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# If the three-digit number 5W2 is evenly divisible by 8,

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Senior Manager
Joined: 21 Oct 2013
Posts: 435
If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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05 Feb 2014, 07:53
00:00

Difficulty:

35% (medium)

Question Stats:

59% (02:05) correct 41% (00:59) wrong based on 116 sessions

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If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?

A. 2
B. 3
C. 4
D. 5
E. 6

OE
[Reveal] Spoiler:
Any number evenly divisible by 8 must also be evenly divisible by 4. An integer is divisible by 4 if and only if its last two digits are a multiple of 4. 22, 42, and 62 are not divisible by 4. This leaves only Choices (B) and (D), so try dividing 532 by 8: 532 + 8 does not divide evenly, so the answer must be (D), 552

Hi, I want to know whether we can solve this without plugging the number in W, please.
I plugged in different numbers before I found the right answer...
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39708
Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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05 Feb 2014, 07:57
1
KUDOS
Expert's post
goodyear2013 wrote:
If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?

A. 2
B. 3
C. 4
D. 5
E. 6

OE
Any number evenly divisible by 8 must also be evenly divisible by 4. An integer is divisible by 4 if and only if its last two digits are a multiple of 4. 22, 42, and 62 are not divisible by 4. This leaves only Choices (B) and (D), so try dividing 532 by 8: 532 + 8 does not divide evenly, so the answer must be (D), 552.

Hi, I want to know whether we can solve this without plugging the number in W, please.
I plugged in different numbers before I found the right answer...

I'd solve this question the same way as in OE. Think it the easiest solution.
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Intern
Joined: 27 Sep 2013
Posts: 17
Location: Netherlands
Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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06 Feb 2014, 03:21
Took me 35 sec. to solve this question:

400 (divisible by 8) --> 480 --> 560 --> 552 (!)
Manager
Joined: 04 Oct 2013
Posts: 162
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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18 Feb 2014, 21:58
If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?

A. 2
B. 3
C. 4
D. 5
E. 6

Given that, the three digit number 5W2 is divisible by 8, then using the divisibility rule, that is 8 is divisible by the number if sum of four times the hundreds digit, twice the tens digit and units digit of the number is divisible by 8.
Or, 4 * 5 + 2 * W + 1 * 2 = 22 + 2W is divisible by 8
Or, W can be 1, 5, 9......

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Joined: 20 Jul 2012
Posts: 25
GMAT 1: 780 Q50 V50
Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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20 Feb 2014, 15:16
D. 5

What is easy number divisible by 8 and close to the 500's? 8*60 = 480.

From here I can add 32, 72 or 112 ( 8*4 or 8*9 or 8*14) to get 512, 552, or 592

552 is only choice allowed.
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Status: The Best Or Nothing
Joined: 27 Dec 2012
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Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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09 Mar 2014, 23:58
Tried to locate a '0' ending multiple of 8 between 500 & 599

Only 560 is present

560 is divisible by 8, so (560 - 8) is also divisible by 8

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Senior Manager
Joined: 06 Aug 2011
Posts: 400
Re: If the three-digit number 5W2 is evenly divisible by 8, [#permalink]

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11 Mar 2014, 08:23
"If the last three digits of a number are divisible by 8, then so is the whole number. "

Y above proprty cant be apply to this question..

i just plug differnt choices and got the ans in 1 mint..
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Re: If the three-digit number 5W2 is evenly divisible by 8,   [#permalink] 11 Mar 2014, 08:23
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