Last visit was: 06 Nov 2024, 08:30 It is currently 06 Nov 2024, 08:30
Close
GMAT Club Daily Prep
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.
Close
Request Expert Reply
Confirm Cancel
555-605 Level|   Geometry|                        
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
 [102]
10
Kudos
Add Kudos
91
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
 [53]
29
Kudos
Add Kudos
24
Bookmarks
Bookmark this Post
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 06 Nov 2024
Posts: 2,010
Own Kudos:
2,248
 [13]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,010
Kudos: 2,248
 [13]
7
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
avatar
ctiger100
Joined: 20 Feb 2012
Last visit: 26 Sep 2013
Posts: 4
Given Kudos: 1
Posts: 4
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If instead, Q were a square, would 1 be sufficient?

In a rectangle, why can't we use the Isosceles Triangle to figure out the third side since the diagonals bisect each other?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
674,522
 [1]
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ctiger100
If instead, Q were a square, would 1 be sufficient?

In a rectangle, why can't we use the Isosceles Triangle to figure out the third side since the diagonals bisect each other?

If we were told that Q is a square instead of a rectangle, then the answer would be D.

As for the second question: can you please explain what you mean? Generally you cannot find the sides of a rectangle just knowing the length of its diagonal, since knowing the length of hypotenuse (diagonal) in a right triangle (created by length and width), is not enough to find the legs of it (length and width).

Hope it's clear.
avatar
kelleygrad05
Joined: 06 Dec 2012
Last visit: 10 Apr 2020
Posts: 3
Own Kudos:
9
 [1]
Given Kudos: 5
Posts: 3
Kudos: 9
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))
User avatar
WoundedTiger
Joined: 25 Apr 2012
Last visit: 25 Sep 2024
Posts: 524
Own Kudos:
2,377
 [10]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
Posts: 524
Kudos: 2,377
 [10]
8
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
kelleygrad05
I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))


Hi Kellygrad05,

There was a similar problem I was attempting yesterday on the forum.

Basically we are told that it is a rectangle but we aren't sure if the sides are Integers or not. For ex.

Diagonal-10, sides can be 6 and 8 (because of PT) or something like Square root 99 and 1...and such other combination

When you consider the st2 with above then we can figure out sides will be 6 and 8 as only in that condition Area will be 48 and Diagonal as 10.

Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
 [10]
10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kelleygrad05
I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))

A right triangle with hypotenuse 10, doesn't mean that we have (6, 8, 10) 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 10 would be (6, 8, 10).

To check this: consider the right triangle with hypotenuse 10 inscribed in circle. We know that a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

So ANY point on circumference of a circle with diameter of 10 would make the right triangle with diameter. Not necessarily sides to be 6 and 8. For example we can have isosceles right triangle, which would be 45-45-90: and the sides would be \(\frac{10}{\sqrt{2}}\). OR if we have 30-60-90 triangle and hypotenuse is \(10\), sides would be \(5\) and \(5*\sqrt{3}\). Of course there could be many other combinations.

Similar questions to practice:
if-the-diagonal-of-rectangle-z-is-d-and-the-perimeter-of-104205.html
what-is-the-area-of-rectangular-region-r-105414.html
what-is-the-perimeter-of-rectangle-r-96381.html

Hope it helps.
avatar
hyder27
Joined: 18 Jul 2015
Last visit: 31 Aug 2015
Posts: 15
Own Kudos:
2
 [2]
Given Kudos: 36
Posts: 15
Kudos: 2
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did not use the math way this is how I did it

it is given that 2L +2w= the perimeter of a rectangle
1. each diagnal of a rectangle is length of 10 which makes the rectangle in half so it cant, but just know the triangle height
= not sufficient
2. the area of a rectangle is 48 so l*w= area not sufficent

both will tell us 2 equations and can find the length an width to get p so it is C
thanks
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,813
Own Kudos:
11,970
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,813
Kudos: 11,970
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
The question asks us to figure out the PERIMETER of rectangle Q. For that, we'll need the length (L) and width (W) of the rectangle.

1) Each diagonal of rectangle Q has length 10.

From this Fact, we can create one equation:

L^2 + W^2 = 10^2

Unfortunately, there are lots of different values for L and W here (and most of them are non-integers), so there are lots of possible perimeters. Here are two possibilities:
L = 6, W = 8... Perimeter = 28
L = 1, W = (Root99)... Perimeters = 2 + 2(Root99)
Fact 1 is INSUFFICIENT

2) The area of rectangle Q is 48.

From this Fact, we can create one equation:

(L)(W) = 48

Again though, there are lots of different values for L and W here, so there are lots of possible perimeters. Here are two possibilities:
L = 6, W = 8... Perimeter = 28
L = 1, W = 48... Perimeter = 98
Fact 2 is INSUFFICIENT

Combined, we know...
L^2 + W^2 = 10^2
(L)(W) = 48

We have a 'system' of equations here - two variables and two unique equations. Since rectangles cannot have "negative sides", there's just one solution to this system (and it happens to be 6 and 8, although you don't have to do that work).
Combined, SUFFICIENT

Final Answer:
It's certainly important to have strong basic 'math skills', but the Quant section of the GMAT is NOT a 'math test' - it's a critical thinking Test - so you should adjust your 'view' of that section accordingly.

GMAT assassins aren't born, they're made,
Rich
User avatar
AnthonyRitz
User avatar
Stacy Blackman Consulting Director of Test Prep
Joined: 21 Dec 2014
Last visit: 05 Nov 2024
Posts: 237
Own Kudos:
403
 [1]
Given Kudos: 166
Affiliations: Stacy Blackman Consulting
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
GPA: 3.11
WE:Education (Education)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
Posts: 237
Kudos: 403
 [1]
Kudos
Add Kudos
Bookmarks
Bookmark this Post
That's exactly right. There are infinitely many right triangles with hypotenuse 10. For instance, sqrt(13), sqrt(87), 10.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
mohamk
Joined: 24 Sep 2017
Last visit: 31 Dec 2017
Posts: 1
Own Kudos:
1
 [1]
Posts: 1
Kudos: 1
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
i chose answer A since this is a rectangle and the diagonal will bisect the right angles, forming 45-45-90 triangle with sides ratios of 1:1:root 2.
using Pythagorean theory , we can get the value of both sides

what did i do wrong here ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Nov 2024
Posts: 96,607
Own Kudos:
674,522
 [1]
Given Kudos: 87,944
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,607
Kudos: 674,522
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
mohamk
i chose answer A since this is a rectangle and the diagonal will bisect the right angles, forming 45-45-90 triangle with sides ratios of 1:1:root 2.
using Pythagorean theory , we can get the value of both sides

what did i do wrong here ?

The diagonals of a rectangle bisect the angle if and only the rectangle is a square. Generally, a diagonal of a rectangle can form any angle with the adjacent sides from 0 to 90, not inclusive.
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,699
Own Kudos:
Given Kudos: 165
Expert reply
Posts: 3,699
Kudos: 18,099
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution:



Given:

    • The perimeter of the rectangle Q = p


Working out:

We need to find out the value of p

Statement 1:

Each diagonal of the rectangle Q has length 10

Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.

From this statement, we can infer that \(\sqrt{l^2 + b^2}\) = 10

    • Squaring both the sides of the equation, we get \(l^2 + b^2 = 100\)

      o There can be more than one possible combination of l and b.

      o And hence, the sum of l and b is not unique.

Thus, Statement 1 alone is not sufficient to answer this question.

Statement 2:

Area of the rectangle Q is 48 units.

Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.

Thus, \(l*b = 48\)

There can be more than one combination of l and b: (6,8), (12, 4), etc. and the values of p will not be unique.

Thus, statement 2 alone is not sufficient to answer this question.

Combining both the statement:

From statement 1, we have \(l^2 + b^2 = 100\)

From statement 2, we have \(l*b = 48\)

    • \((l+b)^2 = l^2 + b^2 + 2l*b\)

    • Or, \((l+b)^2 = 100 + 96\)

    • Or, \((l+b)^2 = 196\)

    • Or, \((l+b) = 14\) units.

From here, we can calculate the value of p.

Thus, combining both the statements, we got our answer.

Answer: Option C
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 03 Oct 2024
Posts: 1,299
Own Kudos:
1,817
 [1]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Posts: 1,299
Kudos: 1,817
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,378
Own Kudos:
Posts: 35,378
Kudos: 904
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Math Expert
96605 posts