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12 Nov 2022, 09:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
44% (02:01) correct
56%
(01:27)
wrong
based on 39
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(m > n\) ?
(1) \(\frac{m}{n} > 1\)
(2) \(\frac{m - n}{n} > \frac{m - n}{m}\)
(1) \(\frac{m}{n} > 1\)
(2) \(\frac{m - n}{n} > \frac{m - n}{m}\)
12 Nov 2022, 10:19
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We need to find if m > n
STAT 1: \(\frac{m}{n} > 1\)
By taking numbers we can easily prove that this option is not sufficient
m = 3, n = 2
=> \(\frac{m}{n}\) = \(\frac{3}{2}\) = 1.5 > 1 and m > n too
m = -3, n = -2
=> \(\frac{m}{n}\) = \(\frac{-3}{-2}\) = 1.5 > 1 BUT m < n
=> NOT SUFFICIENT
STAT 2: \(\frac{m - n}{n} > \frac{m - n}{m}\)
Taking all terms to left hand side we get
\(\frac{m - n}{n} - (\frac{m - n}{m})\) > 0
=> \(\frac{m^2 - n*m - m*n + n^2}{mn})\) > 0
=> \(\frac{m^2 - 2mn + n^2}{mn})\) > 0
=> \(\frac{(m - n)^2}{mn})\) > 0
Now we know that \((m- n)^2\) is non-negative as it is square of a number and will not be equal to 0 also as the expression is > 0
=> \((m- n)^2\) is positive
And we know that if \(\frac{A}{B}\) > 0 and A> 0 then B will also be > 0
=> mn > 0
=> m and n have the same sign
=> EITHER both are positive or both are negative.
But this still doesn't solve the problem as we can take the same cases as the first one to prove it insufficient.
=> NOT SUFFICIENT
Take both the statement together also we have the same problem as we can still use
m = 3, n = 2 and
m = -3 and n = - 2 to prove them insufficient
=> NOT SUFFICIENT
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Inequality Problems
STAT 1: \(\frac{m}{n} > 1\)
By taking numbers we can easily prove that this option is not sufficient
m = 3, n = 2
=> \(\frac{m}{n}\) = \(\frac{3}{2}\) = 1.5 > 1 and m > n too
m = -3, n = -2
=> \(\frac{m}{n}\) = \(\frac{-3}{-2}\) = 1.5 > 1 BUT m < n
=> NOT SUFFICIENT
STAT 2: \(\frac{m - n}{n} > \frac{m - n}{m}\)
Taking all terms to left hand side we get
\(\frac{m - n}{n} - (\frac{m - n}{m})\) > 0
=> \(\frac{m^2 - n*m - m*n + n^2}{mn})\) > 0
=> \(\frac{m^2 - 2mn + n^2}{mn})\) > 0
=> \(\frac{(m - n)^2}{mn})\) > 0
Now we know that \((m- n)^2\) is non-negative as it is square of a number and will not be equal to 0 also as the expression is > 0
=> \((m- n)^2\) is positive
And we know that if \(\frac{A}{B}\) > 0 and A> 0 then B will also be > 0
=> mn > 0
=> m and n have the same sign
=> EITHER both are positive or both are negative.
But this still doesn't solve the problem as we can take the same cases as the first one to prove it insufficient.
=> NOT SUFFICIENT
Take both the statement together also we have the same problem as we can still use
m = 3, n = 2 and
m = -3 and n = - 2 to prove them insufficient
=> NOT SUFFICIENT
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Inequality Problems
13 Nov 2022, 08:05
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The question requires us to find if m lies to the right of n when plotted over a number line.
Statement 1
Once we bring all the terms to one side of the equation we will get
\(\frac{m-n}{n }> 0\)
Two possible cases can result
As the statement is not sufficient to nail down a particular case we can eliminate A and D.
Statement 2
Once we bring all terms to one side of the equation, the only information that we get to know is m and n are of the same sign. However the statement doesn't provide any information to identify the relative position of the two variables. Hence the statement is not sufficient and we can eliminate B.
Combined
The statements combined provide no additional information as we already know from statement 1 that m and n have same sign. Hence combination of the statement does not help. We can eliminate C.
Option E
The detail working is attached.
Statement 1
Once we bring all the terms to one side of the equation we will get
\(\frac{m-n}{n }> 0\)
Two possible cases can result
- m lies to the right of n and both lie to the right of 0
- n lies to the right of m and both lie to the left of 0.
As the statement is not sufficient to nail down a particular case we can eliminate A and D.
Statement 2
Once we bring all terms to one side of the equation, the only information that we get to know is m and n are of the same sign. However the statement doesn't provide any information to identify the relative position of the two variables. Hence the statement is not sufficient and we can eliminate B.
Combined
The statements combined provide no additional information as we already know from statement 1 that m and n have same sign. Hence combination of the statement does not help. We can eliminate C.
Option E
The detail working is attached.
Attachments
Screenshot 2022-11-13 202621.png [ 116.15 KiB | Viewed 1704 times ]
