What is the perimeter of rectangle ABCD?
(1) The longer side of the rectangle is 2 meters shorter than its diagonal
$$(2)The\ ratio\ of\ the\ shorter\ side\ of\ the\ rec\tan gle\ to\ its\ diagonal\ is\ \frac{1}{3}\ $$
Which of the statement is sufficient?
OA C
What is the perimeter of rectangle ABCD
This topic has expert replies

 Moderator
 Posts: 5054
 Joined: 07 Sep 2017
 Followed by:16 members
GMAT/MBA Expert
 Rich.C@EMPOWERgmat.com
 Elite Legendary Member
 Posts: 10347
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:506 members
 GMAT Score:800
Hi lheiannie07,
We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math.
1) The longer side of the rectangle is 2 meters shorter than its diagonal
With the information in Fact 1, we can create 2 equations (with the diagonal represented by D):
L = D  2
L^2 + W^2 = D^2
Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 1 is INSUFFICIENT
2) The ratio of the shorter side to the diagonal is 1/3
With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1):
W/D = 1/3....... D = 3W
L^2 + W^2 = D2
Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 2 is INSUFFICIENT
Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables  and there will be just one solution.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math.
1) The longer side of the rectangle is 2 meters shorter than its diagonal
With the information in Fact 1, we can create 2 equations (with the diagonal represented by D):
L = D  2
L^2 + W^2 = D^2
Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 1 is INSUFFICIENT
2) The ratio of the shorter side to the diagonal is 1/3
With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1):
W/D = 1/3....... D = 3W
L^2 + W^2 = D2
Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 2 is INSUFFICIENT
Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables  and there will be just one solution.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich

 Moderator
 Posts: 5054
 Joined: 07 Sep 2017
 Followed by:16 members
Thanks a lot!Rich.C@EMPOWERgmat.com wrote:Hi lheiannie07,
We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math.
1) The longer side of the rectangle is 2 meters shorter than its diagonal
With the information in Fact 1, we can create 2 equations (with the diagonal represented by D):
L = D  2
L^2 + W^2 = D^2
Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 1 is INSUFFICIENT
2) The ratio of the shorter side to the diagonal is 1/3
With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1):
W/D = 1/3....... D = 3W
L^2 + W^2 = D2
Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 2 is INSUFFICIENT
Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables  and there will be just one solution.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich

 Moderator
 Posts: 5054
 Joined: 07 Sep 2017
 Followed by:16 members
Thanks a lot!Rich.C@EMPOWERgmat.com wrote:Hi lheiannie07,
We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math.
1) The longer side of the rectangle is 2 meters shorter than its diagonal
With the information in Fact 1, we can create 2 equations (with the diagonal represented by D):
L = D  2
L^2 + W^2 = D^2
Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 1 is INSUFFICIENT
2) The ratio of the shorter side to the diagonal is 1/3
With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1):
W/D = 1/3....... D = 3W
L^2 + W^2 = D2
Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 2 is INSUFFICIENT
Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables  and there will be just one solution.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
 Scott@TargetTestPrep
 GMAT Instructor
 Posts: 5549
 Joined: 25 Apr 2015
 Location: Los Angeles, CA
 Thanked: 43 times
 Followed by:24 members
We need to determine the perimeter of rectangle ABCD.lheiannie07 wrote:What is the perimeter of rectangle ABCD?
(1) The longer side of the rectangle is 2 meters shorter than its diagonal
$$(2)The\ ratio\ of\ the\ shorter\ side\ of\ the\ rec\tan gle\ to\ its\ diagonal\ is\ \frac{1}{3}\ $$
Statement One Alone:
The longer side of the rectangle is 2 meters shorter than its diagonal.
We can let the length of the longer side = L and the length of the diagonal = G. Thus we have L = G  2. However, since we don't know the value of L or G, we can't determine the perimeter of ABCD. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The ratio of the shorter side of the rectangle to its diagonal is 1/3.
We can let the length of the shorter side = W and the length of the diagonal = G. Thus we have W = G/3. However, since we don't know the value of W or G, we can't determine the perimeter of ABCD. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using the two statements, we see that L = G  2 and W = G/3. Notice that the perimeter of ABCD is 2L + 2W. Furthermore, L, W and G form a right triangle with G as the hypotenuse. Thus, we have:
L^2 + W^2 = G^2
Now, substituting G  2 for L and G/3 for W, we have:
(G  2)^2 + (G/3)^2 = G^2
From the above equation, we can solve for G. Once we solve for G, we can determine the values of L and W and, hence, we can determine the perimeter of ABCD.
Answer: C
Scott WoodburyStewart
Founder and CEO
scott@targettestprep.com
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews