Given that 8 is not a factor of g, is 8 a factor of 2g?

Question

Please explain detail steps

spaiydz · Answer

How bout 4?

8 isn't a factor of 4, but is a factor of 2x4.

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siddhans · Answer

dont understand what you mean...

JoelCairo · Answer

Here is where prime factorization is really key. When you see "some number is not a factor of some unknown number" the first thing you have to do is break that first number down into its prime factors. In this case, "8" is just another way of saying "2*2*2."

What you are being told is that g does  not  have three 2s in it. (it's not 8 (2*2*2), it's not 24 (2*2*2*3) it's not 40 (2*2*2*5) etc).

Then the question asks if 8 is a factor of 2g. What is really being asked here is "does g have two 2s in it?"

siddhans · Answer

i see, So whats the final answer ..??? Y or N?

fluke · Answer

The answer is MAYBE. Or data not sufficient.

If g=4; 2g=8; g is NOT divisible by 8, but 2g is divisible by 8.
If g=7(Or Any prime number; Note there may be other cases as well); 2g=14; g is NOT divisible by 8, AND 2g is also NOT divisible by 8.

Data Not Sufficient. So, just by knowing that 'g' is NOT divisible by 8, we can't conclude whether 2g is divisible by 8,  kapish ?

jeeteshsingh · Answer

Data insufficient!

Reason:

8 is not a factor of g => g does not have 2x2x2 in its factor list.

This means g is either 2*(2n+1) = 4n + 2
or 
4*(2n+1) = 8n + 4

Therefore 2g will be either 2*(4n+2) = 8n + 4 ----- (1)
or 
2*(8n+4) = 16n + 8 = 8 (2n + 1) ---- (2)

Hence when 2g is divided by 8 we can either get a remainder of 4 (as per eq 1) or 0 (as per eq 2). Therefore insufficient!

Spidy001 · Answer

It depends.

when g =4

2g is 8 and hence 8 is factor of 2g.

when g=3
 
 2g is 6 and here 8 is not a factor of 2g.

rdevorse · Answer

I am working through this problem now in the MGMAT book. I am confused as to the use of 'n' in this explanation.

I can grasp that because g is unknown (and can be any integer) that it means 'Data Insufficient'. I am just having trouble understanding the method used for solving this. I mean, if any other number were used.. (6, or even 2) could they still say that 6 (or 2) is not a factor of g, so is 6 (or 2) a factor of 2g, and we still get the same 'Cannot be Determined' result?

syahasa2 · Answer

It would be really helpful if you'd write the options below the question or the statements if it is a DS.
Can't be answered that way.
I mean, if g=2, then 8 cannot be a factor of 2g.
If g=4 , then 8 is a factor of 2g.

RK84 · Answer

The data not sufficient to tell the answer.
if we take g=4 & g=2 (in both cases g is not a factor of 8)
now for both these cases 2g=8 & 2g=4 (again one is a factor of 8, one not)
Hence we cannot conclude anything. Data Insufficient.

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Given that 8 is not a factor of g, is 8 a factor of 2g?

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