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# Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r

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Math Expert
Joined: 02 Sep 2009
Posts: 59561
Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r  [#permalink]

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11 Nov 2019, 04:08
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71% (01:22) correct 29% (00:53) wrong based on 21 sessions

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Is $$p > q$$ ?

(1) $$p + r > q + s$$ and $$r > s$$
(2) $$p + s < q + r$$ and $$s > r$$
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r  [#permalink]

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11 Nov 2019, 08:01
Is $$p > q$$ ?

(1) $$p + r > q + s$$ and $$r > s$$
say r=-2 and s=-3.......$$p -2> q -3......p>q-1$$ ..here p>q when p=4 and q=2 OR p<q when p=4 and q=4.5

(2) $$p + s < q + r$$ and $$s > r$$
Add $$p + s < q + r$$ and $$s > r$$....$$p + s+r < q + r+s......p<q$$
Suff as our answer is NO

B
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Re: Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r  [#permalink]

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12 Nov 2019, 08:59
Bunuel wrote:
Is $$p > q$$ ?

(1) $$p + r > q + s$$ and $$r > s$$
(2) $$p + s < q + r$$ and $$s > r$$

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 2) is equivalent to $$p > q$$ for the following reason.
Since $$r < s$$, we have $$p + r < p + s$$.
Then we have $$p + r < p + s < q + r$$ or $$p < r$$, since $$p + s < q + r$$.
Thus condition 2) is sufficient.

Condition 1)
If $$p = 2, q = 1, r = 2$$ and $$s = 1$$, then $$p > q$$ and the answer is 'yes'.
If $$p = 1, q = 2, r = 100$$ and $$s = 1$$, then $$p < q$$ and the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not sufficient

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Re: Is p > q ? (1) p + r > q + s and r > s (2) p + s < q + r and s > r   [#permalink] 12 Nov 2019, 08:59
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