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Kindly explain - DS Number Properties

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Kindly explain - DS Number Properties

by manju_ej » Tue Aug 05, 2008 1:32 am
If x is a positive integer , is x^3 - 3x^2+2x divisible by 4?

1. x=4y+4, where y is an integer
2. x=2z+2, where z is an integer

Answer is D ,
but my Q , why the possibility that Z = 0 not taken?
In that case X=2, and product of x,(x-2),(x-1) is Zero and this is not divisible by 4!
Last edited by manju_ej on Tue Aug 05, 2008 2:52 am, edited 1 time in total.
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by parallel_chase » Tue Aug 05, 2008 2:35 am
I think you have answered your own question.

Here is a property of zero which would help you solve the above question.

0 is a multiple of every integer, therefore 0 is divisible by every integer even by 0 itself.

Hope this helps.
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by Ian Stewart » Tue Aug 05, 2008 3:17 am
parallel_chase wrote: Here is a property of zero which would help you solve the above question.

0 is a multiple of every integer, therefore 0 is divisible by every integer even by 0 itself.
That's very close to being right, but there is one (unimportant, for the GMAT) distinction between 'multiple of' and 'divisible by'.

If 'a is a multiple of b', then we can write a = xb, where x is an integer. So 66 is a multiple of 11, because 66 = 6*11. Zero is a multiple of 4, because 0 = 0*4, and zero is a multiple of zero as well, because 0 = 19*0 (I chose 19 randomly here; we can use any integer).

On the other hand, if 'a is divisible by b', that means that a/b is an integer. In almost all cases, that means the same thing as 'a is a multiple of b'. It's only when dealing with zero that we see a difference. Zero is divisible by four, certainly, because 0/4 = 0 is an integer. Zero is not, however, divisible by zero, because 0/0 is undefined.

So zero is a multiple of every integer, and is divisible by every integer except zero. Mind you, the GMAT won't test you on this minor distinction in definition, but you should know for your test that zero is divisible by every positive integer.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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