If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35. What is the perimeter of rectangle R?
24
37
48
50
51
Rectanlge
This topic has expert replies
-
- Legendary Member
- Posts: 882
- Joined: Fri Feb 20, 2009 2:57 pm
- Thanked: 15 times
- Followed by:1 members
- GMAT Score:690
-
- Master | Next Rank: 500 Posts
- Posts: 392
- Joined: Thu Jan 15, 2009 12:52 pm
- Location: New Jersey
- Thanked: 76 times
(L+1)(W+1)=72-->LW+L+W+1=72 (A)
(L-1)(W-1)=35-->LW-L-W+1=35 (B)
Subtract equation B from A.
LW+L+W+1-LW+L+W-1=72-35
2L+2W=37
37 is our answer since the perimeter of rectangle R is equal to 2L+2W.
(L-1)(W-1)=35-->LW-L-W+1=35 (B)
Subtract equation B from A.
LW+L+W+1-LW+L+W-1=72-35
2L+2W=37
37 is our answer since the perimeter of rectangle R is equal to 2L+2W.
-
- Legendary Member
- Posts: 882
- Joined: Fri Feb 20, 2009 2:57 pm
- Thanked: 15 times
- Followed by:1 members
- GMAT Score:690
-
- Master | Next Rank: 500 Posts
- Posts: 124
- Joined: Thu Jun 18, 2009 5:33 am
- Thanked: 35 times
Hey Crackgmat!
I think that the most efficient way to solve this problem is the way Truplayer did. Because we don't have to find both sides' lengths, we just get the answer after the first step of 2 equations solution.
But i can be wrong, because i am the enemy of "picking numbers" strategy in Maths =)
I think that the most efficient way to solve this problem is the way Truplayer did. Because we don't have to find both sides' lengths, we just get the answer after the first step of 2 equations solution.
But i can be wrong, because i am the enemy of "picking numbers" strategy in Maths =)
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let L = the length of rectangle Rcrackgmat007 wrote: ↑Sun Oct 11, 2009 12:40 pmIf the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72. If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35. What is the perimeter of rectangle R?
24
37
48
50
51
Let W = the width of rectangle R
If the length and width of rectangle R are each increased by 1, the area of the new rectangle will be 72.
We can write: (L + 1)(W + 1) = 72
Expand to get: LW + L + W + 1 = 72
If the length and width of rectangle R are each decreased by 1, the area of the new rectangle will be 35.
We can write: (L - 1)(W - 1) = 35
Expand to get: LW - L - W + 1 = 35
What is the perimeter of rectangle R?
The perimeter = L + W + L + W = 2L + 2W
So far we have:
LW + L + W + 1 = 72
LW - L - W + 1 = 35
When we subtract the bottom equation from the top equation we get: 2L + 2W = 37
Since the perimeter = 2L + 2W, we can see that the correct answer is B