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09 Jun 2015, 08:07
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D
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Difficulty:
55%
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Question Stats:
63% (02:00) correct
37%
(01:51)
wrong
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In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144
B. 119
C. 113
D. 88
E. 31
A. 144
B. 119
C. 113
D. 88
E. 31
09 Jun 2015, 08:07
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Bookmarks
Official Solution:
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144
B. 119
C. 113
D. 88
E. 31
First of all, notice that since 144 took geometry and 119 took biology, the number of students who took both geometry and biology cannot be greater than 119.
Therefore, the greatest possible number of students that could have taken both geometry and biology, is 119.
Next:
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
Therefore, the smallest possible number of students that could have taken both geometry and biology, is 31.
Thus, the answer is 119 - 31 = 88.
Answer: D
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144
B. 119
C. 113
D. 88
E. 31
First of all, notice that since 144 took geometry and 119 took biology, the number of students who took both geometry and biology cannot be greater than 119.
Therefore, the greatest possible number of students that could have taken both geometry and biology, is 119.
Next:
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
Therefore, the smallest possible number of students that could have taken both geometry and biology, is 31.
Thus, the answer is 119 - 31 = 88.
Answer: D
General Discussion
anuharidas
Joined: 29 Oct 2014
Last visit: 29 Sep 2016
Posts: 10
Given Kudos: 6
Schools: Molson '19
GMAT Date: 12-06-2014
12 Feb 2016, 13:53
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Bookmarks
HI Bunel,
I approached the problem the same way but eliminated the correct answer in the following grounds,
if the greatest number 0f students learning biology and geometry is 119 , how can the total be 232 ??
the total be just 144 where 119 students study both and 25 students study biology .. if that is the case the total wont be 232 ........please clarify this ambiguity .. Please make me understand where am I going wrong .
I approached the problem the same way but eliminated the correct answer in the following grounds,
if the greatest number 0f students learning biology and geometry is 119 , how can the total be 232 ??
the total be just 144 where 119 students study both and 25 students study biology .. if that is the case the total wont be 232 ........please clarify this ambiguity .. Please make me understand where am I going wrong .
