Data Sufficiency

If p is the perimeter of rectangle q, what is the value of p?

1.) each diagonal of rectangle q has a length of 10.
2.) the area of a rectangle is 48.

Og states answer is c. My contention is that the answer is a. With a rectangle (right angle) and a hypotenuse of 10, the triangle must be a 6-8-10 triangle. I understand why b is wrong. Can someone smarter than I am please explain how a cannot be the answer? Thanks.

wdc1983 wrote:If p is the perimeter of rectangle q, what is the value of p?

1.) each diagonal of rectangle q has a length of 10.
2.) the area of a rectangle is 48.

Og states answer is c. My contention is that the answer is a. With a rectangle (right angle) and a hypotenuse of 10, the triangle must be a 6-8-10 triangle. I understand why b is wrong. Can someone smarter than I am please explain how a cannot be the answer? Thanks.

Why only 6-8-10, why not sqrt(10)-sqrt(10)-10?

Although my example forms a Square, Square is still a sort of rectangle is not it?:)

It is the option 2 which makes sure its 6-8-10.

Hope this helps

Let a and b be the sides of the rectangle

1) sqrt(a^2 + b^2) = 10

2 unknowns, 1 equation, not enough

2) ab = 48

2 unkowns, 1 equations, not enough

combining 1 and 2, 2 equations and 2 unknowns, sufficient.

Great explanation, Shovan - I'll just chime in to help emphasize that point that you have to be VERY CAREFUL with assumptions on this test, and in particular with Data Sufficiency questions. Your goal, really, should be to find a way that a statement is not sufficient, as in doing that you'll be looking for those "exceptions to the assumption".

While it's helpful for problem solving questions to look for ratios like 3-4-5, 6-8-10, 5-12-13, etc. with right triangles, you must have two sides (in their proper places, too - the biggest number must match the hypotenuse) in order to use them.

For Data Sufficiency questions, I might even go as far as to advise that you don't use triangle ratios at all. Why not? Because your only goal with DS questions is to determine whether or not you could get an answer, not what the answer specifically is. And the main role of those ratios is to make Pythagorean Theorem (a^2 + b^2 = c^2) faster - those numbers are simply ratios for a, b, and c that help you to avoid squaring, adding, and taking the square root.

The key on DS problems is to note whether you have enough information, and in that case using the a, b, and c variables in Pythagorean Theorem will help you to avoid the assumption that having one number will get you the answer - you'll more plainly see that you only have one variable (c) and that a and b have many possibilities:

a^2 + b^2 = 100:

a^2 = 99; b^2 = 1
a^2 = 98; b^2 = 2
etc.


Essentially what I'm saying is to beware of calculation shortcuts on Data Sufficiency problems, because those shortcuts don't add much (if any) value on DS problems, but they offer a huge risk of making you think you know more than you do in order to put the numbers in the shortcut.

For example, consider this:

What is the perimeter of triangle Z?

1) Triangle z has a side of 8 and a side of 10


Statement 1 is not sufficient. It could very well be a 6-8-10 triangle...but it could also be an 8-10-sqrt 164 triangle. We don't know that 10 is the hypotenuse, and if 8 and 10 are the shorter sides than the Pythagorean setup would be:

8^2 + 10^2 = c^2

and not:

a^2 + 8^2 = 10^2

One of the primary goals when writing a data sufficiency question is to get you to make assumptions, so you need to make sure that you're considering all the options!