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# If a, b, and c are consecutive integers, where a<b<c, which of the fol

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Intern
Joined: 04 Jan 2018
Posts: 9
If a, b, and c are consecutive integers, where a<b<c, which of the fol  [#permalink]

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02 Dec 2018, 02:03
2
00:00

Difficulty:

75% (hard)

Question Stats:

34% (01:54) correct 66% (02:05) wrong based on 32 sessions

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If a, b, and c are consecutive integers, where a<b<c, which of the following cannot be the value of c^2 - (a^2 + b^2)?

(A) -77
(B) -32
(C) -21
(D) -10
(E) 0
Senior Manager
Joined: 22 Feb 2018
Posts: 412
If a, b, and c are consecutive integers, where a<b<c, which of the fol  [#permalink]

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02 Dec 2018, 02:27
OA:D

Let $$a = n-1$$
$$b=n$$
$$c=n+1$$
$$c^2 - (a^2 + b^2)=(n+1)^2-[(n-1)^2+n^2]=n^2+1+2n-[n^2+1-2n+n^2]=n^2+1+2n-[2n^2+1-2n=-n^2+4n=-n(n+4)$$

$$(A) -77 = -1*7*(7+4)$$
$$(B) -32 = -1*4*(4+4)$$
$$(C) -21 = -1*3*(3+4)$$
$$(D) -10$$ this is the answer as it cannot be expressed as $$-n(n+4)$$
$$(E) \quad 0 = -1*0*(0+4)$$
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If a, b, and c are consecutive integers, where a<b<c, which of the fol &nbs [#permalink] 02 Dec 2018, 02:27
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