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# For how many integers, denoted by "q", is

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Manager
Joined: 23 Sep 2016
Posts: 230
For how many integers, denoted by "q", is  [#permalink]

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Updated on: 28 Mar 2018, 19:50
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Difficulty:

85% (hard)

Question Stats:

39% (01:26) correct 61% (01:17) wrong based on 137 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 15 Mar 2018, 23:29.
Last edited by Bunuel on 28 Mar 2018, 19:50, edited 1 time in total.
Edited the question.
Manager
Joined: 23 Sep 2016
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Re: For how many integers, denoted by "q", is  [#permalink]

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15 Mar 2018, 23:37
1
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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28 Mar 2018, 11:20
1
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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Joined: 02 Sep 2009
Posts: 61282
Re: For how many integers, denoted by "q", is  [#permalink]

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28 Mar 2018, 19:49
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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31 Aug 2019, 02:04
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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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
Re: For how many integers, denoted by "q", is   [#permalink] 31 Aug 2019, 02:10
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