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What is the reminder when n^2 is divided by 4?

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Math Revolution GMAT Instructor
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What is the reminder when n^2 is divided by 4?  [#permalink]

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New post 15 Mar 2018, 02:22
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[GMAT math practice question]3.15

What is the reminder when \(n^2\) is divided by \(4\)?

1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).

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What is the reminder when n^2 is divided by 4?  [#permalink]

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New post 15 Mar 2018, 04:16
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MathRevolution wrote:
[GMAT math practice question]3.15

What is the reminder when \(n^2\) is divided by \(4\)?

1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).


Statement 1: \(n=2k+1=>n^2=4k^2+4k+1\). Clearly if this number is divided by \(4\), then \(1\) will be the remainder. Sufficient

Statement 2: \(n=3k+1=>n^2=9k^2+6k+1=>8k^2+4k+k^2+2k+1=>n^2=4k(2k+1)+(k+1)^2\).

Hence the remainder will depend on the value of \((k+1)^2\) where \(k\) is unknown. if \(k=3\), then remainder will be \(0\) and if \(k=2\), remainder will be \(1\). Insufficient

Option A
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Re: What is the reminder when n^2 is divided by 4?  [#permalink]

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New post 18 Mar 2018, 23:15
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Plugging-in numbers is suggested for remainder questions.
The integers which have a remainder of 1 when divided by 2 are odd.
So,
\(n: 1, 3, 5, 7, 9, …\)
and
\(n^2: 1, 9, 25, 49, 81, …\)
Each value of \(n^2\) has a remainder of \(1\) when it is divided by \(4\).
So, condition 1) is sufficient.

Condition 2)
When \(n = 1, n^2= 1\) has a remainder of \(1\) when it is divided by \(4.\)
When \(n = 4, n^2=16\) has a remainder of \(0\) when it is divided by \(4\).
Since we don’t have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: What is the reminder when n^2 is divided by 4?  [#permalink]

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New post 29 Mar 2018, 04:03
niks18 wrote:
MathRevolution wrote:
[GMAT math practice question]3.15

What is the reminder when \(n^2\) is divided by \(4\)?

1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).


1) When \(n\) is divided by \(2\), the reminder is \(1\).
2) When \(n\) is divided by \(3\), the reminder is \(1\).

St 1: n = 1, 3, 5, 7 (Remainder = 1 when divided by 2)

n^2 = 1, 9, 25, 49 (Remainder = 1 when divided by 4) Sufficient

St 2: n = 1, 4, 7, 10 (Remainder = 1 when divided by 3)

n^2 = 1, 16, 49, 100 Remainder = 1, 0, 1, 0 when divided by 4) Insufficient

(A)
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Re: What is the reminder when n^2 is divided by 4? &nbs [#permalink] 29 Mar 2018, 04:03
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