(a + b)(a - b) = (a + b)(a - b) = a² - b².
Step 1:
(2² + 1)(2² - 1)(2� + 1)(2� + 1)
(2� - 1)(2� + 1)(2� + 1).
Step 2:
(2� - 1)(2� + 1)(2� + 1).
(2� - 1)(2� + 1).
Step 3:
(2� - 1)(2� + 1)
2¹� - 1.
The correct answer is A.
Please what's the way out here? I'm def missing something
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GMATGuruNY
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Last edited by GMATGuruNY on Fri Dec 23, 2016 5:01 am, edited 1 time in total.
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GMATGuruNY wrote:(a + b)(a - b) = (a + b)(a - b) = a² - b².
Step 1:
(2² + 1)(2² - 1)(2� + 1)(2� + 1)
(2� - 1)(2� + 1)(2� + 1).
Step 2:
(2� - 1)(2� + 1)(2� + 1).
(2� - 1)(2� + 1).
Step 3:
(2� - 1)(2� + 1)
2¹� - 1.
The correct answer is A.
Ohhh! I see my mistake. I never went beyond the first difference of squares. I solved completely.
Thank you sir. Please do you have links to similar questions with your solutions?
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DavidG@VeritasPrep
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You can find a couple more examples with solutions here: https://www.veritasprep.com/blog/2015/1 ... -the-gmat/
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[email protected]
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Hi Hallmah_O,
Certain questions can be solved with some 'brute force' work - and that approach applies here. This question has some built-in patterns that you can take advantage of too - and that can help you to quickly narrow down answer choices.
To start, it's worth noting that when dealing with exponents, raising the exponent even a little bit will have a big impact on the total.
For example:
2^2 = 4
2^3 = 8
By raising the exponent by 1 here, we DOUBLE the total value. So for example, 2^10 and 2^11 are NOT 'close' to one another.
In this prompt, if we ignore all of the +1s and -1s for a moment, we'd end up with...
(2^2)(2^2)(2^4)(2^8) = 2^16
Now clearly that is NOT the actual product, but we can use it as an estimate to quickly eliminate Answers C, D and E (they're all far too BIG to be the product. So now we're left with Answers A and B...
Looking at the original equation, we can easily see that the first parentheses = 3, thus the product MUST be evenly divisible by 3.
Answer A: 2^16 - 1
Answer B: 2^16 + 1
These two numbers differ by just 2, so one of them IS divisible by 3 and the other one is NOT. If we can figure out the value of either calculation, then we'll be done... At this point, you can either 'count doubles' or rewrite the calculation...
2^16 = 4^8 = 8^4 = 64^2 = 4096
4096 - 1 = 4095
4096 + 1 = 4097
The first result is divisible by 3 and the second is not (you can use the 'rule of 3' to quickly figure that out).
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
Certain questions can be solved with some 'brute force' work - and that approach applies here. This question has some built-in patterns that you can take advantage of too - and that can help you to quickly narrow down answer choices.
To start, it's worth noting that when dealing with exponents, raising the exponent even a little bit will have a big impact on the total.
For example:
2^2 = 4
2^3 = 8
By raising the exponent by 1 here, we DOUBLE the total value. So for example, 2^10 and 2^11 are NOT 'close' to one another.
In this prompt, if we ignore all of the +1s and -1s for a moment, we'd end up with...
(2^2)(2^2)(2^4)(2^8) = 2^16
Now clearly that is NOT the actual product, but we can use it as an estimate to quickly eliminate Answers C, D and E (they're all far too BIG to be the product. So now we're left with Answers A and B...
Looking at the original equation, we can easily see that the first parentheses = 3, thus the product MUST be evenly divisible by 3.
Answer A: 2^16 - 1
Answer B: 2^16 + 1
These two numbers differ by just 2, so one of them IS divisible by 3 and the other one is NOT. If we can figure out the value of either calculation, then we'll be done... At this point, you can either 'count doubles' or rewrite the calculation...
2^16 = 4^8 = 8^4 = 64^2 = 4096
4096 - 1 = 4095
4096 + 1 = 4097
The first result is divisible by 3 and the second is not (you can use the 'rule of 3' to quickly figure that out).
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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ceilidh.erickson
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Here's a general piece of advice that I give all of my students: for PS problems, treat the answer choices as CLUES!
One trait that most GMAT experts have in common: they scan the answer choices before starting to solve, and ask themselves "why are the answers structured this way? What does it tell me about where to begin?" They if they get stuck, they refer back to the answers regularly.
In this problem, for example, I would have seen that all of the answers were simpler in structure, but with higher exponents than those in the problem. I would have recognized that 2^16 - 1 was a difference of squares, and then seen that the other answer choices were all playing around with variations on the difference of squares idea. So, instead of trying to FACTOR the original expression, I would know that I had to FOIL instead. Or perhaps I would even begin by factoring one of the answer choices to detect a pattern.
Try asking yourself "what do the answer choices tell me?" before beginning any PS problem, and I bet you'll find questions like this one much easier!
One trait that most GMAT experts have in common: they scan the answer choices before starting to solve, and ask themselves "why are the answers structured this way? What does it tell me about where to begin?" They if they get stuck, they refer back to the answers regularly.
In this problem, for example, I would have seen that all of the answers were simpler in structure, but with higher exponents than those in the problem. I would have recognized that 2^16 - 1 was a difference of squares, and then seen that the other answer choices were all playing around with variations on the difference of squares idea. So, instead of trying to FACTOR the original expression, I would know that I had to FOIL instead. Or perhaps I would even begin by factoring one of the answer choices to detect a pattern.
Try asking yourself "what do the answer choices tell me?" before beginning any PS problem, and I bet you'll find questions like this one much easier!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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ceilidh.erickson
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For more on scanning the answer choices for clues, here's an article I wrote for the Manhattan Prep blog:
https://www.manhattanprep.com/gmat/blog ... -pen-down/
https://www.manhattanprep.com/gmat/blog ... -pen-down/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
