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# For an integer n greater than 1, the set Sn={ kn | k is an integer gre

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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For an integer n greater than 1, the set Sn={ kn | k is an integer gre  [#permalink]

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24 Sep 2018, 05:23
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Difficulty:

65% (hard)

Question Stats:

35% (01:24) correct 65% (01:17) wrong based on 22 sessions

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[Math Revolution GMAT math practice question]

For an integer n greater than 1, the set Sn={ kn | k is an integer greater than or equal to 1} is defined. What is the value of n?

1) 2 is contained in the set Sn.
2) 4 is contained in the set Sn.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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" GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 For an integer n greater than 1, the set Sn={ kn | k is an integer gre [#permalink] ### Show Tags 24 Sep 2018, 05:48 1 MathRevolution wrote: [Math Revolution GMAT math practice question] For an integer n greater than 1, the set Sn={ kn | k is an integer greater than or equal to 1} is defined. What is the value of n? 1) 2 belongs to the set Sn. 2) 4 belongs to the set Sn. $$n \geqslant 2\,\,\,\operatorname{int}$$ $${S_n} = \left\{ {\,k \cdot n\,\left. {} \right|\,\,\,k \geqslant 1\,\,\operatorname{int} } \right\}$$ $$? = n$$ Let´s understand what each S_n means: $${S_2} = \left\{ {\,2k\,\,\left. {} \right|\,\,\,k \geqslant 1\,\,\operatorname{int} } \right\} = \left\{ {2,4,6,8, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{even}}\,\,{\text{integers}}$$ $${S_3} = \left\{ {\,3k\,\,\left. {} \right|\,\,\,k \geqslant 1\,\operatorname{int} } \right\} = \left\{ {3,6,9,12, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{multiples}}\,\,{\text{of}}\,\,3$$ $${S_4} = \left\{ {\,4k\,\left. {} \right|\,\,\,k \geqslant 1\,\operatorname{int} } \right\} = \left\{ {4,8,12,16, \ldots } \right\}\,\,{\text{ = }}\,\,{\text{positive}}\,\,{\text{multiples}}\,\,{\text{of}}\,\,4$$ and so on... $$\left( 1 \right)\,\,\,2 \in {S_n}\,\,\, \Rightarrow \,\,\,\,n = 2\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.$$ $$\left( 2 \right)\,\,\,4 \in {S_n}\,\,\, \Rightarrow \,\,\,\,n = 2\,\,\,{\text{or}}\,\,\,n = 4\,\,\,\, \Rightarrow \,\,\,\,{\text{INSUFF}}.$$ The right answer is therefore (A). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7999 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For an integer n greater than 1, the set Sn={ kn | k is an integer gre [#permalink] ### Show Tags 26 Sep 2018, 04:58 => 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. Condition 1) Only S2 = { 2, 4, 6, … } includes 2. Therefore, n = 2. Condition 1) is sufficient. Condition 2) Two sets, S2 = { 2, 4, 6, … } S4 = { 4, 8, 12, … } contain 4. So, n could be 2 or 4. Since we don’t have a unique solution, 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: For an integer n greater than 1, the set Sn={ kn | k is an integer gre   [#permalink] 26 Sep 2018, 04:58
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