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04 Mar 2022, 08:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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44% (02:36) correct
56%
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Let a be the sum of x consecutive positive integers. Let b be the sum of y consecutive positive integers. For which of the following values of x and y is it NOT possible that a =b?
(A) x = 2; y = 6
(B) x = 3; y = 6
(C) x = 6; y = 4
(D) x = 6; y = 7
(E) x = 7; y = 5
Are You Up For the Challenge: 700 Level Questions
(A) x = 2; y = 6
(B) x = 3; y = 6
(C) x = 6; y = 4
(D) x = 6; y = 7
(E) x = 7; y = 5
Are You Up For the Challenge: 700 Level Questions
PyjamaScientist
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04 Mar 2022, 14:02
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Let's dive into option choices.
A. \(x = 2; y = 6\)
\(x = 2\); If I have two consecutive no.s one will be even and the other will be odd thus it's sum would be ODD.
\(y = 6\); I will have three odd no.s and three even no.s. Sum of 3 odds no.s is odd. Sum of 3 even no.s is even. Combined sum would be ODD. Thus, Thus \(a\) and \(b\) can be equal.
B. \(x = 3; y = 6\)
\(x = 3\) For three consecutive no.s two can be odd and can be even giving the sum EVEN OR it can be two even and one odd and thus the sum will be ODD. Both possibilities are there.
\(y = 6\) Same as first option. Sum will be ODD. Thus \(a\) and \(b\) can be equal.
C. \(x = 6; y = 4\)
x=6 Sum will be ODD. Refer above.
y = 4 For four consecutive no.s there will be 2 odd no.s and 2 even no.s. Thus the sum will be EVEN.
Here \(a \) and \(b\) can NOT be equal, and thus this is our answer.
You can similar check for other answer choices and eliminate then with the same logic used above.
A. \(x = 2; y = 6\)
\(x = 2\); If I have two consecutive no.s one will be even and the other will be odd thus it's sum would be ODD.
\(y = 6\); I will have three odd no.s and three even no.s. Sum of 3 odds no.s is odd. Sum of 3 even no.s is even. Combined sum would be ODD. Thus, Thus \(a\) and \(b\) can be equal.
B. \(x = 3; y = 6\)
\(x = 3\) For three consecutive no.s two can be odd and can be even giving the sum EVEN OR it can be two even and one odd and thus the sum will be ODD. Both possibilities are there.
\(y = 6\) Same as first option. Sum will be ODD. Thus \(a\) and \(b\) can be equal.
C. \(x = 6; y = 4\)
x=6 Sum will be ODD. Refer above.
y = 4 For four consecutive no.s there will be 2 odd no.s and 2 even no.s. Thus the sum will be EVEN.
Here \(a \) and \(b\) can NOT be equal, and thus this is our answer.
You can similar check for other answer choices and eliminate then with the same logic used above.
General Discussion
rajshreeasati
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23 May 2022, 04:55
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PyjamaScientist thanks for this approach. Its much more efficient than my approach. I used the more algebraic approach and then by taking the Sum in an AP sequence, but it took a lot of time.
Also, just a quick tip which I read in Kaplan- when going through options, start backwards from E to A. More often than not, the GMAT hides the Answer to "the following" type questions in these options. Majority of times, it turns out to be D or E.
Anyways, thanks!
Also, just a quick tip which I read in Kaplan- when going through options, start backwards from E to A. More often than not, the GMAT hides the Answer to "the following" type questions in these options. Majority of times, it turns out to be D or E.
Anyways, thanks!
