If z=(m + m/3)(n+2/(n^(-1)) and mn#0, what is the value of Z?

You need to simplify the given expression for z --->


\(z=\frac{m+\frac{m}{3}}{n+\frac{2}{n^{-1}}\) ---> \(z=\frac{\frac{4m}{3}}{3n} = \frac{4m}{9n}\). Thus any statement that gives us the value for the ratio m/n should be sufficient.

Per statement 1, m = 15n. exactly what we need. If you plug this into the expression for z, you get, z = 20/3. Sufficient.

Per statement 2, m =5. No information about n. Clearly not sufficient.

A is thus the correct answer.

Hope this helps.

P.S.: Do note that \(\frac{2}{n^{-1}\) = 2/n^(-1) and NOT 2/(n-1)
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Hi! How does \({n+\frac{2}{n^{-1}}\) become 3n?

Because it is \(n+2/(n^{-1})\)and NOT \(n+2/(n-1)\) as you might be treating it. This is a limitation of the display.

As \(n^{-1}\) = \(1/n\) and \(2/n^{-1} = 2n\) ---> \(n+2/(n^{-1})\) = \(n+2n=3n\).

Hope this helps.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


If z=(m + m/3)(n+2/(n^(-1)) and mn#0, what is the value of Z?

(1) m=15/n−1
(2) m=5


When you modify the original condition and the question, they become z=4m/9n?. In 1), m/n=15 is derived from m=15n, which is sufficient. Therefore, the answer is A.


 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.

Thank you for a nice question, though is it possible to edit the question and clarify that this part is 2/n^(-1) and NOT 2/(n-1) to avoid any confusion.

had the same problem, on my screen it looked like (n-1)
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Bunuel, IanStewart, ccooley, VeritasKarishma,
Hi Expert,
We know that statements of DS don't tell a lie!
In statement 2, the value of m is 5. Whatever it is going with question stem and statement 1, it is always true that m=5 is 100% true. I mean m MUST have a value in statement 1, too (which should be m=5 too).
From question stem it seems that
z=\(\frac{4m}{9n}\)
From statement 1, m=15n
IF we put the value of m=15n in the question stem we get z=\(\frac{20}{3}\), right?
So, if we put z=\(\frac{20}{3}\) in the question stem or in z=\(\frac{4m}{9n}\), HOW can we get m=5 in statement 1 (as statement 2 is NOT a liar !)?
Thanks__
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Yes, DS statements do not contradict each other.
m = 5 should be compatible with statement 1 too.
Statement 1 tells us that m = 15n. Here m can be 5 (and in that case n = 1/3) and z will be 20/3 (all good).
Just that you do not need to know the actual value of m since statement 1 gives you that m/n = 15 which directly gives us z = 20/3.
Stmnt 1 and stmnt 2 are compatible.

Thank you so much VeritasKarishma
This one is NOT YES/NO question; this one is "value" (what is the value of 'Z'?) question, right? In this question, the value of 'Z' is \(\frac{20}{3}\) (applying statement 1). As we get an specific value (\(\frac{20}{3}\)), it is sure that the correct choice is definitely A (as statement 2 does not make sense). To get this value (\(\frac{20}{3}\)), the value of "m" could be 10 when the value of "n" is \(\frac{2}{3}\). So, why don't we consider m=10? Don't you think that these statements are contradicting each other?
Note: The value of 'n' is NOT specific in this question. So, we can consider m=10, too.
Thanks__
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