If $-0.5 < p < 0.5 < q < 2$, which of the followin... | Free GMAT Practice Question | GMAT Panda

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If - 0.5 < p < 0.5 < q < 2, which of the following must be less than 1? I. p + q II. pq III. \frac{q}{p}

Explanation	Calculations	Help
$We know "p<0.5" and "q<2" . Using "Adding Two Inequalities", we add them to get "p+q<2.5", which is greater than 1, so "p+q" is not always less than 1.$	$p < 0.5 q < 2 p + q < 2.5 2.5 > 1$	Theory & Tactics Method Card INEQ1-D Click to view full details
$We know "p<0.5" and "q>0" . Using "Multiplying/Dividing Inequalities by Positive", we get "pq<0.5q" . Since "q<2", applying "Multiplying/Dividing Inequalities by Positive" again gives "0.5q<1", and thus "pq<1" for all permissible values of p and q .$	$p < 0.5 q > 0 pq < 0.5 q q < 2 0.5 q < 1 pq < 1$	Theory & Tactics Method Card INEQ1-A Click to view full details
$We test sample values, for example "p=0.4" and "q=1" . Then we calculate \frac{q}{p} which equals 2.5 > 1, so "q/p" is not always less than 1.$	$p = 0.4 q = 1 \frac{q}{p} = 2.5 > 1$

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B

If - 0.5 < p < 0.5 < q < 2, which of the following must be less than 1? I. p + q II. pq III. \frac{q}{p}

Explanation	Calculations	Help
$We know "p<0.5" and "q<2" . Using "Adding Two Inequalities", we add them to get "p+q<2.5", which is greater than 1, so "p+q" is not always less than 1.$	$p < 0.5 q < 2 p + q < 2.5 2.5 > 1$	Theory & Tactics Method Card INEQ1-D Click to view full details
$We know "p<0.5" and "q>0" . Using "Multiplying/Dividing Inequalities by Positive", we get "pq<0.5q" . Since "q<2", applying "Multiplying/Dividing Inequalities by Positive" again gives "0.5q<1", and thus "pq<1" for all permissible values of p and q .$	$p < 0.5 q > 0 pq < 0.5 q q < 2 0.5 q < 1 pq < 1$	Theory & Tactics Method Card INEQ1-A Click to view full details
$We test sample values, for example "p=0.4" and "q=1" . Then we calculate \frac{q}{p} which equals 2.5 > 1, so "q/p" is not always less than 1.$	$p = 0.4 q = 1 \frac{q}{p} = 2.5 > 1$

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B