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

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by gmattesttaker2 » Sat May 10, 2014 7:25 pm
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
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by [email protected] » Sat May 10, 2014 11:52 pm
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).

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by Matt@VeritasPrep » Mon May 12, 2014 11:37 am
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!)
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by sanju09 » Wed May 14, 2014 2:46 am
gmattesttaker2 wrote: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!
The mind is everything. What you think you become. -Lord Buddha



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