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Updated on: 24 Aug 2019, 22:12
Originally posted by freedom128 on 20 Aug 2019, 09:04.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 7 times in total.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 7 times in total.
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D
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48% (02:11) correct
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If \(n\) is a positive integer, is the value of \(x - y\) at least three times the value of \(5^n−3^n\) ?
(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)
(2) \(n=2\), \((x+y)=32\) and \(xy=135\)
Source: adapted from OG 15
(1) \(x=5^{n-1}\) and \(y=3^{n+1}\)
(2) \(n=2\), \((x+y)=32\) and \(xy=135\)
Source: adapted from OG 15
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Updated on: 24 Aug 2019, 22:12
Originally posted by freedom128 on 20 Aug 2019, 09:13.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 13 times in total.
Last edited by freedom128 on 24 Aug 2019, 22:12, edited 13 times in total.
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(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT
(2) We can calculate the value of \((x-y)\) from:
\((x-y)^2= (x+y)^2-4xy\)
\((x-y)^2= 32^2-4*135 =484\)
\((x-y)=22\) or \(-22\).
Since three times the value of \((5^2-3^2)=16\) is always greater than both possible values of \((x-y)\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT
Answer is (D)
+1 kudo is appreciated
SUFFICIENT
(2) We can calculate the value of \((x-y)\) from:
\((x-y)^2= (x+y)^2-4xy\)
\((x-y)^2= 32^2-4*135 =484\)
\((x-y)=22\) or \(-22\).
Since three times the value of \((5^2-3^2)=16\) is always greater than both possible values of \((x-y)\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT
Answer is (D)
+1 kudo is appreciated
20 Aug 2019, 18:08
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chondro48
(1) \(x-y=5^{n-1}-3^{n+1}=3*(5^n-3^n) - \frac{14}{5}*5^n\). Since \(\frac{14}{5}*5^n > 0\), then it must be true that \(x-y < 3*(5^n-3^n)\).
SUFFICIENT
(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT
Answer is (D)
+1 kudo is appreciated =)
SUFFICIENT
(2) \(x-y=5^{n+1}-3^{n+1}=3*(5^n-3^n) + 2*5^n\). Since \(2*5^n > 0\), then it must be true that \(x-y > 3*(5^n-3^n)\).
SUFFICIENT
Answer is (D)
+1 kudo is appreciated =)
Can you please explain, how you got 14/5 or *5^n in the first equation and 2*5^n in the second?
