If x is a pos. int., which of the following cannot be n^2?

[gmattesttaker2]

Hello,

For the following:

If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A) x^5
B) x^2 - 1
C) sq. root (x^8)
D) x^2 + 1
E) sq. root (x^5)

OA: D

This is from Veritas test. The OA asks us to plug in x = 1. When I was solving it, I plugged in x = 2 and therefore selected the wrong answer. Since the question says x is a positive integer, I was wondering how to know which value of x to pick for these kinds of questions? Thanks for your help.

Regards,
Sri

[[email protected]]

Hi Sri,

The phrase "...which of the following CANNOT be expressed as N^2...?" actually means "which of the following CANNOT EVER, no matter how many times you try, be expressed as N^2?"

By testing X = 2, you would find one answer that COULD be expressed as N^2 (answer C) and 4 answers that CANNOT (the other 4). This means that you would have to test again, using different values (until you knocked out the other 3).

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

Another way of approaching this is listing the first few squares of the positive integers:

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
etc.

Notice how the distance between the squares is increasing from term to term? That means that the least distance between two positive squares is between 1 and 4, and that difference is 3. Hence it's impossible to have x² and x² + 1 both be positive squares, so (D) makes sense.

(Note that there ARE two squares that fit this description, but they're 0 and 1 ... and 0 isn't positive!)

[sanju09]

Hello,

For the following:

If x is a positive integer, which of the following CANNOT be expressed as n^2, where n is an integer?

A) x^5
B) x^2 - 1
C) sq. root (x^8)
D) x^2 + 1
E) sq. root (x^5)

OA: D

This is from Veritas test. The OA asks us to plug in x = 1. When I was solving it, I plugged in x = 2 and therefore selected the wrong answer. Since the question says x is a positive integer, I was wondering how to know which value of x to pick for these kinds of questions? Thanks for your help.

Regards,
Sri

When looking for CANNOT BE option, choose numbers that can make a choice as it CAN BE. For example:

A. x^5 CAN BE expressed as n^2 for any perfect square integer x. Eliminate

B. x^2 - 1 CAN BE expressed as n^2 for x = 1 only. Eliminate

C. sq. root (x^8) CAN BE expressed as n^2 for any integer x. Eliminate

D. There's no positive integer x, integer next to whose square is also a perfect square; don't plug in x = 0, as x is a positive integer. Click [spoiler]D[/spoiler] and move to next problem!