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# The four-digit number 486X, where X is the units digit of 486X, is a m

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Math Revolution GMAT Instructor
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The four-digit number 486X, where X is the units digit of 486X, is a m  [#permalink]

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01 Nov 2018, 00:37
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45% (medium)

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69% (01:44) correct 31% (01:12) wrong based on 93 sessions

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[Math Revolution GMAT math practice question]

The four-digit number $$486X$$, where $$X$$ is the units digit of $$486X$$, is a multiple of $$36$$. What is the value of $$X$$?

$$A. 0$$
$$B. 2$$
$$C. 4$$
$$D. 6$$
$$E. 8$$

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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" Senior Manager Joined: 09 Jun 2014 Posts: 352 Location: India Concentration: General Management, Operations Re: The four-digit number 486X, where X is the units digit of 486X, is a m [#permalink] ### Show Tags 01 Nov 2018, 01:18 MathRevolution wrote: [Math Revolution GMAT math practice question] The four-digit number $$486X$$, where $$X$$ is the units digit of $$486X$$, is a multiple of $$36$$. What is the value of $$X$$? $$A. 0$$ $$B. 2$$ $$C. 4$$ $$D. 6$$ $$E. 8$$ So,here is my approach .. I would divide 486 by 36 and see what is the remainder. If you divide 486/36 the remainder is 18..Now what the next digit of quotient should come after 18 and that is x such that 18x/36 is divisible...clearly x is zero..so 180/36=5 hence OA is A Press Kudos if it helps!! Manager Joined: 14 Jun 2018 Posts: 217 Re: The four-digit number 486X, where X is the units digit of 486X, is a m [#permalink] ### Show Tags 01 Nov 2018, 01:32 2 Divisibility of 4 : Last 2 digits should be divisible by 4 Divisibility of 9 : Sum of digits should be divisible by 9 Only A fits GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: The four-digit number 486X, where X is the units digit of 486X, is a m [#permalink] ### Show Tags 01 Nov 2018, 06:42 MathRevolution wrote: [Math Revolution GMAT math practice question] The four-digit number $$486X$$, where $$X$$ is the units digit of $$486X$$, is a multiple of $$36$$. What is the value of $$X$$? $$A. 0$$ $$B. 2$$ $$C. 4$$ $$D. 6$$ $$E. 8$$ $$? = X$$ $${{\left\langle {486X} \right\rangle } \over {{2^2} \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,\,\left\langle {486X} \right\rangle \,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,4\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {6X} \right\rangle \,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,4\,\,\,\,\, \Rightarrow \,\,\,\,X \in \left\{ {0,4,8} \right\}\,\,\,\left( * \right) \hfill \cr \,\,\left\langle {486X} \right\rangle \,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,9\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {18 + X\,\,,\,\,{\rm{hence}}} \right)\,\,X\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,9\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,? = X = 0 \hfill \cr} \right.$$ 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 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8109 Location: United States (CA) Re: The four-digit number 486X, where X is the units digit of 486X, is a m [#permalink] ### Show Tags 02 Nov 2018, 17:10 1 MathRevolution wrote: [Math Revolution GMAT math practice question] The four-digit number $$486X$$, where $$X$$ is the units digit of $$486X$$, is a multiple of $$36$$. What is the value of $$X$$? $$A. 0$$ $$B. 2$$ $$C. 4$$ $$D. 6$$ $$E. 8$$ Since 36 = 4 x 9, we see that 486X must be divisible by 4 and 9. From the divisibility rules, we see that the sum of the digits must be a multiple of 9, and the number formed by the last two digits, 6X, must be a multiple of 4. Since 4 + 8 + 6 = 18, so X can be 0 or 9 if 486X is divisible by 9, or it can be 0, 4 or 8 if 486X is divisible by 4. However, since 486X is divisible by both 9 and 4, X must be 0. Answer: A _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The four-digit number 486X, where X is the units digit of 486X, is a m [#permalink] ### Show Tags 04 Nov 2018, 20:13 => Since X is a one-digit integer, $$0 ≤ X ≤ 9.$$ $$36 = 4*9$$, so $$486X$$ is a multiple of both $$4$$ and $$9$$. Since $$486X$$ is a multiple of $$4, 6*10 + X$$ must be a multiple of $$4$$. Thus, $$X$$ is one of values $$0, 4$$ and $$8$$. In addition, since $$486X$$ is a multiple of $$9,$$ the sum of all of its digits, $$4 + 8 + 6 + X = X + 18$$ is a multiple of $$9$$. Thus, $$X$$ must be $$0$$ or $$9$$. $$0$$ is the only one of these digits for which $$486X$$ is a multiple of $$36$$. Therefore, the answer is A. Answer: A _________________ 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: The four-digit number 486X, where X is the units digit of 486X, is a m   [#permalink] 04 Nov 2018, 20:13
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