BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OFFICIAL GMAT REVIEW 11th Edition Question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Thu Mar 27, 2008 4:42 pm
Location: Houston
Thanked: 10 times

OFFICIAL GMAT REVIEW 11th Edition Question

by Sakina » Thu Mar 27, 2008 9:22 pm
On page 64, number 48:

The data sufficiency question explanation states that answer C is the answer.

But why isn't answer A the answer? The diagonal is 10, and it divides the rectangle into 2 right triangles. So doesn't this become a 3-4-5 triangle? In this case, the measurements are 6-8-10. The solution even states this. So why isn't A the correct answer?
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 423
Joined: Thu Dec 27, 2007 1:29 am
Location: Hyderabad, India
Thanked: 36 times
Followed by:2 members
GMAT Score:770

by simplyjat » Thu Mar 27, 2008 9:37 pm
Kindly show courtesy to type the full question.
As per the question is concerned, you are taking one of the infinite number of possibilities. For any given line, there are infinite right triangles that can be formed, all of which will have the given line as hypotenuse...
simplyjat
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Fri Mar 28, 2008 9:08 am
simplyjat wrote:Kindly show courtesy to type the full question.
As per the question is concerned, you are taking one of the infinite number of possibilities. For any given line, there are infinite right triangles that can be formed, all of which will have the given line as hypotenuse...
Simplyjat is correct. If all you know is the hypotenuse, there's no way to determine the legs of the triangle.

With a hypotenuse of 10, we know that:

a^2 + b^2 = 10^2

or

a^2 + b^2 = 100

There's no way to solve for a and b with this equation.

For example, we could pick a=6, b=8 as you suggest.

We could also pick a=root50 and b=root50 (this would give us a 45/45/90 triangle with a hypotenuse of 10).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Thu Mar 27, 2008 4:42 pm
Location: Houston
Thanked: 10 times

by Sakina » Fri Mar 28, 2008 11:20 am
Ok here is the question:

If p is the perimeter of rectangle O, what is the value of p?
(1) Each daigonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.


So, it is given that it is a rectangle, therefore it cannot be a 45-45-90. And it definitely WILL be a right triangle. This being the case, the only values that work for this hypotenuse, since it is a right triangle, will be 6 and 8 for the sides. This is 6-8-10 is consistent with a 3-4-5 triangle. True, we don't know WHICH leg is the 6 and which is the 8 but that doesn't matter, since all we need is the perimeter.

So I am having trouble understanding why the answer isn't just A. What other values could work for the legs that would still yield a hypotenuse of 10?
Top
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Feb 19, 2008 10:04 am
Thanked: 2 times

by mba.dude » Sat Mar 29, 2008 8:33 am
Just to add to the above explanations :
A square is a rectangle, for which length and width are equal.
All the Best!
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Sat Mar 29, 2008 7:53 pm
Sakina wrote:Ok here is the question:

If p is the perimeter of rectangle O, what is the value of p?
(1) Each daigonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.


So, it is given that it is a rectangle, therefore it cannot be a 45-45-90. And it definitely WILL be a right triangle. This being the case, the only values that work for this hypotenuse, since it is a right triangle, will be 6 and 8 for the sides. This is 6-8-10 is consistent with a 3-4-5 triangle. True, we don't know WHICH leg is the 6 and which is the 8 but that doesn't matter, since all we need is the perimeter.

So I am having trouble understanding why the answer isn't just A. What other values could work for the legs that would still yield a hypotenuse of 10?
I still don't understand why it has to be 6-8-10.

First, as mba.dude pointed out, a square IS a rectangle, it's just a special one.

Second, even if we weren't allowed to pick a square, there are infinite other possibilities.

All we have to work with is the equation:

a^2 + b^2 = 10^2

or

a^2 + b^2 = 100

So, we could pick:

(root99)^2 + (root1)^2

or

(root98)^2 + (root2)^2

and so on, and so on, and so on.

Just because

(root36)^2 + (root64)^2 happen to work out to integers doesn't mean that they're the only possible values.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Post new topic Post Reply
• Page 1 of 1