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Possible value!

by GmatKiss » Sun Oct 16, 2011 8:48 am
If x is an integer, which of the following is a possible value of (x² +2x - 7)/9?

A. 0.268

B. 4.555 repeating

C. -2.4

D. 1.166 repeating

E. 8.125
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by Abhishek009 » Sun Oct 16, 2011 9:10 am
GmatKiss wrote:If x is an integer, which of the following is a possible value of (x² +2x - 7)/9?

A. 0.268

B. 4.555 repeating

C. -2.4

D. 1.166 repeating

E. 8.125
Is it 4.55 ?
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by Anurag@Gurome » Sun Oct 16, 2011 9:13 am
GmatKiss wrote:If x is an integer, which of the following is a possible value of (x² + 2x - 7)/9?
We can discard options A, C, and E as dividing any integer by 9 will either result in an integer or a repeating decimal.

Now, 1.1666... is a possible value of the expression then,
--> (x² + 2x - 7)/9 = 1.1666... = 4/3
--> (x² + 2x - 7) = 12
--> (x² + 2x - 19) = 0

The above expression has no integral solution.
Hence, option D is not a possible value.

Therefore, option B must be the correct option.

Though not necessary, we can cross check option B as follows.
--> (x² + 2x - 7)/9 = 4.555... = 41/9
--> (x² + 2x - 7) = 41
--> (x² + 2x - 48) = 0
--> (x - 6)(x + 8) = 0

Hence, for x = -6 and x = 8, the expression will have the value 4.555...
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