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
To find the least perfect square
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If n is a perfect square, then √n is an integer.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 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
GMAT/MBA Expert
- Brent@GMATPrepNow
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- Posts: 16207
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Another approach is the input/output approach.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
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