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Updated on: 28 Mar 2019, 01:21
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.
Last edited by EgmatQuantExpert on 28 Mar 2019, 01:21, edited 1 time in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:41) correct
20%
(01:44)
wrong
based on 318
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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
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
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
Archit3110
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
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
