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190 students go to a school bake sale. 95 buy a chocolate

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190 students go to a school bake sale. 95 buy a chocolate

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Princeton Review

190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie?

A. 10
B. 24
C. 30
D. 32
E. 45

OA D.

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Hi All,

We're told that 190 students go to a school bake sale. Of those students, 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and AT LEAST 12 buy both. We're asked for the LEAST number of students who could have bought NEITHER type of cookie. This question is a variation on a standard Overlapping Sets question (although there is a 'twist'; AT LEAST 12 students bought both types of cookie), but we can still use the Overlapping Sets Formula:

Total = (1st group) + (2nd group) - (Both) + (Neither)

Based on the given information, the equation would look like this:

190 = (95) + (75) - (AT LEAST 12) + (Neither)
190 = 170 - (AT LEAST 12) + (Neither)
20 = (Neither) - (AT LEAST 12)

To minimize the "neither group", we have to make the "both" group as SMALL as possible. In this case, that would be exactly 12 people...

20 + 12 = Neither
32 = Neither

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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AAPL wrote:
Princeton Review

190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie?

A. 10
B. 24
C. 30
D. 32
E. 45
Excellent opportunity for the Venn diagram (aka overlapping sets)!



$$? = {\left( R \right)_{\min }}$$
$$R = 190 - \left( {95 + 75 - {\rm{both}}} \right) = 20 + {\rm{both}}$$
$${\rm{both}} \ge 12\,\,\,\left( {{\rm{given}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 32$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
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