If a, b, and c are consecutive integers, where a

Question

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. -21
B. -12
C. -6
D. 0
E. 3

a,b and c are consecutive integers where a<b<c. which of the following could not be the value of c^2-b^2-a^2?

GMATinsight · Accepted Answer

if a = x-1, then b = x and c = x+1

c^2 - (a^2 + b^2) = (x+1)^2 -   = x^2+1+2x - x^2 - x^2 - 1 +2x = -x^2 +4x = x(4-x)

A. -21 = (-3)*(4-(-3)) hence POSSIBLE
B. -12 = (-2)*(4-(-2)) hence POSSIBLE
  C. -6 ≠ (-1)*(4-(-1)) hence NOT POSSIBLE  
D. 0 = (0)*(4-(0)) hence POSSIBLE
E. 3 = (1)*(4-(1)) hence POSSIBLE

ANswer: Option C

Purnank · Answer

where a<b<c, x < x+1 < x+2
c^2−(a^2+b^2) = (x+2)^2 - (x^2 + (x+1)^2) = x^2 + 4x + 4 - x^2 - x^2 - 2x - 1
= -x^2 + 2x + 3 = -x^2 + 3x - x + 3 = -x(x-3) - 1 (x-3) = (-x-1)*(x-3) = -1(x+1)*(x-3)
as given a,b,c are all consecutive integers so put any value of integer for a = x = 1,2,3,4,.........n.
and check for options you will get values 3,0,-12 and -21 for x = 2,3,5,6 respectively 
Therfore answer C.

Gemmie · Answer

a b c are consecutive integers that a < b < c

$c^2 - (a^2 + b^2) $
$= (a+2)^2 - (a^2 + (a+1)^2)$
$= a^2 + 4a + 4 - (a^2 + a^2 + 2a + 1)$
$= - a^2 + 2a + 3$
$= - a^2 + 2a - 1 + 4$
$= - (a+1)^2 + 4$
= X

=> X-4 must be the negative of square of an integer

A. -21 => $- 21 - 4 = -25 = -5^2$
B. -12 => $- 12 - 4 = -16 = -4^2$
C. -6 => $- 6 - 4 = -10$
D. 0 => $- 0 - 1 = -1 = -1^2$
E. 3 => $3 - 4 = -1 = -1^2$

gmatmonster805 · Answer

If $a$, $b$, and $c$ are consecutive integers, where $a < b < c$, we can let:
- $a = x-1$
- $b = x$
- $c = x+1$

Then, we need to determine which of the following cannot be the value of $c^2 - (a^2 + b^2)$.

First, we express $c^2 - (a^2 + b^2)$ in terms of $x$:
\ 
\]

Calculating each term, we get:
\ 
\ 
\ 
Thus:
\  = x^2 + 2x + 1 -   
\]
\ 
\ 
\ 
\ 
We need to determine which of the given values cannot be produced by the expression $x(4-x)$:
\ 
\ 
\ 
\ 
\ 
The value $-6$ cannot be the product of $x(4-x)$ for any integer $x$.

bumpbot · Answer

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

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