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25 Dec 2009, 13:22
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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
A. 0.268
B. 4.555 repeating
C. -2.4
D. 1.166 repeating
E. 8.125
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25 Dec 2009, 13:51
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We know from the repeating decimals section of the GmatClub mathbook that for repeating decimal, divide the repetition by 9 or 99 ... depending on the number of repeating numbers.
Here I would try fitting in the numbers.
Since there is just one 9 in the denominator, 4.5555 .. is my first suspect.
To get it I need 5/9
The expression in question can be written as
\((x^2+2x-7-5+5)/9\)
which is
\((x^2+2x-12)/9+5/9\) = \((x^2+2x-12)/9\) + 0.555555..
see is \((x^2+2x-12)/9\) can be solvable for value = 4
\((x^2+2x-12)/9=4\)
\((x^2+2x-12)=36\)
\(x^2+2x-48=0\)
\((x-6)(x+8)=0\) integer roots 6 and -8
s0 4.55555... is possible
There should be another way to solve this as well.
Ans is B
Here I would try fitting in the numbers.
Since there is just one 9 in the denominator, 4.5555 .. is my first suspect.
To get it I need 5/9
The expression in question can be written as
\((x^2+2x-7-5+5)/9\)
which is
\((x^2+2x-12)/9+5/9\) = \((x^2+2x-12)/9\) + 0.555555..
see is \((x^2+2x-12)/9\) can be solvable for value = 4
\((x^2+2x-12)/9=4\)
\((x^2+2x-12)=36\)
\(x^2+2x-48=0\)
\((x-6)(x+8)=0\) integer roots 6 and -8
s0 4.55555... is possible
There should be another way to solve this as well.
Ans is B
25 Dec 2009, 13:59
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prasadrg
As nominator is an integer and denominator equals to 9, their division will result either integer or the repeating decimal (A, C, E are out). Plus repeating decimal will be one digit long (eg 111... or 333... not 123123...) and right after the decimal point (D out).
Answer: B.
To elaborate further: we have \(\frac{integer}{9}\), don't get trapped by the expression x^2+2x-7. What is important here is that numerator will be integer as x is an integer.
\(\frac{integer}{9}\) can be either an integer 18/9=2, 27/9=3 ... or repeating decimal of the form k.aaaa..., where k is an integer >=0 and a is <9. Only B offers such number.
