Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Figure ABCD is a rectangle with sides of length x centimete [#permalink]

Show Tags

15 Jul 2007, 19:45

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

69% (02:08) correct
31% (01:25) wrong based on 365 sessions

HideShow timer Statistics

Attachment:

Untitled.png [ 7.04 KiB | Viewed 3504 times ]

Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD ?

Re: Figure ABCD is a rectangle with sides of length x [#permalink]

Show Tags

03 Feb 2014, 04:12

dynocomet wrote:

Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD? (The diagram shows line segment AD labeled as "x" and line segment DC labeled as "y")

(1) x - y = 7 (2) z = 13

I read that the answer is C, but cannot understand why. First of all, statement 1 seems like a contradiction -- how can the hypotenuse be SMALLER than either of the two sides?

Thanks.

The answer to the questions shows C. However why can we not state that from statement (2) we are dealing with a 5,12,13 triangle? Hence B would be sufficient to answer the question.

Re: Figure ABCD is a rectangle with sides of length x [#permalink]

Show Tags

03 Feb 2014, 05:37

1

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

Mattd wrote:

dynocomet wrote:

Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD? (The diagram shows line segment AD labeled as "x" and line segment DC labeled as "y")

(1) x - y = 7 (2) z = 13

I read that the answer is C, but cannot understand why. First of all, statement 1 seems like a contradiction -- how can the hypotenuse be SMALLER than either of the two sides?

Thanks.

The answer to the questions shows C. However why can we not state that from statement (2) we are dealing with a 5,12,13 triangle? Hence B would be sufficient to answer the question.

The point is that a right triangle with hypotenuse 13, doesn't mean that we have (5, 12, 13) right triangle. If we are told that the lengths of all sides are integers, then yes: the only integer solution for right triangle with hypotenuse 13 would be (5, 12, 13). Or in other words: \(x^2+y^2=13^2\) DOES NOT mean that \(x=5\) and \(y=12\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=13^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=5\) and \(y=12\).

For example: \(x=1\) and \(y=\sqrt{168}\) or \(x=2\) and \(y=\sqrt{165}\)...

So knowing that the diagonal of a rectangle (hypotenuse) equals to one of the Pythagorean triple hypotenuse values is not sufficient to calculate the sides of this rectangle.

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]

Show Tags

15 Jul 2014, 02:13

How can we use the both statement to find the answer? I marked B and Bunuel explained how it is wrong. My second answer would be E I mean I know 12-5 = 7 and that with z =13 so we can say that three sides "can" be 5,12,13 but can we say that's the only possible value?

Figure ABCD is a rectangle with sides of length x centimete [#permalink]

Show Tags

15 Jul 2014, 02:35

Expert's post

2

This post was BOOKMARKED

b2bt wrote:

How can we use the both statement to find the answer? I marked B and Bunuel explained how it is wrong. My second answer would be E I mean I know 12-5 = 7 and that with z =13 so we can say that three sides "can" be 5,12,13 but can we say that's the only possible value?

Given that \(x - y = 7\) and \(z = 13\). We also know that \(x^2 + y^2 = z^2 = 169\). We want to find the perimeter which is \(2x+2y = 2(x+y)\).

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]

Show Tags

24 Sep 2015, 04:24

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]

Show Tags

24 Dec 2015, 15:00

I knew there's a trick with B. since we are not told that x and y are integers, B alone is not sufficient. we have statement 1: x-y=7 thus x^2+y^2 -2xy=49. so not sufficient.

statement 2 alone: z=13, well, z^2 = x^2 + y^2. we have 169=x^2 + y^2. not sufficient.

we need to find the perimeter, or 2(x+y).

we are told that x^2+y^2-2xy = 49 now we have 169=x^2 + y^2. combine both: 169-2xy=49 120=2xy 60=xy.

now: xy=60 x^2+y^2=169.

combine both: x^2+y^2 + 2xy = 169+120 (x+y)^2 = 289. now, this is sufficient, as we can find x+y, and thus find 2(x+y)

gmatclubot

Re: Figure ABCD is a rectangle with sides of length x centimete
[#permalink]
24 Dec 2015, 15:00

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...