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GRE Math Challenge #40-For all number n
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Updated on: 18 Feb 2020, 13:04
Updated on: 18 Feb 2020, 13:04
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Question Stats:
69% (00:39) correct
30% (00:47) wrong based on 101 sessions
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For all numbers n, \(n* = 32-n\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\( (n*)*\) |
\(n\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #40
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12 Apr 2015, 06:32
12 Apr 2015, 06:32
sandy wrote:
------------------------------------------------------------
For all numbers n, n* = 32-n
column A: (n*)*
column B: n
For all numbers n, n* = 32-n
column A: (n*)*
column B: n
-------------------------------------------------------------
This kind of question (which I call a Strange Operator question) looks tricky, so let's see what happens when we plug in some values of n.
Try n = 0
column A: (n*)* = (32 - 0)* = 32* = 32 - 32 = 0
column B: n = 0
Here, the two columns are equal.
Try n = 10
column A: (n*)* = (32 - 10)* = 22* = 32 - 22 = 10
column B: n = 10
Here, the two columns are equal.
Try n = 33
column A: (n*)* = (32 - 33)* = (-1)* = 32 - (-1) = 33
column B: n = 33
Here, the two columns are equal.
Try n = -5
column A: (n*)* = (32 - -5)* = 37* = 32 - (37) = -5
column B: n = -5
Here, the two columns are equal.
Well, it certainly seems like the two columns are always equal.
So, let's go with answer choice
Show: ::
C
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
GRE Math Challenge #40-For all number n
[#permalink]
12 Apr 2015, 06:37
12 Apr 2015, 06:37
sandy wrote:
------------------------------------------------------------
For all number n, n* = 32 - n
column A: (n*)*
column B: n
For all number n, n* = 32 - n
column A: (n*)*
column B: n
-------------------------------------------------------------
Here's an algebraic solution:
column A: (n*)*
First let's examine the part in the brackets: n*
This we are told is equal to 32 - n
So, (n*)* = (32 - n)*
= 32 - (32 - n)
= n
Aha, so (n*)* ALWAYS EQUALS n.
So, we really have:
column A: (n*)* = n
column B: n
The two columns are always equal.
Answer:
Show: ::
C
Cheers,
Brent
