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If w represents the tens digit in a = 2,125,4w6

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by VJesus12 » Wed Jun 20, 2018 2:34 am

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Answers

A

B

C

D

E

Stats

Difficulty—

If w represents the tens digit in
a = 2,125,4w6.

What is the value of w?

(1) a is divisible by 6
(2) a is divisible by 4

The OA is the option E.

I don't know how to conclude that none of the statements is correct. Could anyone help me? Thanks in advance.
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Source: — Data Sufficiency |
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by Vincen » Wed Jun 20, 2018 6:39 am
Hello Vjesus12.

Let's consider the number $$a=2,125,4w6.$$ Now, let's try to find the value of w.

First statement
(1) a is divisible by 6
If a is divisible by 6 then a is divisible by 2 and 3.

Since a is divisible by 3, then the sum of the digits of a must be divisible by 3. $$2+1+2+5+4+w+6=20+w.$$ To get a value that is divisible by 3 w can have the following values:
w=1
w=4
w=7

Since we didn't get only one option, then this statement is not sufficient.

Second statement
(2) a is divisible by 4
Now, if a is divisible by 4 then the number composed by the last two digit (to the right) must be divisible by 4. That is to say, we have that w6 is divisible by 4.

To get it, w can be any of the following values:
w=1
w=3
w=5
w=7
w=9

Since we didn't get only one option, then this statement is not sufficient.

First statement + Second statement
(1) a is divisible by 6
(2) a is divisible by 4
Using both statements the list of the possible values for w is:
w=1
w=7

So, we didn't get a single value for w. Therefore this statement is not sufficient.

In conclusion, the correct answer is the option E.

I hope it helps you. <i class="em em-smiley"></i>
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