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# The area of a rectangle is 28 square centimeter. What is the perimeter

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Manager
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The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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01 Jun 2017, 12:34
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The area of a rectangle is 28 square centimeter. What is the perimeter of the rectangle?

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.

(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.
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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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02 Jun 2017, 09:01
niteshwaghray wrote:
The area of a rectangle is 28 square centimeter. What is the perimeter of the rectangle?

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.

(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.

Dear niteshwaghray,

I'm happy to respond.

What is the source? When you post any GMAT practice problem, please please please cite the source. I believe the OA you have listed here is not the correct answer.

Let x be the length and y be the breadth. From the prompt, we know xy = 28, which doesn't really get used in the solution. We want the perimeter.
perimeter = 2x + 2y
That's the "original perimeter."

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.
new length = x + 10
new breadth = x - 5
new perimeter = 2(x + 10) + 2(y - 5)

2(x + 10) + 2(y - 5) = 8(2(x + y))

At this point in a DS question, it's enough to notice that x and y always will have equal coefficients. This means, we can solve for (x + y), and that means we can find the value of 2(x + y). It's not necessary, but I will continue the solution.

x + 10 + y - 5 = 8x + 8y

5 = 7x = 7y

5/7 = x + y

10/7 = 2(x + y)

We got a numerical answer. Statement #1, alone and by itself, is sufficient.

(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.

new length = 3.5x
new perimeter = 7x + 7y

7x + 7y = 2x + 2y + 63

Again, we see we will have equal coefficients for x & y. We see that we will be able to solve for (x + y). In DS terms, we would be done already. I am going to continue the solution.

5x + 5y = 63

x + y = 63/5

2x + 2y = 126/5

Again, we got a numerical answer. Statement #2, alone and by itself, is sufficient.

The answer of the question as you have it posted is (D). If the two percents in statement #2 were not identical in the source, then the answer would be (A), what the source seems to indicate.

If there are no typos, then this is a really really bad question. We get two different numerical answers from the two statements, so they are not mathematically consistent. That's a major gaffe in writing GMAT math questions. If what you have here is identical to how it is printed in the book, then burn that book. It's very veyr hard to write high quality GMAT Verbal questions, but it's easy to write reasonably good Quant questions: if this source can't even do that much, they are worthless.

Does all this make sense?
Mike
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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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02 Jun 2017, 11:07
mikemcgarry wrote:
niteshwaghray wrote:
The area of a rectangle is 28 square centimeter. What is the perimeter of the rectangle?

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.

(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.

Dear niteshwaghray,

I'm happy to respond.

What is the source? When you post any GMAT practice problem, please please please cite the source. I believe the OA you have listed here is not the correct answer.

Let x be the length and y be the breadth. From the prompt, we know xy = 28, which doesn't really get used in the solution. We want the perimeter.
perimeter = 2x + 2y
That's the "original perimeter."

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.
new length = x + 10
new breadth = x - 5
new perimeter = 2(x + 10) + 2(y - 5)

2(x + 10) + 2(y - 5) = 8(2(x + y))

At this point in a DS question, it's enough to notice that x and y always will have equal coefficients. This means, we can solve for (x + y), and that means we can find the value of 2(x + y). It's not necessary, but I will continue the solution.

x + 10 + y - 5 = 8x + 8y

5 = 7x = 7y

5/7 = x + y

10/7 = 2(x + y)

We got a numerical answer. Statement #1, alone and by itself, is sufficient.

(2) If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle.

new length = 3.5x
new perimeter = 7x + 7y

7x + 7y = 2x + 2y + 63

Again, we see we will have equal coefficients for x & y. We see that we will be able to solve for (x + y). In DS terms, we would be done already. I am going to continue the solution.

5x + 5y = 63

x + y = 63/5

2x + 2y = 126/5

Again, we got a numerical answer. Statement #2, alone and by itself, is sufficient.

The answer of the question as you have it posted is (D). If the two percents in statement #2 were not identical in the source, then the answer would be (A), what the source seems to indicate.

If there are no typos, then this is a really really bad question. We get two different numerical answers from the two statements, so they are not mathematically consistent. That's a major gaffe in writing GMAT math questions. If what you have here is identical to how it is printed in the book, then burn that book. It's very veyr hard to write high quality GMAT Verbal questions, but it's easy to write reasonably good Quant questions: if this source can't even do that much, they are worthless.

Does all this make sense?
Mike

Hi Mike,

Thanks for the solution.

Sorry about missing the source tag. This question is from e-gmat. I tried adding the tag now, but unfortunately i don't seem to be able to find how. (could you please help with that?)

By the way, as per the solution that e-gmat had given, the 2nd statement has to be interpreted as L=4.5x and B=3.5y (increased by vs. increased to i suppose).

I'm adding the solution below so that it can be reviewed.

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Let the length and breadth of rectangle be L and B respectively
•LB = 28…..............................................(1)

To find: The value of 2(L+B)
•To find perimeter, we need to know the value of L and B.

Step 3: Analyze Statement 1 independently

(1) If the length of the rectangle is increased by 10 centimeter and the breadth is decreased by 5 centimeter, the perimeter of the rectangle is eight times the original length of the rectangle.
•New L = L +10
•New B = B - 5

So,
•New Perimeter = 2(L+10 + B-5)
•2(L+10 + B-5) = 8L
•2L + 2B + 10 = 8L
•6L – 2B – 10 = 0
•3L – B – 5 = 0
•B = 3L - 5 . . . . . . . . . . . . . . .. . . . .(2)

Substituting (2) in (1):
•L(3L – 5) = 28
•$$3L^2$$ – 5L – 28 = 0

$$L^2$$−$$\frac{5}{3}$$L−$$\frac{28}{3}$$=0

◦2 values of L (roots) will be obtained from this quadratic equation

Comparing this with the standard quadratic form : ax2 + bx + c = 0, we get :

a = 1 ; b = -5/3 ; c = -28/3
◦Product of these 2 values = (c/a) −28/3

◦Since the product is negative, one root is positive and the other is negative

◦The negative root will be rejected ◦L, being the length of a rectangle, cannot be negative

◦Thus, a unique value of L is obtained ◦Using Equation (2), a unique value of B is also obtained

Hence, Statement 1 alone is sufficient.

Step 4: Analyze Statement 2 independently
•If the length of the rectangle is increased by 350% and the breadth is increased to 350% of the original breadth, the perimeter of the rectangle is 63 centimeters more than the original perimeter of the rectangle
•New L = 4.5L
•New B = 3.5B

So,
•New Perimeter = 2(4.5L + 3.5B)
•2(4.5L + 3.5B) = 63 + 2(L+B)
•9L + 7B = 63 + 2L + 2B
•7L + 5B = 63
•B=$$\frac{(63−7L)}{5}$$. . .. . . . . . . . . .. . . . .. . . . . . . (3)

Substituting (3) in (1):

L($$\frac{63−7L}{5}$$)=28
L($$\frac{9−L}{5}$$)=4

9L – $$L^2$$ = 20

$$L^2$$ - 9L + 20 = 0
◦2 values of L (roots) will be obtained from this quadratic equation

Comparing this with the standard quadratic form : ax2 + bx + c = 0, we get :

a = 1 ; b = - 9 ; c = 20
◦Product of these 2 values = (c/a) = 20 ◦Since the product is positive, the two roots are either both positive or both negative

◦Sum of roots = (-b/a) = -(-9) = 9 ◦Since the sum is positive, it means both roots are positive

◦Thus, St. 2 leads to 2 values of L ◦From Equation (3), 2 values of B will be obtained
◦So, 2 values of Perimeter will be obtained.

St. 2 is not sufficient to obtain a unique value of the perimeter.

Step 5: Analyze Both Statements Together (if needed)

Since we get a unique answer in Step 3, this step is not required

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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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02 Jun 2017, 11:50
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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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03 Jun 2017, 08:40
Can anyone explain difference between increase by and increase to ?

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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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03 Jun 2017, 10:12
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imyuva wrote:
Can anyone explain difference between increase by and increase to ?

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Hi. Let me try.

Lets say we start with a number 100. Now if we are going to increase this number by 120%, the result will be:
100 + 120% of 100 = 100+120 = 220

But if we are going to increase this number to 120.. then the result simply will be 120 (earlier the number was 100, now we have increased it to 120).

If I am going to increase x by 250% of its original value, I will do: x + 250% of x = x + 2.5x = 3.5x

BUT - If I am going to increase x to 250% of its original value, then I will simply do: 250% of x = 2.5x

Please notice the difference in both cases; in both the examples.
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Re: The area of a rectangle is 28 square centimeter. What is the perimeter  [#permalink]

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13 Jan 2019, 20:50
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Re: The area of a rectangle is 28 square centimeter. What is the perimeter &nbs [#permalink] 13 Jan 2019, 20:50
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