In a graduating class of 232 students, 144 took geometry and 119 took

Question

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

Kudos for a correct solution.

A. 144
B. 119
C. 113
D. 88
E. 31

Bunuel · Accepted Answer

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

Kudos for a correct solution.

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 .

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

cutegirlsimran · Answer

Total = 232 
Geometry = 144
Biology = 119

What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?

Greatest Possible Number taken both should be 144 (As it is maximum for One)

Smallest Possible Number taken both should be given by

Total - Neither = A + B - Both

Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 232 = 31

Greatest - Smallest is 144-31 = 113

So answer must be C. 113

NavenRk · Answer

Since no of students who took Biology =119 ,greatest = 119

greatest - smallest = 119-31 = 88 
Hence D

peachfuzz · Answer

The max number of students who took both bio and geometry is 119 because we can have 0 students who had bio but no geometry, and 0 students who had geometry but not bio.

the smallest number of students who took both bio and geometry is 31 because we can have 88 students who took bio and no geometry. (To minimize the students who took bio and geo, maximize students who took bio but no geo). 119-88=31

119-31=88

Answer: D

lipsi18 · Answer

Greatest possible # = 119 (as all the bio will be studies by 144 geo students)
Least possible #= 31 (119+144-232)
Therefore Difference between greatest and lease possible #= 119-31=88
Hence answer is D

Thanks,

EMPOWERgmatRichC · Answer

Hi cutegirlsimran,

You have to be careful with how you set up your work on this question.

Since there are 144 students who took Geometry and 119 who took Biology, there cannot be any more than 119 who took BOTH. If you swap that number into your calculation, you'll end up with the correct answer.

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

htridn · Answer

Smallest Possible Number taken both should be given by

Total - Neither = A + B - Both

The greatest is between 144 and 119 is: 119.
The Smallest can be calculated by the formula
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 232 = 31

Greatest - Smallest is 119-31 = 88 
So the answer is D

D3N0 · Answer

Ans: D
Solution: This can be done with or without Venn Diagram
total is 232
Maximum common can be 119 for both G ad B
minimum common can be 144+119= 263, 263-232=31
so the difference is 119-31=88

cutegirlsimran · Answer

Yes I got it Now I Swapped the Numbers to calculate the both

hsbinfy · Answer

D-88

highest number can come to 119(both g and biology is max) and lowest to 31(when students studying geometry adn not biology is max)

hope it helps

reto · Answer

Dear Rich
Why is that so "natural" that no more than 119 can take BOTH of the classes? The question is in a very conditional form and does not come with any constrains. It seems that I don't understand this concept ... Total 233 in the Class, which means, they're all allowed and able to visit both courses right?
Thank you

Bunuel · Answer

There can be students who took both classes but there cannot be more than 119 students who took both.

We are told that 144 took geometry and  119  took biology. How can then the number of students who took both geometry and biology be more than  119 ?

reto · Answer

I understand that BUT, the question virtually asks "... that COULD have taken both geometry and biology". Since this is conditional, my thoughts go back to the roots where we have 232 students and none of them have chosen biology or geometry yet, so 232 COULD have taken both geometry and biology. Again, I guess it's my english which makes me misunderstanding the question here ...

EMPOWERgmatRichC · Answer

Hi reto,

In real basic terms, you have to use ALL of the information that is given to get to the correct answer. You're told 3 different facts about the group of students, but your 'deduction' is based on just the first of those facts. THAT is why the answer is NOT 232 (and since that answer doesn't appear among the 5 choices, you KNOW that it cannot be correct).

And for what it's worth, your English "skills" seem to be just fine.

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

GMATinsight · Answer

Greatest Number of students who took both Geometry and Biology = 119 (Smaller of the two numbers)

Smallest Number of students who took both Geometry and Biology = x Let

Then total people = (144-x) + x + (119-x) = 232 (Given)

i.e. 263-x = 232

i.e. x = 31

The required difference = 119 - 31 = 88

Answer: Option D

bumpbot · Answer

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In a graduating class of 232 students, 144 took geometry and 119 took

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