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The integer x lies in the range – 15 < x < 15. Also, x is an odd
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Updated on: 28 Mar 2019, 01:21
Question Stats:
79% (01:45) correct 21% (01:57) wrong based on 102 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?
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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd
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28 Mar 2019, 00:15
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: \(\frac{142}{2}\)+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
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29 Mar 2019, 01:41
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 = 5649 ; 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?



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Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd
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31 Mar 2019, 22:08
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
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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
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03 Jun 2019, 14:45
(1413)+(1211)+(109)+(87)+(65)+(43)+(21)=7 We don't need any formula, if we arrange them in above pattern.




Re: The integer x lies in the range – 15 < x < 15. Also, x is an odd
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03 Jun 2019, 14:45






