of 1, 2, 3, and 4.   2. She never got the same score in consecutive steps.   Taking that into account, the greatest possible score that Angel could have gotten is  4 + 1 + 4 + 2 + 4 + 3= 
 4 + 1 + 4 + 2 + 4 + 3 = 18
18.   Answer: 18.
Answer: B
The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter  Choose the correct choice from the following: A) Rs.16500 B) Rs.15500 C) Rs.17500 D) Rs.18500 E) Rs.19500

Solution: l=5.5m w=3.75m   area of the floor = 5.5 x 3.75 = 20.625 sq m   cost of paving = 800 x 20.625 = Rs. 16500 Rs.16500nswer: Rs.16500
Answer: A
Look at this series: 83, 73, 93, 63, __, 93, 43, ... What number should fill the blank?
Choose the correct choice from the following options:
A) 55
B) 59
C) 52
D) 53
E) 51

Solution: D   53   This is a simple subtraction series in which a random number, 93, is interpolated as every third number. In the subtraction series, 10 is subtracted from each number to arrive at the next.
Answer: D
81,162,49,98,25,50,62	Choices:
A) 124	B) 127	C) 129	D) 128	E) 131

Solution: 81*2= 
81*2 = 162
162   49*2= 
49*2 = 98
98   25*2= 
25*2 = 50
50   62*2= 
62*2 = 124
124   124NSWER:124
Answer: A
The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 116. Find their present ages.	Choose the correct choice from the following options:
A) 20,35,45	B) 28,49,63	C) 16,28,36	D) 16,28,46	E) None of these

Solution: Let the present ages of three persons be 4K,7K and 9K respectively.   (4K - 8) + (7K - 8) + (9K - 8) = 116   20K = 140   K = 7   Therefore, then present ages are 28,49,63.   ANSWER:28,49,63
Answer: B
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team X, but each box of Team A’s has 60% fewer booklets than each box of Team X’s. Which of the following could be the total number of booklets distributed by the two groups?
Choose the correct choice: A) 2,000 B) 3,200 C) 4,100 D) 4,800 E) 4,900

Solution: Let x be the no of booklets in each box that team X distributes. So, Team A has 60% fewer - 0.4x.   Let y be the no. of boxes distributed by team X. So, Team A distributes 60% more - 1.6y   Total booklets distributed by team A = xy   Total booklets distributed by team X=0.64xy   Total booklets distributed = xy+0.64xy=1.64xy   As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.   Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.   Similarly all answer choices, except choice C, fail to provide an integer value.   4,100hoice 4,100 = 4100/1.64= 
4100/1.64 = 2_500
2500 and is the correct answer.
Answer: C
The mean of set P does not exceed mean of any subset of set P. Which of the following must be true about set P?
I. Set P contains only one element
II. All elements in set P are equal
III. The median of set P equals the mean of set P  Choose the correct answer: A) of the three qualities is necessary B) II only C) III only D) II and III only E) I, II, and III

Solution: The only necessary condition seems to be II.   If all nos are equal.... them mean of any subset is the same.   I is obviously ruled out ( e.g. P = {1,1,1} )   But III, what about 3?   It is not necessary in itself, rather, is automatically implied by II.   All sets that satsify II satisfy III=II and III only
Answer: D
If the sides of a cube are in the ratio 9:7. What is the ratio of their diagonals?
Options:
A) 4:3
B) 16:9
C) 9:7
D) 3:4
E) 3:8

Solution: Explanation:   Diagonal of a 9:7ube=a√3 where a is side   a1:a2 = 9:7   d1:d2 = 9:7 where√3 cancelled both side   ANSWER:9:7
Answer: C
If you roll a fair-sided die twice, what is the probability of getting a (2 ,2)? Choose the correct choice from the following answers:
A) 1/4! B) 1/3! C) 1/2! D) 1/36 E) 1/24

Solution: total no. in two dice (1,1) ,(2,2) .....(6,)   Total number of events= 6*6   Total events of getting same pair(2, 2) = 6   Probability= 6/6*6= 1/6=1/3!   1/3!
Answer: B
What is the difference between the largest number and the least number written with the digits 7, 3, 1, 4? Choose the correct choice from the following choices:
A) 6084 B) 6184 C) 5084 D) 6048 E) 6049

Solution: 1347   7431   ------------   6084   6084NSWER:6084
Answer: A
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 9?  Choose the correct choice.
A) 1/13 B) 1/26 C) 5/13 D) 1/4 E) 1/52

Solution: The question should ask about the probability not the odds.   There are 13 spades, the probability that the spade we already have is 9 is therefore 1/13.   1/13nswer: 1/13.
Answer: A
Each shelf of a bookcase contains 20 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
Choose the correct choice:
A) A)4 B) B)12 C) C)6 D) D)8 E) E)9

Solution: Denoting x the number of the shelves,   we can build an equation: 20x=16(x−1)+22+42   Solving the equation, we get x=12   Answer: 12
Answer: B
A sum fetched a total simple interest of $4061.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum? Choose the correct choice.
A) $8829  B) $2840  C) $6578  D) $7782  E) $8926

Solution: $8926   8926   Principal   = $100 x 4016.25/9 x 5   = $406125/45   = $8926.
Answer: E
A fair 2 sided coin is flipped 3 times. What is the probability that tails will be the result at least twice, but not more than 3 times?	Choices.
A) 5/8
B) 3/4
C) 3/8
D) 7/4
E) 5/6

Solution: at least twice, but not more than 3 timesmeans exactly 2 times, 3 times   The probability of getting exactly k results out of n flips is n3/8k/2^n   33/82/2^3=3/8   Option: 3/8
Answer: C
A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is	Choose the correct choice:
A) 280
B) 285
C) 290
D) 295
E) 275

Solution: Explanation:   As the month begin with sunday, so there will be five sundays in the month. So result will be:   =(510×5+240×25 / 30)=(8550 / 30)= 
(8550 / 30) = 285
285   Option 285
Answer: B
Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win or draw?	Choose the most appropriate option:
A) 5/6	B) 2/3	C) 1/2	D) 5/12	E) 1/3

Solution: There are 3*3= 
3*3 = 9
9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Jim winning the game is (favorable outcomes)+Drawing the game / (total # of outcomes)= 6/9 = 2/3.   Or: no matter what sign Renee will select Jim can select 1 sign to win, 1 sign to get tie and 1 sign to loose, so the probability Jim winning the game or drawing is 2/3.   Answer: 2/3
Answer: B
If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a heart and the other will be a club?
A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts(red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.	Choose the correct choice from the following answers:
A) 1/8	B) 1/16	C) 1/32	D) 1/64	E) 1/128

Solution: P(1 heart and 1 club) = 2(1/4*1/4) = 1/8   The answer is 1/8.
Answer: A
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?  Choose the correct option.
A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) 84 sec

Solution: Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.   = 36 x	5/18	m/sec   = 10 m/sec.   Distance to be covered = (240 + 120)= 
(240 + 120) = 360
360 m. Answer: Option 36 sec   Time taken= 360/10= 
360/10 = 36
36 sec.
Answer: C
A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
Choose the correct choice from the following
A) 100 m
B) 120 m
C) 130 m
D) 150 m
E) None of these

Solution: Explanation :   Solution: Relative speed = (9 - 8)= 
(9 - 8) = 1
1 km/hr.   Distance covered in 3 minutes= (1 * 3/60) km = 1/20 km = 50 m.   .'. Distance between the criminal and policeman = (180 - 50)= 
(180 - 50) = 130
130 m.   Answer : 130 m
Answer: C
What percent of 500 is 125? Choose the most appropriate option:
A) 0.25%	B) 4%	C) 25%	D) 40%	E) 250%

Solution: 500*x /100 = 125   x = 125/5= 
125/5 = 25
25   Ans: 25%
Answer: C
Tough and Tricky questions: Word Problems.
Micheal , Saren and Donald decided to club together to buy a present. Each of them gave equal amount of money. Luckily Saren negotiated a 20% discount for the present so that each of them paid 4 dollars less. How much did they pay for a present? Choose the most appropriate option
A) 20  B) 36  C) 48  D) 60  E) 72

Solution: Answer C.   We know that Saren negotiated a discount of 20%, so each of them paid $4 less. Since there are three people, the 20% of the original price amounts to $12. 5 times 12$ is 60$, so the original price, before Saren negotiated the discount, had been $60. They paid $12 less than the base price, so they spent $48.
Answer: C
The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 80% profit?
Select the correct option:
A) 1152	B) 230	C) 960	D) 780	E) 400

Solution: C.P. = Rs. x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 180% of Rs. 640 = 180/100 * 640 = Rs. 1152.   1152
Answer: A
How many meters are there in 550 centimeters?
Select the correct option: A) 550 meters B) 5.5 meters C) 100 meters D) 2.5 meters E) 1 meter

Solution: Solution:   1 meter = 100 centimeters   Just divide 550 by 100   550 Ã· 100 = 5.5, so there are 5.5 meters in 550 centimeters   Option 5.5 meters
Answer: B
The length of a rectangle is 5 more than the width. What are the dimensions of the rectangle if the perimeter is 34?  Choose the correct choice from the following choices:
A) 11  B) 12  C) 13  D) 14  E) None

Solution: Pretend width = 1, then length = 6 ( 1 + 5)   2 × 1 + 2 × 7 = 2 + 14= 
2 + 14 = 16
16. Notice that 16 is far from a perimeter of 34   Try much bigger number.   How about if we...   Pretend width= 4, then length = 9 ( 4 + 5)   2 × 4 + 2 × 9 = 6 + 18= 
6 + 18 = 24
24. We are getting closer to a perimeter of 34   Pretend width= 5, then length = 10 ( 5 + 5)   2 × 5 + 2 × 10 = 10 + 30 = 30.   Pretend width = 7, then length = 12 ( 7 + 5)   2 × 7 + 2 × 12 = 14 + 24= 
14 + 24 = 38
38. This is higher than a perimeter of 34. So width should be higher than 5 and smaller than 7. May be a width of 6 will work.   Pretend width= 6, then length = 11 ( 6 + 5)   2 × 6 + 2 × 11 = 12 + 22= 
12 + 22 = 34
34.   Use of algebra:   Let width= x   Let length = x + 5   P = 2 × L + 2 × W   34 = 2 × ( x + 5) + 2 × x   34 = 2x + 10 + 2x   34 = 4x + 10   34 - 10 = 4x + 10 - 10   24 = 4x   24/4 = 4x/4   6 = x   Therefore, width = 6 and length = x + 5 = 6 + 5= 
6 + 5 = 11
11   11nswer 11
Answer: A