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01 May 2020, 05:53
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:34) correct
30%
(01:59)
wrong
based on 60
sessions
History
Date
Time
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Not Attempted Yet
If k>0, is \(\frac{1}{k} - \frac{1}{(k+1)} < 0.05?\)
(1) k is odd
(2) k is a multiple of 9
(1) k is odd
(2) k is a multiple of 9
firas92
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01 May 2020, 06:39
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This simplifies to
Is \(\frac{k+1-k}{k(k+1)}<\frac{5}{100}\)?
Or is \(\frac{1}{k(k+1)}<\frac{1}{20}\)
Since \(k\) is positive, multiply both sides by \(20*k(k+1)\)
Is \(k(k+1)>20\)?
Or simply, is \(k>4\)?
(1) \(k\) is odd
\(k\) may be \(3\) or \(k\) may be \(5\) among many other possibilities
Not sufficient
(2) \(k\) is a multiple of \(9\)
Since \(k>0\), \(k\) is at least \(9\)
Sufficient
Answer is (B)
Posted from my mobile device
Is \(\frac{k+1-k}{k(k+1)}<\frac{5}{100}\)?
Or is \(\frac{1}{k(k+1)}<\frac{1}{20}\)
Since \(k\) is positive, multiply both sides by \(20*k(k+1)\)
Is \(k(k+1)>20\)?
Or simply, is \(k>4\)?
(1) \(k\) is odd
\(k\) may be \(3\) or \(k\) may be \(5\) among many other possibilities
Not sufficient
(2) \(k\) is a multiple of \(9\)
Since \(k>0\), \(k\) is at least \(9\)
Sufficient
Answer is (B)
Posted from my mobile device
07 May 2020, 04:31
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We know that k>0, so k is positive.
The question stem, “Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05?” can be simplified in the following way:
Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05? Note than 0.05 can be substituted by \(\frac{1}{20}\). Therefore,
Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < \(\frac{1}{20}\)?
The LCM of the terms on the LHS is k(k+1). Taking the LCM and simplifying, we have,
Is \(\frac{(k+1) – k }{ k(k+1)}\) < \(\frac{1}{20}\)? OR
Is \(\frac{1}{k(k+1)}\) < \(\frac{1}{20}\)?
Since k is positive, k(k+1) is positive. Therefore, we can directly cross multiply the terms in the inequality. So,
Is k(k+1)>20? OR
“Is k>4?” becomes our question now
.
From statement I alone, k is odd. Knowing k is odd is not sufficient to know whether k>4.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, k is a multiple of 9. Although 0 is also a multiple of 9, the question data has made our life easier by telling us that k>0. Therefore, the possible values of k = 9, 18,27 and so on. Clearly, in all these cases, k>4.
In other words, in all these cases, \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05.
Statement II alone is sufficient to obtain a definite YES to the question asked. Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
The question stem, “Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05?” can be simplified in the following way:
Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05? Note than 0.05 can be substituted by \(\frac{1}{20}\). Therefore,
Is \(\frac{1}{k} – \frac{1}{(k+1)}\) < \(\frac{1}{20}\)?
The LCM of the terms on the LHS is k(k+1). Taking the LCM and simplifying, we have,
Is \(\frac{(k+1) – k }{ k(k+1)}\) < \(\frac{1}{20}\)? OR
Is \(\frac{1}{k(k+1)}\) < \(\frac{1}{20}\)?
Since k is positive, k(k+1) is positive. Therefore, we can directly cross multiply the terms in the inequality. So,
Is k(k+1)>20? OR
“Is k>4?” becomes our question now
.
From statement I alone, k is odd. Knowing k is odd is not sufficient to know whether k>4.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, k is a multiple of 9. Although 0 is also a multiple of 9, the question data has made our life easier by telling us that k>0. Therefore, the possible values of k = 9, 18,27 and so on. Clearly, in all these cases, k>4.
In other words, in all these cases, \(\frac{1}{k} – \frac{1}{(k+1)}\) < 0.05.
Statement II alone is sufficient to obtain a definite YES to the question asked. Answer options C and E can be eliminated.
The correct answer option is B.
Hope that helps!
