GreenlightTestPrep wrote:

If x and y are positive integers less than 10, which of the following COULD be true?

i) √x + √y = √(x + y)

ii) y√x = x√y

iii) √x - √y = √(x - y)

A) i only

B) i and ii only

C) i and iii only

D) ii and iii only

E) i,ii and iii

When I scan the statements, I see that ii and iii look easier, so I'll start with those.

ii) y√x = x√yWe can quickly see that, if x = y, then this statement is TRUE.

For example, if x = 1 and y = 1, we get 1√1 = 1√1, which is true.

So,

statement ii COULD be true.

Check the answer choices......ELIMINATE A and C

iii) √x - √y = √(x - y)Once again, this statement is TRUE when x = y.

For example, if x = 1 and y = 1, we get √1 - √1 = √(1 - 1), which is true.

So,

statement iii COULD be true.

Check the answer choices......ELIMINATE B

i) √x + √y = √(x + y)This is a tough one.

I can't think of any values for x and y that make this statement true, so now what?

Well, we might just conclude that statement i cannot be true.

However, we can do a bit of algebra to further convince ourselves.

Given: √x + √y = √(x + y)

Square both sides to get: (√x + √y)² = [√(x + y)]²

Expand to get: x + 2√(xy) + y = x + y

Subtract x and y from both sides to get: 2√(xy) = 0

This means that xy = 0, but

xy cannot equal 0 since we're told that x and y are POSITIVE integers.

So,

statement i cannot be true. Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for our free GRE Question of the Day emails