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Which of the integers 312, 98, 112, and 144 are divisible by

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Which of the integers 312, 98, 112, and 144 are divisible by [#permalink] New post 22 May 2019, 10:53
Expert's post
Which of the integers 312, 98, 112, and 144 are divisible by 8?

[Reveal] Spoiler: OA
312, 112, and 144


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Re: Which of the integers 312, 98, 112, and 144 are divisible by [#permalink] New post 23 May 2019, 07:27
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Carcass wrote:
Which of the integers 312, 98, 112, and 144 are divisible by 8?

[Reveal] Spoiler: OA
312, 112, and 144




Before you call up the GRE's onscreen calculator (and divide each value by 8), first recognize that dividing by 8 is the same as dividing by 2 THREE times.

For example, 24 ÷ 2 = 12, and 12 ÷ 2 = 6 and 6 ÷ 2 = 3
This is the SAME AS 24 ÷ 8 = 3

Now let's check each value....
312 ÷ 2 = 156, and 156 ÷ 2 = 78 and 78 ÷ 2 = 39
This means 312 ÷ 8 = 39
So, 312 IS divisible by 8

ALTERNATE APPROACH:
Notice that 312 = 320 - 8
Since 320 is divisible by 8, and since 8 is divisible by 8, it must be true that (320 - 8)is divisible by 8
In other words, 312 is divisible by 8
---------------------------------------

98 ÷ 2 = 49, and 49 ÷ 2 = 24.5
STOP
98 is clearly NOT divisible by 8
---------------------------------------

112 ÷ 2 = 56, and 56 ÷ 2 = 28 and 28 ÷ 2 = 14
This means 112 ÷ 8 = 14
So, 112 IS divisible by 8
---------------------------------------

144 ÷ 2 = 72, and 72 ÷ 2 = 36 and 36 ÷ 2 = 18
This means 144 ÷ 8 = 18
So, 144 IS divisible by 8

Cheers,
Brent
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Re: Which of the integers 312, 98, 112, and 144 are divisible by   [#permalink] 23 May 2019, 07:27
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Which of the integers 312, 98, 112, and 144 are divisible by

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