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by phoenix9801 » Mon May 07, 2012 10:40 am
Problem 6:

n= Square root (2/7+1/3+4/9+2/3+5/9+5/7+x)

In the equation above, if n is an integer, which of the following could be a possible value of x?

Indicate all such values:

A) 0
B) 2/63
C) 1
D) 65/63
E) 4

the way I solved it was reorder the fractions as follows

n = Square root ((1/3+2/3)+(3/7+5/7)+(4/9+5/9)+x) =
n = Square root (1+1+1+x)
n = Square root (3+x)

But the problem for me is i do not know what to do next? to answer the chooses.
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Last edited by phoenix9801 on Mon May 07, 2012 2:32 pm, edited 1 time in total.
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by jrakhe » Mon May 07, 2012 12:22 pm
As per your solution if X=1 then n will be 2 which is an integer.
So answer is X=1 :)
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by phoenix9801 » Mon May 07, 2012 1:07 pm
Can you explain in detail please how to get from n= Square root(3+x) to x = 1 ????
jrakhe wrote:As per your solution if X=1 then n will be 2 which is an integer.
So answer is X=1 :)
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by phoenix9801 » Tue May 08, 2012 6:58 am
Can Anyone help me for further explanation in greater detail please.
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by gmacpup » Tue May 08, 2012 8:08 am
phoenix,
your working is correct, got to test it with the available options.
Say, Sqr root of (3+X)

first, substitute 0 for X which would be SR of 3 - not an integer.
second value, x=2/65 results in 3 + 0.0(value) - again not an integer
if x=1, then SR of 3+1=4 is 2 - an integer.
Hence the answer is 1.
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by Stuart@KaplanGMAT » Tue May 08, 2012 11:07 am
phoenix9801 wrote:Can you explain in detail please how to get from n= Square root(3+x) to x = 1 ????
From the question stem, we know that n is an integer. Accordingly, we know that sqrt(3+x) is an integer. What numbers have roots that are integers? Perfect squares.

Consequently, (3+x) must be a perfect square, i.e. 1, 4, 9, 16, 25, 36, ...

Now we just need to plug in each answer to see which ones give us perfect squares (on the GMAT you'll never see "indicate all such values" questions - is this a GRE question? Please always indicate the source!).

A) 3+0 = 3... not a perfect square.
B) 3+ (2/63) = fraction... not a perfect square.
C) 3 + 1 = 4... ding ding ding!
D) 3 + 65/63 = fraction... not a perfect square.
E) 3 + 4 = 7... not a perfect square.

Only (C) gives us a perfect square: choose C!
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