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2^36 - 2^30 = x
Source: Beat The GMAT — Problem Solving |
I can't remember where I have this question from, but I think it is not solvable since multiple answers are possible...
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prateek_guy2004
- Master | Next Rank: 500 Posts
- Posts: 398
- Location: India
- Thanked: 41 times
2^36 - 2^30 = x
x is divisble by... ?
2^36-30 = 2^6 =64
Only divisible by 2
Hence A
x is divisble by... ?
2^36-30 = 2^6 =64
Only divisible by 2
Hence A
Don't look for the incorrect things that you have done rather look for remedies....
https://www.beatthegmat.com/motivation-t90253.html
https://www.beatthegmat.com/motivation-t90253.html
you are wrong, you are not allowed to do that!prateek_guy2004 wrote:2^36 - 2^30 = x
x is divisble by... ?
2^36-30 = 2^6 =64
Only divisible by 2
Hence A
what you wanna do just works with a division:
2^36 : 2^30 = 2^36 - 2^30 = 2^6
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Brian@VeritasPrep
- GMAT Instructor
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- Location: Malibu, CA
- Thanked: 716 times
- GMAT Score:750
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...
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 Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
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bharathram
- Newbie | Next Rank: 10 Posts
- Posts: 2
Brian, thx a lot for your confirmationBrian@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...
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 rulesbharathram wrote:Is it possible to do like this?
2^36- 2^30 = 2^(36-30) = 2^6.
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