BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:33 am

If x and y are the lengths of the legs of a right triangle, what is the value of xy ?

(1) The hypotenuse of the triangle is 10√2.
(2) The area of the triangular region is 50.

Answer: B
Source: Official Guide

Given: x and y are the lengths of the legs of a right triangle
We have something like this:


Target question: What is the value of xy?

Statement 1: The hypotenuse of the triangle is [m]10[square_root]2[/square_root][/m].
There are infinitely-many different right triangles that meet this condition. Here are two:
Case a: x = 10 and y = 10

CHECK: If h = the hypotenuse, then we get 10² + 10² = h²
Solve: 200 = h²
So, h = √200 = 10√2
In this case, the answer to the target question is xy = (10)(10) = 100

Case b: x = √50 and y = √150

CHECK: If h = the hypotenuse, then we get (√50)² + (√150)² = h²
Solve: 200 = h²
So, h = √200 = 10√2
In this case, the answer to the target question is xy = (√50)(√150) = √7500 = 50√3

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: The area of the triangular region is 50
Area of triangle = (base)(height)/2
So, we can write: (x)(y)/2 = 50
Multiply both sides by 2 to get: xy = 100
So, the answer to the target question is xy = 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:33 am

If x and y are the lengths of the legs of a right triangle, what is the value of xy ?

(1) The hypotenuse of the triangle is 10√2.
(2) The area of the triangular region is 50.

Answer: B
Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the value of xy given that x and y are the lengths of the legs of a right triangle.

Statement One Alone:

Knowing the length of the hypotenuse of the triangle is not sufficient to answer the question. Obviously, the triangle can be an isosceles right triangle and having a hypotenuse = 10√2 means both legs are 10. So xy = (10)(10) = 100. However, the triangle can also be a non-isosceles right triangle. For example, x can be 2 and y can be 14 (notice that 2^2 + 14^2 = 4 + 196 = 200 = (10√2)^2). In this case, xy = (2)(14) = 28. Statement one alone is not sufficient.

Statement Two Alone:

Recall that the area of a right triangle is 1/2 the product of the lengths of its legs. Here, the area of the triangle will be 1/2 * xy. Since we are given that the area is 50, we have:

1/2 * xy = 50

xy = 100

Statement two alone is sufficient.

Answer: B