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The integer x lies in the range – 15 < x < 15. Also, x is an odd

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EgmatQuantExpert
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The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   Updated on: 28 Mar 2019, 01:21
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E

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15% (low)

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81% (01:42) correct 19% (01:47) wrong based on 278 sessions
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The integer x lies in the range – 15 < x < 15. Also, x is an odd number, if it is negative, and an even number, if it is positive. What is the sum of all the possible values of x?

    A. -8
    B. -7
    C. 0
    D. 7
    E. 22

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D

Originally posted by EgmatQuantExpert on 27 Mar 2019, 23:00.
Last edited by EgmatQuantExpert on 28 Mar 2019, 01:21, edited 1 time in total.
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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   29 Mar 2019, 01:41
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values of odd; -13,-11,-9,-7,-5,-3,-1
value of even ; 2,4,6,8,10,12,14

sum of consective odd integers ; (n+1)^2/4 ; (13+1)^2/4 ; 14 * 14/ 4 = 49 -ve
sum of even consective integers ; n* (n+2) /4 ; 14* 16/4 = 56 +ve
so sum = 56-49 ; 7
IMO D

EgmatQuantExpert wrote:
The integer x lies in the range – 15 < x < 15. Also, x is an odd number, if it is negative, and an even number, if it is positive. What is the sum of all the possible values of x?

    A. -8
    B. -7
    C. 0
    D. 7
    E. 22

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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   03 Jun 2019, 14:45
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(14-13)+(12-11)+(10-9)+(8-7)+(6-5)+(4-3)+(2-1)=7
We don't need any formula, if we arrange them in above pattern.
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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   28 Mar 2019, 00:15
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I don't know if I was supposed to see any pattern or any shortcut to solve this question in 25 secs.
I used my old friend "Brute Force",
Here it is:

1) Count odd negatives:
\(\frac{-1-(-13)}{2}\)+1=7 number of possible values
\(\frac{-1+(-13)}{2}\)=-7 Average of possible values
Sum=Number*Average=-49

2) Count even positives:
\(\frac{14-2}{2}\)+1=7 number of possible values
\(\frac{14+2}{2}\)=8 Average of possible values
Sum=Number*Average=56

56+(-49)=7

IMO
Ans: D
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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   31 Mar 2019, 22:08
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Solution


Given:
    • The integer x lies in the range – 15 < x < 15.
    • x is an odd number, if it is negative.
    • x is an even number, if it is positive.

To find:
    • The sum of all the possible values of x.

Approach and Working:
If x is an odd number, then the possible values of x = (-13, -11, -9, -7, -5, -3, -1)
    • Sum of all values of x, when x is odd = -49

If x is an even number, then the possible values of x = (2, 4, 6, 8, 10, 12, 14)
    • Sum of all values of x, when x is even = 56

Therefore, sum of all possible values of x = 56 + (-49) = 7

Hence, the correct answer is option D.

Answer: D
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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd [#permalink] New post   03 Jun 2019, 01:25
Our potential negative numbers would be -13,-11,-9 ...
Our potential positive numbers would be 14,12,10 ...

As we see a pattern here we know that our sum is going to be the number of pairs, hence 7.
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Re: The integer x lies in the range 15 < x < 15. Also, x is an odd [#permalink] New post   17 Apr 2023, 03:34
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Re: The integer x lies in the range 15 < x < 15. Also, x is an odd [#permalink]
17 Apr 2023, 03:34
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