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Manager  S
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For how many integers, denoted by "q", is  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 38% (01:25) correct 62% (01:18) wrong based on 130 sessions

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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.

Originally posted by rishabhmishra on 16 Mar 2018, 00:29.
Last edited by Bunuel on 28 Mar 2018, 20:50, edited 1 time in total.
Edited the question.
Manager  S
Joined: 23 Sep 2016
Posts: 233
Re: For how many integers, denoted by "q", is  [#permalink]

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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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Joined: 18 Oct 2016
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Re: For how many integers, denoted by "q", is  [#permalink]

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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. Math Expert V
Joined: 02 Sep 2009
Posts: 58442
Re: For how many integers, denoted by "q", is  [#permalink]

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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]

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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-

All the best!
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Re: For how many integers, denoted by "q", is  [#permalink]

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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.

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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