2^36 - 2^30 = x

I can't remember where I have this question from, but I think it is not solvable since multiple answers are possible...

2^36 - 2^30 = x

x is divisble by... ?

2^36-30 = 2^6 =64

Only divisible by 2

Hence A

prateek_guy2004 wrote:2^36 - 2^30 = x

x is divisble by... ?

2^36-30 = 2^6 =64

Only divisible by 2

Hence A

you are wrong, you are not allowed to do that!

what you wanna do just works with a division:

2^36 : 2^30 = 2^36 - 2^30 = 2^6

2^36 - 2^30 = 2^30(2^6 - 1)
= 2^30 * 63

Thus x can be divided by 7.

I like this thread!

Lots of good contributions here:

-Fractal - I love the setup, but you're right...there are multiple correct answers as it's written

-amsm - great process. That's what I'd do almost every time given this setup. With exponents, we're really good with rules when there is multiplication present. But as we saw with some other contributions, we don't know what to do when there's addition/subtraction. Why not? Exponents are repetitive multiplication. So nearly every rule we have for exponents applies to multiplication/division. When in doubt, factor common terms since that creates a multiplication problem and not an add/subtract problem.

2^36 - 2^30 has a common 2^30, so you can factor it to:

2^30 (2^6 - 1)
2^30 (64 - 1)
2^30 (63)
2^30 (7 * 3 * 3)

So this number is divisible by 2, 3, and 7 from the answer choices.


Now...if I saw this exact question, I might not even get that far because 2^36 - 2^30 is clearly an even number minus an even number, and even - even = even. So without even factoring I already knew that it would be divisible by 2, so if A were 2 and the other answer choices were different, I'd be done. That this question has multiple answers is the problem with that logic - but an official GMAT question wouldn't have multiple correct answers...

Is it possible to do like this?

2^36- 2^30 = 2^(36-30) = 2^6.

Brian@VeritasPrep wrote:I like this thread!

Lots of good contributions here:

-Fractal - I love the setup, but you're right...there are multiple correct answers as it's written

-amsm - great process. That's what I'd do almost every time given this setup. With exponents, we're really good with rules when there is multiplication present. But as we saw with some other contributions, we don't know what to do when there's addition/subtraction. Why not? Exponents are repetitive multiplication. So nearly every rule we have for exponents applies to multiplication/division. When in doubt, factor common terms since that creates a multiplication problem and not an add/subtract problem.

2^36 - 2^30 has a common 2^30, so you can factor it to:

2^30 (2^6 - 1)
2^30 (64 - 1)
2^30 (63)
2^30 (7 * 3 * 3)

So this number is divisible by 2, 3, and 7 from the answer choices.


Now...if I saw this exact question, I might not even get that far because 2^36 - 2^30 is clearly an even number minus an even number, and even - even = even. So without even factoring I already knew that it would be divisible by 2, so if A were 2 and the other answer choices were different, I'd be done. That this question has multiple answers is the problem with that logic - but an official GMAT question wouldn't have multiple correct answers...

Brian, thx a lot for your confirmation

bharathram wrote:Is it possible to do like this?

2^36- 2^30 = 2^(36-30) = 2^6.

Not allowed. 2^(36-30) would have been the answer if it was 2^36/2^30. Two exponents in the form 2^36- 2^30 can't directly be added. Please refer to this attachment. It has all the exponent rules