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20 Jun 2020, 13:30
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From Problem Solving Practice Questions on the GMAT Official Guide 2020:
If x is a positive integer and \(4^x\) -3 = y, which of the following cannot be a value of Y?
(A) 1
(B) 7
(C) 13
(D) 61
(E) 253
The solution explanation reads as follows:
"This can be solved by observing that \(4^x\) always has units digit 4 or 6 - the product of two integers with units digits 4 has units digit 6, the product of two integers with units digit 6 has units digit 4, etc.- and therefore any integer that does not have units digit 4-3 = 1 or 6-3 = 3 cannot be the value of \(4^x\) -3 = y for some positive integer value of x."
For the bolded portion above, I present the following counterexample: 16 times 16 is equal to 256. That is, product of two integer with units digit 6 has units digit 6, not units digit 4 like they said.
I understand how to arrive at the solution, but i'm just worried that my book is wrong in this one example because then that means that the book is liable to be incorrect on other problems that I don't quite understand and they'll be leading me down the wrong path.
Can someone help me see what I am missing? Or is my book indeed just incorrect and they stated something that was false?
If x is a positive integer and \(4^x\) -3 = y, which of the following cannot be a value of Y?
(A) 1
(B) 7
(C) 13
(D) 61
(E) 253
The solution explanation reads as follows:
"This can be solved by observing that \(4^x\) always has units digit 4 or 6 - the product of two integers with units digits 4 has units digit 6, the product of two integers with units digit 6 has units digit 4, etc.- and therefore any integer that does not have units digit 4-3 = 1 or 6-3 = 3 cannot be the value of \(4^x\) -3 = y for some positive integer value of x."
For the bolded portion above, I present the following counterexample: 16 times 16 is equal to 256. That is, product of two integer with units digit 6 has units digit 6, not units digit 4 like they said.
I understand how to arrive at the solution, but i'm just worried that my book is wrong in this one example because then that means that the book is liable to be incorrect on other problems that I don't quite understand and they'll be leading me down the wrong path.
Can someone help me see what I am missing? Or is my book indeed just incorrect and they stated something that was false?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
20 Jun 2020, 13:33
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felipet190
This question is discussed here: if-x-is-a-positive-integer-and-4-x-3-y-which-of-the-following-can-268685.html In case of questions please post there. Hope it helps.
Also, please read carefully and follow our posting rules: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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