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To find the least perfect square

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by gmattesttaker2 » Sat Jan 11, 2014 4:49 pm
Hello,

Can you please assist with this:

A perfect square is a number obtained by squaring an integer. If n is a perfect square,
then in terms of n the least perfect square which is more than n is

(A) n^2
(B) (n + 1)^2
(C) n + 2√n + 1
(D) 2√n + 1
(E) n + 2√n

OA: C
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by Brent@GMATPrepNow » Sat Jan 11, 2014 4:57 pm
gmattesttaker2 wrote: A perfect square is a number obtained by squaring an integer. If n is a perfect square,
then in terms of n the least perfect square which is more than n is

(A) n^2
(B) (n + 1)^2
(C) n + 2√n + 1
(D) 2√n + 1
(E) n + 2√n
If n is a perfect square, then √n is an integer.
If √n is an integer, then the next biggest integer equals √n + 1
So, the next biggest perfect square equals (√n + 1)²

When we check the answer choices, we see that none of them looks like (√n + 1)²
So, let's take (√n + 1)² and expand and simplify it.

(√n + 1)² = (√n)² + √n + √n + 1
= n + 2√n + 1
= C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sat Jan 11, 2014 5:05 pm
gmattesttaker2 wrote:A perfect square is a number obtained by squaring an integer. If n is a perfect square,
then in terms of n the least perfect square which is more than n is

(A) n^2
(B) (n + 1)^2
(C) n + 2√n + 1
(D) 2√n + 1
(E) n + 2√n
Another approach is the input/output approach.

Let's begin by choosing a value for n (where n is a perfect square)
Let's say n = 4
If n = 4, then the next biggest perfect square equals 9

So, we're looking for an answer choice that, when we plug in 4 for n, the output is 9 (the next largest perfect square)

(A) n² = 4² = 16 (NOPE)
(B) (n + 1)² = (4 + 1)² = 25 (NOPE)
(C) n + 2√n + 1 = 4 + 2√4 + 1 = 9 (BINGO!!)
(D) 2√n + 1 = 2√4 + 1 = 5 (NOPE)
(E) n + 2√n = 4 + 2√4 = 8 (NOPE)

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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