Question : is p > q ?
$$Statement\ :\ \frac{1}{q\ }\ <\ \frac{1}{q}$$
We have 3 possible outcomes.
-- both q and p are positive integer
$$\frac{1}{-1}\ <\ \frac{1}{2}\ =\ 1\ <\ 0.5\ \left[wrong\right]$$
-- both q and p are negative integers
$$\frac{1}{-1}\ <\ \frac{1}{-2}\ =\ -1\ <\ -0.5$$
--q = negative integer and p = positive integer
$$\frac{1}{1}\ =\ \frac{1}{-2}\ =\ \frac{1}{-1}\ =\ \frac{1}{2}\ =\ -1\ <\ 0.5$$
Statement is insufficient because not all actions proves whether p > q or not
$$Statement\ 2:\ \frac{p}{q\ }>\ 0.25$$
Therefore, 2 possible outcomes
-- both q and p are positive.
$$\frac{1}{2}>\ 0.25$$
-- both q and p are negative
$$\frac{-1}{2}>\ -0.25$$
Statement 2 is not sufficient because outcomes did not answer the questions combining statement 1 and 2 together
$$\frac{1}{q\ }\ <\ \frac{1}{p}$$
$$\frac{p}{q}\ <\ 0.25$$
If both p and q are positive integers,
P is not greater than Q.
If both p and q are negative integers,
P is also not greater than Q.
Both statement combined is sufficient to answer the question.
Answer is Option C.
Is p > q?
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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