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For how many integers, denoted by "q", is
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rishabhmishra
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For how many integers, denoted by "q", is [#permalink] New post  Updated on: 28 Mar 2018, 19:50
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For how many integers, denoted by "q", is \(2^{|q|} =q^2\)?

A. ONE
B. TWO
C. THREE
D. FOUR
E. MORE THAN FOUR.
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Originally posted by rishabhmishra on 15 Mar 2018, 23:29.
Last edited by Bunuel on 28 Mar 2018, 19:50, edited 1 time in total.
Edited the question.
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rishabhmishra
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Re: For how many integers, denoted by "q", is [#permalink] New post  15 Mar 2018, 23:37
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rishabhmishra wrote:
For how many integers, denoted by "q", is \(2^{[q]} =q^2\)?
A. ONE
B. TWO
C. THREE
D. FOUR
E. MORE THAN FOUR.

This is possible for 4 integers 2, 4, -2 and -4
as \(2^4\) = 16
\(4^2\)=16
\(2^2\)= 4
and for - from the equation above those negative will converted into + by squaring or by [q]
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Re: For how many integers, denoted by "q", is [#permalink] New post  28 Mar 2018, 11:20
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Hi, I have a discrepancy with the answer and approach to the solution, it is not mentioned that [q] is absolute value of q, generally |q| is taken to be so. Also, in many cases the square brackets are used for greatest or smallest integer above or below a value type of questions, or it could simply mean square brackets. So i believe it is necessary for the symbol to be expressed correctly. Please correct me if I am wrong. :)
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Re: For how many integers, denoted by "q", is [#permalink] New post  28 Mar 2018, 19:49
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ShriyaMisra wrote:
Hi, I have a discrepancy with the answer and approach to the solution, it is not mentioned that [q] is absolute value of q, generally |q| is taken to be so. Also, in many cases the square brackets are used for greatest or smallest integer above or below a value type of questions, or it could simply mean square brackets. So i believe it is necessary for the symbol to be expressed correctly. Please correct me if I am wrong. :)


You are right. If it's meant to be the absolute value of q, then it should have been written as |q| NOT [q]. Edited.
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Re: For how many integers, denoted by "q", is [#permalink] New post  31 Aug 2019, 02:04
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rishabhmishra wrote:
For how many integers, denoted by "q", is \(2^{|q|} =q^2\)?

A. ONE
B. TWO
C. THREE
D. FOUR
E. MORE THAN FOUR.


Here is the video explanation-



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Re: For how many integers, denoted by "q", is [#permalink] New post  31 Aug 2019, 02:10
rishabhmishra wrote:
For how many integers, denoted by "q", is \(2^{|q|} =q^2\)?

A. ONE
B. TWO
C. THREE
D. FOUR
E. MORE THAN FOUR.


Asked: For how many integers, denoted by "q", is \(2^{|q|} =q^2\)?

For q = 2, -2
\(2^{2} =2^2\)
For q = 4, -4
\(2^{4} =4^2\)

IMO D
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