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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
The four-digit number 486X, where X is the units digit of 486X, is a m  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 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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Re: The four-digit number 486X, where X is the units digit of 486X, is a m  [#permalink]

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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

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Joined: 14 Jun 2018
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Re: The four-digit number 486X, where X is the units digit of 486X, is a m  [#permalink]

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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 P
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]

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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.
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Re: The four-digit number 486X, where X is the units digit of 486X, is a m  [#permalink]

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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.

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Math Revolution GMAT Instructor V
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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]

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=>

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.
_________________ 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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