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# If x is an integer, which of the following is a possible value of (x²

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Math Expert
Joined: 02 Sep 2009
Posts: 60480
If x is an integer, which of the following is a possible value of (x²  [#permalink]

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21 Aug 2015, 05:07
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Difficulty:

65% (hard)

Question Stats:

61% (02:12) correct 39% (02:25) wrong based on 190 sessions

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If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

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Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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21 Aug 2015, 07:48
4
1
x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer

Answer choice D seems to fit
##### General Discussion
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Joined: 01 Jul 2015
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Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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21 Aug 2015, 08:14
1
This question is actually testing the test taker's knowledge about property of number "9".
Any number, which is not divisible by 9, if divided by 9, the remainder repeats after decimal infinetely.
This property matches with option "D".
It is 41/9, which after multiplied with 9 leaves 41. Hence forming a quadratic equation X^2+2x-48=0, whose factors can be derived -> X=-8 or X=6
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If x is an integer, which of the following is a possible value of (x²  [#permalink]

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21 Aug 2015, 08:19
2
Convert to fraction and multiply by 9, if you get an integer, then you've the solution.
As only one answer is correct, if I prove one to be correct, I have the solution.

For repeating decimals - I tried in order -
C)
a = 1.166
10a = 11.666 -- i
100a = 116.6666 -- ii

ii - i
90a = 105
a = 105/90
a*9 = 105/10 = 10.5 - not an answer

D)
x = 4.555
10x = 45.5555
9x = 41
x= 41/9
x*9 = 41 -- can be the answer

putting back in original equation we get x = 6,-8 as possible solutions. So this is the correct answer.

Rest of all can be tested simply by converting them into fractions.

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Posts: 60480
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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23 Aug 2015, 12:11
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

We don’t have to start plugging in. We know that when divided by 9, the remainder will be a number repeating to the right of the decimal place. Only choice (D) fits that description.
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Posts: 60480
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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23 Aug 2015, 12:13
Bunuel wrote:
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

We don’t have to start plugging in. We know that when divided by 9, the remainder will be a number repeating to the right of the decimal place. Only choice (D) fits that description.

As nominator is an integer and denominator equals to 9, their division will result either integer or the repeating decimal (A, B, E are out). Plus repeating decimal will be one digit long (eg 111... or 333... not 123123...) and right after the decimal point (C out).

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 the 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 D offers such number.
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Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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31 Aug 2015, 20:09
Solution : Let's try and see if we can get a pattern upon division of an integer by 9.

Trying 1/9 : 1/9 = 0.111111...

So, for any x by 9, the decimal part will be a multiple of 0.111111... That leaves us only with option D
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If x is an integer, which of the following is a possible value of (x²  [#permalink]

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25 Oct 2015, 10:21
1
a more rapid approach is understanding that x/9 will yield 0.xxxxxx repeating. Only D has this pattern, so D is the answer choice.
if to try, we can pick up x=6, 36+12-7 = 41/9 and this is equal to 4.55555 repeating.

we can as well notice that in C, the repeating decimal is 1666666.., this is clearly 1/6, but from the given fraction, we cannot get to smth/6.
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Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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15 Oct 2017, 09:07
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

Short cut to this is the know number properties from the arithmetic section. Number not-nine is divided by nine, its digits repeat infinitely. Knowing this, focus on options c, d.

For option c, let x = 4. 16 + 8 - 7 /9 = 17/9 = 1 8/9 = 1.888; therefore, eliminate option d

let x = 6; 41/9 = 4 5/9 = 4.555
Thus, the answer is D) 4.555
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Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

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03 Jun 2019, 03:14
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Re: If x is an integer, which of the following is a possible value of (x²   [#permalink] 03 Jun 2019, 03:14
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