Hi All,
This question can be solved by TESTing VALUES.
The prompt comes with an interesting 'restriction' though. You CANNOT have a fraction of a person (e.g. 2/3 of girl, 1/8 of a boy, etc.), so we have to TEST VALUES that "fit" with the percentages that are given...
We're told that 55% of the females and 35% of the males in a class passed an exam. We're asked if MORE than half passed the exam. This is a YES/NO question.
Since we're dealing with 55% of females and 35% of males, there must be a MULTIPLE of 20 females AND a MULTIPLE of 20 males in the class. NO other possible numbers exist that will "fit" with this data. As an example, you could NOT have 2 females and 3 males, since the percents would then give us "fractions of a person."
Since 55% of 20 = 11 and 35% of 20 = 7, we now also have a "math shortcut" (we can use those multiples to save some time) that we can take advantage of. Knowing that, we can now deal with the two Facts in a more efficient way...
Fact 1: More than half of the students are FEMALE.
This is important; it tells us that we do NOT have an equal number of females and males.
IF....we have...
40 females and 20 males
22 females passed and 7 males passed
29/60 is LESS than half and the answer to the question is NO
IF....we have....
60 females and 20 males
33 females passed and 7 males passed
40/80 is EXACTLY HALF and the answer to the question is NO
IF....we have....
80 females and 20 males
44 females passed and 7 males passed
51/100 is MORE than half and the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: The number of females is 20 more than the number of males... The first TEST that we ran in Fact 1 will ALSO "fit" here:
IF....we have...
40 females and 20 males
22 females passed and 7 males passed
29/60 is LESS than half and the answer to the question is NO
IF....we have...
60 females and 40 males
33 females passed and 14 males passed
47/100 is LESS than half and the answer to the question is NO
IF....we have...
80 females and 60 males
44 females passed and 21 males passed
65/140 is LESS than half and the answer to the question is NO
From this work, you might notice how the numerator gets further and further "away" from exactly half. This is a pattern.
The answer is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer:
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Rich
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