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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the reminder when n^2 is divided by 4?  [#permalink]

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15 Mar 2018, 02:22
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35% (medium)

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68% (01:38) correct 32% (01:29) wrong based on 85 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1196 Location: India GPA: 3.82 What is the reminder when n^2 is divided by 4? [#permalink] Show Tags 15 Mar 2018, 04:16 1 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the reminder when n^2 is divided by 4? [#permalink] Show Tags 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: What is the reminder when n^2 is divided by 4?  [#permalink]

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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?   [#permalink] 29 Mar 2018, 04:03
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