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What is the greatest possible value of X?

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What is the greatest possible value of X?

by Mormuse » Thu Nov 21, 2013 7:58 am
1) X is an integer
2) 6<x<7



the solution is both statement are needed. Why statement 2 isn't sufficient by itself? i mean in that case the greatest possible value of x = 6,9 since nothing in the problem says that x has to be an integer? I obviously miss something here. please help, anyone.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Nov 21, 2013 8:01 am
claudayst wrote:1) X is an integer
2) 6<x<7

the solution is both statement are needed. Why statement 2 isn't sufficient by itself? i mean in that case the greatest possible value of x = 6,9 since nothing in the problem says that x has to be an integer? I obviously miss something here. please help, anyone.
thx
Are you sure you transcribed the question correctly?
In Data Sufficiency questions, the two statements won't contradict each other as they do here.
If x is an integer (statement 1) then it can't be the case that 6 < x < 7 (statement 2)

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by Mormuse » Thu Nov 21, 2013 8:04 am
sorry, i meant for statement 2: 6<x<8...
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by Brent@GMATPrepNow » Thu Nov 21, 2013 8:10 am
claudayst wrote:1) X is an integer
2) 6<x<7



the solution is both statement are needed. Why statement 2 isn't sufficient by itself? i mean in that case the greatest possible value of x = 6,9 since nothing in the problem says that x has to be an integer? I obviously miss something here. please help, anyone.
thx
Your question about whether or not statement 2 is sufficient is a little too esoteric for the GMAT.
You suggest that 6.9 is the greatest possible value of x, but 6.99 is greater than 6.9.
And 6.999 is greater than 6.99
And 6.9999 is greater than 6.999
etc.

Given this, someone might conclude that if 6 < x < 7, then the greatest possible value of x is 6.99999 repeating indefinitely.
HOWEVER, 6.9999999... is actually EQUAL TO 7 (this is where things get pretty esoteric)

How can 6.9999999... be EQUAL to 7?
Well, if they're NOT equal, then there must exist some number BETWEEN these two values.
In other words, there must be some number k such that 6.9999... < k < 7
What would that number be?
Since there can be no such number BETWEEN 6.999.... and 7, we must conclude that the two values are equal.

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Brent
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by Brent@GMATPrepNow » Thu Nov 21, 2013 8:19 am
claudayst wrote:sorry, i meant for statement 2: 6<x<8...
That's fine, but my points about statement 2 remain (except now we're talking about whether or not 7.999... is the greatest value of x)

Bottom line: You will not be tested on this concept.

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