Of three persons, two take relish, two take pepper, and two take salt. The one who takes no salt...

Question

Of three persons, two take relish, two take pepper, and two take salt. The one who takes no salt takes no pepper, and the one who takes no pepper takes no relish. Which of the following statements must be true? I. The person who takes no salt also takes no relish. II. Any of the three persons who takes pepper also takes relish and salt. III. The person who takes no relish is not one of those who takes salt.

GMAT Panda · Accepted Answer

E We first name the person who takes no salt as S. S = person taking no salt We translate "the one who takes no salt takes no pepper" and "the one who takes no pepper takes no relish" into mathematical form. S takes no pepper S takes no relish We note that "two take pepper", and because counts must be whole numbers, the other two persons must take pepper. Similarly, since exactly two take salt and two take relish, those same persons take both salt and relish. Number taking pepper = 2 S takes no pepper Number taking salt = 2 Number taking relish = 2 Other two persons take pepper, salt, and relish

Explanation	Calculations	Help
$We first name the person who takes no salt as S .$	$S = person taking no salt$
$We translate "the one who takes no salt takes no pepper" and "the one who takes no pepper takes no relish" into mathematical form.$	$S takes no pepper S takes no relish$
$We note that "two take pepper", and because counts must be whole numbers, the other two persons must take pepper. Similarly, since exactly two take salt and two take relish, those same persons take both salt and relish.$	$Number taking pepper = 2 S takes no pepper Number taking salt = 2 Number taking relish = 2 Other two persons take pepper, salt, and relish$

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