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# * represents a certain function for all real numbers. If (1*)*=6

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Intern
Joined: 08 Sep 2018
Posts: 1
* represents a certain function for all real numbers. If (1*)*=6  [#permalink]

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Updated on: 08 Sep 2018, 12:30
2
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:11) correct 27% (01:56) wrong based on 22 sessions

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* represents a certain function for all real numbers. If (1*)* = 6, which of the following could be true for all values of m?

(A) m*= 2m$$^3$$
(B) m* = m(m+1)
(C) m* = (2m)$$^3$$
(D) m* = 3m$$^2$$
(E) m* = m(m-1)(m+1)

Does anyone knows how to solve this question? I have tried to solved and unserstand it but it is not making any sence to me! I know the answer but even like that I just don´t understand it.Thank you for your help!

Originally posted by FilipaFontao on 08 Sep 2018, 02:47.
Last edited by generis on 08 Sep 2018, 12:30, edited 2 times in total.
Edited and formatted the question, renamed the topic
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Re: * represents a certain function for all real numbers. If (1*)*=6  [#permalink]

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08 Sep 2018, 05:07
2
FilipaFontao wrote:
"*" represents a certain function for all real numbers. If (1*)* = 6, which of the following could be true for all values of m?

(A) m*= 2m^3
(B) m* = m(m+1)
(C) m* = (2m)^3
(D) m* = 3m^2
(E) m* = m(m-1)(m+1)

Does anyone knows how to solve this question? I have tried to solved and unserstand it but it is not making any sence to me! I know the answer but even like that I just don´t understand it.

Here the '*' represents a function.
Given, (1*)* = 6 implies that the function under discussion has been applied twice on the real number 1 and the result is 6.

Since it is a COULD BE TRUE type question, we have to analyze each of the options till we arrive at the correct answer.

A. m*= $$2m^3$$
Our only reference in hand is (1*)* = 6.-----------(a)
Let's put m=1, then 1*=2(1^3)=2---------------(b)
Let's apply '*' function again, we have (1*)*=2* (Since 1*=2 from (b))
Now, 2*=$$2(2^3)=8\neq{6}$$ (DISCARD)

B. m* = m(m+1)
Put m=1, we have
1*=1(1+1)=2
Let's apply '*' function again, we have (1*)*=2* (Since 1*=2 from (b))
Now, 2*=2(2+1)=6.
So, (1*)*=2*=6 (MATCHED)

Ans. (B)

P.S:- We have tried m=1 since we have given (1*)*=6.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: * represents a certain function for all real numbers. If (1*)*=6 &nbs [#permalink] 08 Sep 2018, 05:07
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# * represents a certain function for all real numbers. If (1*)*=6

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