BTGmoderatorDC wrote:What is the remainder when a is divided by 4?
(1) a is the square of an odd integer.
(2) a is a multiple of 3.
Statement 1:
An odd integer can be written as follows:
2x+1, where x is an integer.
Since
a is the square of an odd integer, we get:
a = (2x+1)² = (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1 = 4(x²+x) + 1 = (multiple of 4) + 1
Since
a is equal to 1 more than a multiple of 4, dividing
a by 4 will yield a remainder of 1.
SUFFICIENT.
Statement 2:
Case 1: a=6, with the result that a/4 = 6/4 = 1 R2
Case 2: a=9, with the result that a/4 = 9/4 = 2 R1
Since the remainder can be different values, INSUFFICIENT.
The correct answer is
A.
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