Carcass wrote:
Which of the integers 312, 98, 112, and 144 are divisible by 8?
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
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98 ÷ 2 = 49, and 49
÷ 2 = 24.5
STOP
98 is clearly NOT divisible by 8
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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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Brent Hanneson - founder of Greenlight Test Prep