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Which one of p + q and pq + 1 greater than the other one?

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Which one of p + q and pq + 1 greater than the other one?

by Max@Math Revolution » Fri Nov 29, 2019 12:13 am
[GMAT math practice question]

Which one of p + q and pq + 1 greater than the other one?

1) -1 < p < 1.
2) -1 < q < 1.
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Source: — Data Sufficiency |
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by deloitte247 » Sat Nov 30, 2019 1:34 pm
Statement 1: -1 < p < 1; hence, p=0
p+q = 0+q = q; and pq+1 = 0+1 = 1
The value of 'q' is unknown, so, we cannot determine if 'q' is greater than 1 or not.
Therefore, statement 1 is NOT SUFFICIENT.

Statement 2: -1 < q < 1; hence, q=0
p+q = p+0 = p; and pq+1 = 0+1 = 1
The value of 'p' is unknown, so, we cannot determine if 'p' is greater than 1 or not.
Therefore, statement 1 is NOT SUFFICIENT.

Combining both statements together:
-1 < p < 1 ------ (1)
-1 < q < 1 ------ (2)
p=0 and q=0
Hence, (p+q) = 0+0 = 0, and (pq+1) = 0 + 1 = 1.
From the result obtained, (pq+1) > (p+q), hence, both statements combined together ARE SUFFICIENT.
Therefore, the correct option is C.

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by Max@Math Revolution » Sun Dec 01, 2019 7:41 pm
=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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.

pq + 1 - ( p + q )
= pq - p - q + 1
= (p-1)(q-1)

The question asks if (p-1)(q-1) is positive or negative.
If we have p>1, q>1 or p<1, q<1, then (p-1)(q-1) is positive.

Thus, both conditions together are sufficient, since they tell p < 1 and q < 1.

Therefore, C is the answer.
Answer: C
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