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Gurpreet singh Senior | Next Rank: 100 Posts
Joined
28 Apr 2016
Posted:
38 messages
1
Thu Jun 09, 2016 6:10 pm
Hi Brent,

In case the question stem had asked for the length instead of dimension will the statement 1 still be sufficient? since we are getting 2 values.
Thanks
Gurpreet

Brent@GMATPrepNow wrote:
sparkles3144 wrote:
A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle?

(1) The area of the rectangle is 40 inches squared.

(2) The length is 6 inches more than the width

I know how to solve this.
However, I am wondering if I can assume that l and w are integers.
It is not stated.

Thanks!
No, we cannot assume that the lengths are integers.
Here's one solution:

Target question: What are the dimensions of the rectangle?

Given: A rectangle has a perimeter of 28 inches.
Let L = length of rectangle
Let W = width of rectangle

If the perimeter is 28, then 2L + 2W = 28
We can simplify this by dividing both sides by 2 to get: L + W = 14

Statement 1: The area of the rectangle is 40 inches squared.
In other words, LW = 40

Since we already know that L + W = 14, we can solve for W to get W = 14 - L
Now take the equation LW = 40, and replace W with (14 - L) to get . . .
L(14 - L) = 40
Expand: 14L - L^2 = 40
Rearrange to get: L^2 - 14L + 40 = 0
Factor: (L - 4)(L - 10) = 0
So, L = 4 or 10

If L = 4, then W = 10, which means the dimensions are 4 by 10
If L = 10, then W = 4, which means the dimensions are still 4 by 10
In other words, the the dimensions must be 4 by 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length is 6 inches more than the width
In other words, L = W + 6

Since we already know that L + W = 14, we can solve for W to get W = 14 - L
Now take the equation L = W + 6, and replace W with (14 - L) to get . . .
L = (14 - L) + 6
Rearrange: 2L = 20
Solve: L = 10
If L = 10, then W = 4, which means the dimensions are 4 by 10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

Rohit_Prakash88@yahoo.in Newbie | Next Rank: 10 Posts
Joined
29 Mar 2016
Posted:
9 messages
Fri Apr 01, 2016 10:24 am
Thanks a lot . A key point I missed out and was scratching my head .. Thanks a lot for your guidance again

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
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Posted:
11192 messages
Followed by:
1221 members
5254
GMAT Score:
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Fri Apr 01, 2016 10:21 am
Rohit_Prakash88@yahoo.in wrote:
Hello Together,

Please clarify as I believe answer should be option B not D because When solve statement 1 we get 2 values of W and L i.e when l = 10 then W = 4 and when W = 4 then l =10 since this statement does lock L and W to have one particular value I believe it is insufficient and Option B should be the right choice.

Yes, we do get two different values for W (W = 4 or W = 10).
However, the target question does not ask us to determine the value of W. The target question asks us to determine the dimensions of the rectangle.
A rectangle with dimensions 4 x 10 is identical to a rectangle with dimensions 10 x 4

Cheers,
Brent

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Rohit_Prakash88@yahoo.in Newbie | Next Rank: 10 Posts
Joined
29 Mar 2016
Posted:
9 messages
Fri Apr 01, 2016 10:13 am
Hello Together,

Please clarify as I believe answer should be option B not D because When solve statement 1 we get 2 values of W and L i.e when l = 10 then W = 4 and when W = 4 then l =10 since this statement does lock L and W to have one particular value I believe it is insufficient and Option B should be the right choice.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11192 messages
Followed by:
1221 members
5254
GMAT Score:
770
Fri May 10, 2013 2:20 pm
sparkles3144 wrote:
A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle?

(1) The area of the rectangle is 40 inches squared.

(2) The length is 6 inches more than the width

I know how to solve this.
However, I am wondering if I can assume that l and w are integers.
It is not stated.

Thanks!
No, we cannot assume that the lengths are integers.
Here's one solution:

Target question: What are the dimensions of the rectangle?

Given: A rectangle has a perimeter of 28 inches.
Let L = length of rectangle
Let W = width of rectangle

If the perimeter is 28, then 2L + 2W = 28
We can simplify this by dividing both sides by 2 to get: L + W = 14

Statement 1: The area of the rectangle is 40 inches squared.
In other words, LW = 40

Since we already know that L + W = 14, we can solve for W to get W = 14 - L
Now take the equation LW = 40, and replace W with (14 - L) to get . . .
L(14 - L) = 40
Expand: 14L - L^2 = 40
Rearrange to get: L^2 - 14L + 40 = 0
Factor: (L - 4)(L - 10) = 0
So, L = 4 or 10

If L = 4, then W = 10, which means the dimensions are 4 by 10
If L = 10, then W = 4, which means the dimensions are still 4 by 10
In other words, the the dimensions must be 4 by 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length is 6 inches more than the width
In other words, L = W + 6

Since we already know that L + W = 14, we can solve for W to get W = 14 - L
Now take the equation L = W + 6, and replace W with (14 - L) to get . . .
L = (14 - L) + 6
Rearrange: 2L = 20
Solve: L = 10
If L = 10, then W = 4, which means the dimensions are 4 by 10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

Thanked by: sparkles3144, freyesinsb
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

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