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# If x is an integer, and 169 < x^2 < 324, which of the following is the

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If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 01:27
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If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0

(B) 61

(C) 62

(D) 75

(E) 93

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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 01:37
Quote:
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

x could take values -14,-15,-16,-17,17,16,15, and 14
The sum of all the values which satisfy this inequality is 0.
The reason for this is the negative numbers cancel out the positive terms.

0(Option A) is the correct answer
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If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 01:39
Bunuel wrote:
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0

(B) 61

(C) 62

(D) 75

(E) 93

$$169 < x^2 < 324$$

$$(-13)^2$$ or $$13^2 < x^2 < (-18)^2$$ or $$18^2$$

Therefore $$x$$ could be $$= -14, 14,-15, 15,-16, 16,-17, 17$$

Sum of all possible values of $$x = -14 + 14 -15 + 15 -16 + 16 -17 + 17 = 0$$

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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 01:43
Its 62, Option C.
Lower limit is 169 = 13^2, upper limit is 324 = 18^2.
So possible values between limits are 14,15,16,17 and sum of these is 62.
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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 04:39
Bunuel wrote:
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0

(B) 61

(C) 62

(D) 75

(E) 93

169 < x^2 < 324
=> 13^2 < x^2 < 18^2

X can take values 14, 15 , 16 , 17 and - 14 , -15 , -16 , -17
Sum = 0

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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 06:13
Bunuel wrote:
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0

(B) 61

(C) 62

(D) 75

(E) 93

Hi...
since x is an integer and it has an EVEN power, don't get into calculation ..
ans is 0, as every positive value of x will have a corresponding similar negative value. these will cancel out when added..

so finally ans will be ZERO..
A
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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 06:36
X can take 14,15,16,17 and -14,-15,-16,-17. So summation equals to zero.
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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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01 Aug 2017, 07:01
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

This question is logical and answering it should not take more than 30 sec.
169 < x^2 < 324, means 13<X<18 or -18<X<-13

means X will take same positive and negative values . Hence addition of all values = 0
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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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02 Aug 2017, 13:28
Bunuel wrote:
If x is an integer, and 169 < x^2 < 324, which of the following is the sum of all possible values of x?

(A) 0

(B) 61

(C) 62

(D) 75

(E) 93

We are given that 169 < x^2 < 324. That is, 13 < |x| < 18. If x is positive, x = 14, 15, 16, 17. If x is negative, x = -14, -15, -16, -17. We see that for every positive value of x, the opposite (or negative) is also a possibility. Thus, the sum of all values of x will be zero.

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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the  [#permalink]

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08 Aug 2017, 20:42
Okay.
The possible values of x =>
14,-14
15,-15
16,-16
17,-17

Hence sum => Zero.

The presence of zero in the options signifies that this is a Novel question...

Best
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Re: If x is an integer, and 169 < x^2 < 324, which of the following is the   [#permalink] 08 Aug 2017, 20:42
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