MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?	Choose the correct answer:
A) 281
B) 132
C) 882
D) 279
E) 277

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2= Rs.132   Answer: 132
Answer: B
An insect leaps 42 centimeters in 1.2 seconds. What is its speed?
Choose the correct choice from the following answers:  A) 3.5 meters per second  B) 0.35 meters per second  C) 5 centimeters per second  D) 0.5 meters per second  E) 3.5 centimeters per second

Solution: 42 / 1.2= 
42 / 1.2 = 35
35 cm/s= 0.35 m/s   The answer is 0.35 meters per second.
Answer: B
Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Pick one
A) 250
B) 300
C) 350
D) 400
E) 450

Solution: Explanation :   Here's the solution :   Let the sum paid to Y per week be Rs. z.   Then, z + 120% of z = 550.   => z + (120/100) * z = 550   => (11 / 5) * z = 550   => z = 550 * 5 / 11   => z = 250   Hence (A) is the correct answer.   250nswer : 250
Answer: A
Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is:	Choose the correct choice from the following answers.
A) 32 years B) 36 years C) 38 years D) 40 years E) 42 years

Solution: Let Rajan's present age be x years.   Then, his age at the time of marriage = (x - 8) years.   x = 6/5 (x - 8)   5x = 6x - 48 => x = 48   Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.   Rajan's sister's present age = (30 + 8)= 
(30 + 8) = 38
38 years.   ANSWER:38 years
Answer: C
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Choose the correct answer
A) 11 B) 60 C) 77 D) 55 E) 12

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer: 77
Answer: C
If x < 0 and 0 < y < 1, which of the following has the greatest value Q?
Choose the correct choice from the following answers:  A) x^2  B) (xy)^2  C) (x/y)^2  D) x^2/y  E) x^2*y

Solution: Given, x < 0 and 0 < y < 1   Let, x = -2 and y = 1/2   A. x^2 = (-2)^2 =4   B. (xy)^2 = (-2*1/2)^2 =1   C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16   D. x^2/y = (-2)^2 / (1/2) = 4*2= 
4*2 = 8
8   E. x^2*y= (-2)^2*(1/2) =2   Answer: option (x/y)^2
Answer: C
man is 15 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: Choices
A) 13years
B) 26 years
C) 17 years
D) 18 years
E) 22 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 20) years.   (x + 15) + 2 = 2(x + 2)   x + 17 = 2x + 4   x = 13.   answer :13years
Answer: A
A man complete a journey in 10 hours. 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.
Choices:  A) 220  B) 222  C) 223  D) 224  E) 225

Solution: distance = speed x time   Let time taken to travel the first half = x hr   then time taken to travel the second half = (10 - x) hr   224istance covered in the the first half = 21x   224istance covered in the the second half = 24(10 - x)   But distance covered in the the first half = 224istance covered in the the second half   => 21x = 24(10 - x)   => 21x = 240 - 24x   => 45x = 240   => 9x = 48   => 3x = 16   ⇒x=16/3   Hence 224istance covered in the the first half = 21x=21×16/3=7×16=112 km   Total distance = 2×112=224 km   Answer is 224.
Answer: D
The ratio of two quantities is 4 : 3. If each of the quantities is decreased by 8, their ratio changes to 3:1 then the smallest number is?
Pick one
A) 5.2 B) 6.9 C) 9.6 D) 7.8 E) 4.7

Solution: Let the numbers be 4x and 3x   Then 4x-8 / 3x-8 = 3/1   4x-8 = 9x-24   5x = 16   x = 3.2   smallest number = 3*3.2= 
3*3.2 = 9.6
9.6   Answer is 9.6
Answer: C
Find the missing in the series: 70, 54, 45, 34,___	Choose the most appropriate option: A) 22 B) 287 C) 266 D) 2767 E) 2771

Solution: Answer:266
Answer: C
Nine friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 9-person seating arrangements are possible?  Choose the correct answer:	A) 122,400	B) 162,920	C) 202,180	D) 242,360	E) 282,240

Solution: The number of ways to arrange 9 people in a row is 9!   From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 7 other friends is 8! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 9 friends with the 2-person unit together is 8!*2   The total number of permutations where these two friends are not seated next to each other is 9! - 8!*2 = 7*8! = 282,240   The answer is 282,240.
Answer: E
A man is 37 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is  Choose the correct choice from the following choices.
A) 78 years B) 22 years C) 88 years D) 35 years E) 65 years

Solution: Let's Son age is x, then Father age is x+37.   => 2(x+2) = (x+37+2)   => 2x+4 = x+39   => x = 35 years   Answer: 35 years
Answer: D
85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?	Pick one.
A) 75	B) 80	C) 85	D) 90	E) 95

Solution: 75nswer = 75   Please refer diagram below     85 - 10= 
  85 - 10 = 75
75
Answer: A
CONVERT 1.8 hectares in ares Choose the most appropriate option
A) 130 ares.	B) 160 ares.	C) 180 ares.	D) 230 ares.	E) 250 ares.

Solution: 1.8 hectares in ares   1 hectare = 100 ares   Therefore, 1.8 hectares = 1.8 × 100 ares   = 180 ares.   ANSWER- 180 ares.
Answer: C
How many 4-letter words with or without meaning can be formed out of the letters of the word,'LOGARITHMS',if repetition of letters is not allowed? Choose the correct choice from the following choices:
A) 5040
B) 2520
C) 400
D) 40
E) 1502

Solution: 'LOG5040RITHMS' contains 10 different letters   Required number of words=Number of arrangements of 10 letters taking 4 at a time   =10P4   =10*9*8*7= 
10*9*8*7 = 5_040
5040   Option 5040
Answer: A
A Jar contains a mixture of A & B in the ratio 4:1. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.	Choose the correct choice from the following answers: A) 12 B) 15 C) 16 D) 20 E) 25

Solution: 10 litres of mixture that is replaced will contain 8 litres of A and 2 litres of B (as A:B = 4:1)   Let the initial volume of the mixture be 4K + 1K = 5K   So by condition ,   [ 4K-8 ]/ [ K-2+10 ]   4  + 1= 
  4  + 1 = 5
5K   So by condition ,   [ 4K-8 ]/ [ K-2+10 ]= 2/3   Solve for K which is K = 4   So initial volume of liquid A = 4K = 16 litres   ANSWER:16
Answer: C
Dravid rented a power tool from a rental shop. The rent for the tool was $8 for the first hour and $3 for each additional hour. If Dravid paid a total of $38, excluding sales tax, to rent the tool, for how many hours did she rent it?	Pick one: A) 10 B) 11 C) 12 D) 13 E) 15

Solution: 8 + 3n = 38   n = 10   Total time = n+1 hrs = 10+1= 
10+1 = 11
11 hrs   Answer : 11
Answer: B
If x,y ,and z are positive real numbers such that x+y-z =100 , y-z+x =120 , and z-x+y = 50, then find the x+y+z value?  Choose the correct choice from the following choices.
A) 100	B) 120	C) 150	D) 200	E) 160

Solution: x+y-z =100, ------1)   y-z+x =120 , ------2)   z-x+y = 50------3)   from (1)&(2)   2z=20   z=10   from (2)&(3)   2y = 170   y=85   then x=100-75= 
100-75 = 25
25   x+y+z= 120   correct option is 120
Answer: B
A seven-digit phone number is divisible by 7. After adding the two digits of the area code the number is not divisible by 7, which of the following cannot be the area code?	Choices:
A) 07.
B) 07.
C) 05.
D) 04.
E) 02.

Solution: Given that 7 digit number is divisible by 3   we know any number will not be divisible by 7 if the sum of all digits of the number is not the multiple of 7.   Hence looking at the option we can say that the number that should be added to the seven digit number must be 07 as adding it will make it divisible by 7... hence answer is 07.
Answer: B
Find the principle on a certain sum of money at 11% per annum for 2 2/5 years if the amount being Rs.1120?
Answers.
A) 1000	B) 812.88	C) 827.78	D) 826.82	E) 886.08

Solution: 1120 = P [1 + (5*12/5)/100]   P= 886.08   Answer: 886.08
Answer: E
The ratio of buses to cars on River Road is 1 to 3. If there are 40 fewer buses than cars on River Road, how many cars are on River Road?  Choose the correct choice from the following options:
A) 60
B) 75
C) 85
D) 95
E) 105

Solution: B/C=1/3   C-B=40.........> B=C-40   (C-40)/C=1/3   Testing answers. Clearly Eliminate BCDE   Put C=60.........> (60-40)/60=20/60=1/3   60nswer: 60
Answer: A
Three numbers are in the ratio 5 : 4 : 6 and their average is 750. The largest number is :	Choose the correct choice from the following answers:	A) 30	B) 98	C) 900	D) 21	E) 22

Solution: Explanation:   Let the numbers be 5x, 4x and 6x, Then, (5x + 4x + 6x ) / 3 = 750   => 15x = 750*3   => x = 150   Largest number 6x = 6*150= 
6*150 = 900
900   Answer: 900
Answer: C
The sides of a square region, measured to the nearest centimeter, are 9 centimeters long. The least possible value of the actual area of the square region is
Choose the correct choice from the following answers.
A) 60.25 sq cm  B) 66.25 sq cm  C) 56.25 sq cm  D) 72.25 sq cm  E) 58.25 sq cm

Solution: Though there might be some technicalities concerning the termnearest(as 7.5 is equidistant from both 7 and 8) the answer still should be : 7.5^2=56.25.   Answer: 56.25 sq cm
Answer: C
In a garden, 26 trees are planted at equal distances along a yard 500 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?  Pick:
A) 20
B) 8
C) 12
D) 14
E) 16

Solution: 26 trees have 25 gaps between them.   Length of each gap = 500/25= 
500/25 = 20
20   i.e., distance between two consecutive trees= 20   20nswer is 20.
Answer: A
Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 18 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.	Choose the correct answer:
A) 25 days	B) 100 days	C) 120 days	D) 110 days	E) 90 days

Solution: Rate of both = 1/20   Together they do = 1/20*18 = 9/10   Left work = 1 - 9/10 = 1/10   Adam completes 1/10 work in 10 day   so he took 10*10= 
10*10 = 100
100 days to complete the left work alone.   Thus the rate of adam is 1/100   Rate of Micheal= 1/20 - 1/100 = 1/25   Thus micheal takes 25 days to complete the whole work.   ans. 25 days.
Answer: A
In a given set of X = {70,55,98,45,62} what is the difference of median and mean of the set X?	Choose the correct option
A) 25	B) 30	C) 32	D) 40	E) 45

Solution: mean = 70+55+98+45+62 / 5 = 330/5= 
330/5 = 66
66   Median= 98   Difference = 98-66= 
98-66 = 32
32   Answer is 32
Answer: C
Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 8. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
Choices:  A) (4m-10)/[m(m-8)]  B) (4m-24)/[m(m-2)]  C) (4m-24)/[m(m-3)]  D) (4m-24)/[m(m-6)]  E) (4m-24)/[m(m-8)]

Solution: Three of the sandwiches were evenly divided among the students   i.e. Amount of Sandwiches with each students = 3/m   Amount of 4th Sandwich with remaining (m-8) students = 1/(m-8)   The amount of Sandwich that carol ate = 3/m + 1/(m-8) = (3m-24+m)/[m(m-8)] = (4m-24)/[m(m-8)]   Answer: (4m-24)/[m(m-8)]
Answer: E
Two partners in a business (Carol and Ben) invested $500 and $850 in a business respectively. At the end of the year they made a profit of $250. Find share of each partner?  Choices:
A) $92.59,$157.41
B) $96.59,$157.41
C) $92.59,$159.41
D) $92.59,$127.41
E) $12.59,$157.41

Solution: $92.59,$157.41:B = 500:850   $92.59,$157.41:B = 10 : 17   $92.59,$157.41's share = 250*10/27 = $92.59   B's share = 250*17/27 = $157.41   $92.59,$157.41nswer is $92.59,$157.41
Answer: A
There are 13 clubs in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a club, you win. If the card is not a club, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a club, and the point is to measure how many draws it took before the person picked a club and, thereby, won. What is the probability that one will pick the first club on the forth draw or later? Choose the correct answer:  A) 1/2  B) 3/4  C) 7/8  D) 27/32  E) 27/64

Solution: Favorable case = the club is picked in the third draw or later   Unfavorable cases = The club is picked in either first draw, second draw or third draws   Probability = Favorable outcomes / Total out comes   Also probability = 1-(Unfavorable outcomes / Total out comes)   Unfavorable case 1: probability of club picked in first draw = 13/52 =1/4   Unfavorable case 2: probability of club picked in Second draw (i.e. first draw is not club)= (39/52)*(13/52) =(3/4)*(1/4)= 3/16   Unfavorable case 3: probability of club picked in Third draw (i.e. first and 2nd draws are not clubs)= (39/52)*(39/52)*(13/52) =(3/4)*(3/4)*(1/4)= 9/64   Total Unfavorable Probability = (1/4)+(3/16)+(9/64) = (16/64)+(12/64)+(9/64)=37/64   i.e., Favorable Probability = 1 - (37/64) = 27/64   Answer: Option 27/64
Answer: E
If a and b are positive integers of T such that a/b=2.86, which of the following must be a divisor of a? Choose the correct choice from the following answers:
A) 10
B) B.13
C) 18
D) 26
E) 50

Solution: The prompt gives us a couple of facts to work with:   1) A and B are positive INTEGERS   2) A/B = 2.86   We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).   The simplest place to start is with...   A = 286   B = 100   286/100= 
286/100 = 143/50 = around 2.86
2.86   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 143   B = 50   143/50= 
143/50 = 143/50 = around 2.86
2.86   There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.   Final Answer:   B.13
Answer: B
John was 35 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?	Choose the correct choice from the following choices
A) 24
B) 35
C) 28
D) 30
E) 32

Solution: Assume Betty's age on marriage = x years.   John's age on marriage = 35   John's age after 5 years = 40 years.   35etty's age after 5 years = x + 5   Given: x + 5 = 7/8 (40) = 35   Therefore 35etty's current age = 35   Option 35
Answer: B
five mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the five arrange themselves in line such that Frankie’s requirement is satisfied?	Select the correct option
A) 80	B) 66	C) 60	D) 72	E) 75

Solution: 5 mobsters can stand in 5! ways = 120   in half of the cases one person will be ahead and in the other person in the other half.   thus 60 cases.   60
Answer: C
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3146 in 3 years. Find the rate percent?
Pick one.
A) 11	B) 30	C) 28	D) 24	E) 82

Solution: Explanation:   2420 --- 726   100 --- ? => 30%   Answer: Option 30
Answer: B
The circumference of a circle is equal to 72 pi. Find the radius of this circle. Choose the correct answer.
A) 32 B) 33 C) 36 D) 37 E) 39

Solution: The circumference of a circle is given by   C = 2 pi r, where r is the radius of the circle.   Substitute 36 by 72 pi to obtain the equation   72 pi = 2 pi r   Simplify and solve for r to obtain   r = 36   correct answer 36
Answer: C
The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 4 months. At this time, the construction was behind schedule by how many projects?
Pick one:
A) 28
B) 96
C) 198
D) 204
E) 504

Solution: Project/month :   612/18= 
  612/18 = 34
34   Project in 6 month to be completed= 34*4= 
34*4 = 136
136   Lag :  136-108= 
  136-108 = 28
28   28 is the answer
Answer: A
A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 3 feet in circumference?	Select:
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: total circuit=16/4= 
16/4 = 4
4   total feet squirrel travels=4*3= 
4*3 = 12
12 feet   12NSWER:12
Answer: A
The difference of the squares of two consecutive odd integers is divisible by which of the following integers ? Choose the correct answer
A) 4
B) 6
C) 2
D) 8
E) 0

Solution: Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,   (2n + 3)^2 - (2n + 1)^2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)   = (4n + 4) x 2   = 8(n + 1), which is divisible by 8.   ANSWER 8
Answer: D
Having scored 94 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?  Choose the correct choice from the following choices.
A) 28 B) 27 C) 26 D) 22 E) 24

Solution: Explanation :   Let the average score of the first 18 innings be n   18n + 94 = 19(n+4)=> n = 18   So, Average score after 19th innings = x+4 =22.   Answer : 22
Answer: D
The probability that A speaks truth is 3/5 and that of B speaking truth is 3/7. What is the probability that they agree in stating the same fact?
Choose the correct choice from the following answers:
A) 17/35  B) 17/37  C) 17/39  D) 17/33  E) 17/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 3/7 + 2/5 * 4/7   = 17/35   17/35nswer:17/35
Answer: A
A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Pick one
A) 337  B) 268  C) 198  D) 646  E) 168

Solution: 840 = P [1 + (10*3)/100]   P = 646'   Answer:646
Answer: D
Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is	Choices:
A) 70 B) 71 C) 72 D) 73 E) 74

Solution: Explanation:   Let the second number is x, then first is 2x, and third is 1/3(2x)   =>2x+x+2x/3=264   <=>11x/3=264   =>x=72   Answer: Option 72
Answer: C
Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4.6 times the amount of the second solution?	Choose the correct choice from the following answers
A) 62.0	B) 65.25	C) 68.75	D) 70.15	E) 72.35

Solution: SOL:   Lets assume that 46L of sol1 was mixed with 10L of sol2.   Alcohol in Sol1: 46*3/4 = 34.5L   Alcohol in Sol2: 10*2/5 = 4L   Total Alcohol in the mixed solution of 56L = 34.5 + 4= 
34.5 + 4 = 38.5
38.5L   Alcohol concentration in the new sol: (38.5/56)*100= 
(38.5/56)*100 = 68.75
68.75%   ANSWER:68.75
Answer: C
A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition? Choose the correct option.
A) 92.5%	B) 89.0%	C) 85.2%	D) 96.8%	E) 78.9%

Solution: Total number of fruits shopkeeper bought = 600 + 400= 
600 + 400 = 1_000
1000   Number of rotten oranges= 15% of 600   = 15/100 × 600   = 9000/100= 
9000/100 = 90
90   Number of rotten bananas= 5% of 400   = 20   Therefore, total number of rotten fruits = 90 + 20= 
90 + 20 = 110
110   Therefore Number of fruits in good condition= 1000 - 110= 
1000 - 110 = 890
890   Therefore Percentage of fruits in good condition= (890/1000 × 100)%   = (89000/1000)= 
(89000/1000) = 89
89.0%   Answer:89.0%
Answer: B
A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 10 minutes. How much time will be take to cover a distance of 10 kilometres? Select the correct option:  A) 148 min.  B) 150 min.  C) 145 min.  D) 155 min.  E) None of these

Solution: Rest time = Number of rest Ã— Time for each rest   = 9 Ã— 10 = 90 minutes   Total time to cover 10 km   = (10 â„10 Ã— 60)minutes + 90 minutes = 150 minutes   Answer 150 min.
Answer: B
The average of runs of a cricket player of 20 innings was 36. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Select the correct option:
A) 96	B) 106	C) 122	D) 116	E) 120

Solution: Average = total runs / no.of innings = 36   So, total = Average x no.of innings = 36 * 20= 
36 * 20 = 720
720   Now increase in avg= 4 runs. So, new avg = 36+4= 
36+4 = 40
40 runs   Total runs= new avg x new no. of innings = 40 * 21= 
40 * 21 = 840
840   Runs made in the 11th inning= 840-720= 
840-720 = 120
120   ANSW120R:120
Answer: E
Find the length of a rectangle isdecreased by 40cm & the width is increased by 3cm, a square with the samearea as the original rectangle result. Find the perimeter of the original rectangle?  Select the correct option:
A) 30 cm	B) 40 cm	C) 50 cm	D) 64 cm	E) 70 cm

Solution: Let x and y be the length and breadth of the rectangle respectively.   Then, x - 4 = y + 3 or x - y = 7 ----(1)   Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)   (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(2)   Solving 1 & 2 , we get x = 16 and y = 9.   Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.   50 cm
Answer: C
If the LCM of two integers M, N (where N> M and M>1) is M*N, then which of the following can not be true?  Pick one.
A) Both M and N can be Prime Numbers.
B) Both M and N can be consecutive integers.
C) M and N do not share any Prime factors.
D) All Prime factors of M must be Prime factors of N.
E) M and N do not have a common factor.

Solution: If LCM of two numbers M and N is the product MN then both numbers are Co- prime.   (Co-prime numbers are any two numbers which have an HCF of 1 i.e. when two numbers have no common prime factor apart from the number 1).   Numbers that can be Co-Prime are :   1) Two consecutive natural numbers.   2) Two consecutive odd numbers.   3) Two prime numbers.   4) One prime number and the other a composite number such that the composite number is not a multiple of the prime number.   With above four statements it can be concluded that Options A, B, C and E are all true.   Only Option D cannot be true.   Hence answer is All Prime factors of M must be Prime factors of N..
Answer: D