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27 May 2017, 08:37
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If k is a positive integer, is the value of x-y less than half the value of 3^k-2^k?
(1) x = 3^k-1 and y = 2^k-1
(2) k = 2
(1) x = 3^k-1 and y = 2^k-1
(2) k = 2
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27 May 2017, 20:38
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Clearly, k=2 alone is insufficient as we know nothing of x and y. Therefore, B and D choices are gone.
Let us take z = 3^k - 2^k
If x = 3^(k - 1) and y = 2^(k - 1) then
x - y = 3^k/3 - 2^k/2
= (2.3^k - 3.2^k)/6
= (2.3^k - 2.2^k - 1.2^k)/6
= 2(3^k - 2^k - 2^(k - 1))/6
= (3^k - 2^k - 2^(k - 1))/3
= (z - 2^(k - 1))/3
Since, 2^(k - 1) > 0, we get (x - y) < z. Therefore, 1st statement is sufficient alone. Answer is A.
Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Let us take z = 3^k - 2^k
If x = 3^(k - 1) and y = 2^(k - 1) then
x - y = 3^k/3 - 2^k/2
= (2.3^k - 3.2^k)/6
= (2.3^k - 2.2^k - 1.2^k)/6
= 2(3^k - 2^k - 2^(k - 1))/6
= (3^k - 2^k - 2^(k - 1))/3
= (z - 2^(k - 1))/3
Since, 2^(k - 1) > 0, we get (x - y) < z. Therefore, 1st statement is sufficient alone. Answer is A.
Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
29 May 2017, 04:45
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ankitsaroha
Clearly, k=2 alone is insufficient as we know nothing of x and y. Therefore, B and D choices are gone.
Let us take z = 3^k - 2^k
If x = 3^(k - 1) and y = 2^(k - 1) then
x - y = 3^k/3 - 2^k/2
= (2.3^k - 3.2^k)/6
= (2.3^k - 2.2^k - 1.2^k)/6
= 2(3^k - 2^k - 2^(k - 1))/6
= (3^k - 2^k - 2^(k - 1))/3
= (z - 2^(k - 1))/3
Since, 2^(k - 1) > 0, we get (x - y) < z. Therefore, 1st statement is sufficient alone. Answer is A.
Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Let us take z = 3^k - 2^k
If x = 3^(k - 1) and y = 2^(k - 1) then
x - y = 3^k/3 - 2^k/2
= (2.3^k - 3.2^k)/6
= (2.3^k - 2.2^k - 1.2^k)/6
= 2(3^k - 2^k - 2^(k - 1))/6
= (3^k - 2^k - 2^(k - 1))/3
= (z - 2^(k - 1))/3
Since, 2^(k - 1) > 0, we get (x - y) < z. Therefore, 1st statement is sufficient alone. Answer is A.
Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
I agree with you, but I think the solution is even simpler. Based on the question, I don't think x = 3^(k-1) is the correct interpretation. The author would have put brackets if he intended for "k-1" to be the exponent. The way I read it was (3^k)-1, which is what order of operations would suggest. As a result, if I plug the equations for x and y into "x-y", I get ((3^k)-1)-((2^k)-1), which can be rewritten as (3^k) - (2^k) - 1 + 1, which simplifies to (3^k) - (2^k). (3^k) - (2^k) cannot possibly 1/2 of itself. Hence, A is sufficient.
If the author intended for your interpretation, can he / she please modify the question to make it more clear?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
