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.
OA A
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What is the remainder when a is divided by 4?
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BTGmoderatorDC
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Let's take each statement one by one.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.
OA A
Source: Manhattan Prep
(1) a is the square of an odd integer.
The squares of first odd numbers are 1^2 = 1; 3^2 = 9; 5^2 = 25; 7^2 = 49
The numbers are 1, 9, 25, 49, 81 and so on. Each number divided by 4 leaves a remainder 1. Sufficient.
(2) a is a multiple of 3.
Few multiples of 3 are 3, 6, 9, 12...
While 3 divided 4 leaves remainder 3, 6 divided 4 leaves remainder 2. No unique answer. Insufficient.
The correct answer: A
Hope this helps!
-Jay
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Statement 1: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.
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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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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