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

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

pandeyashwin · Accepted Answer

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

prabsahi · Answer

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!!

fskilnik · Answer

? = 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.

ScottTargetTestPrep · Answer

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

MathRevolution · Answer

=>

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

bumpbot · Answer

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

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

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