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In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 04:21
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 04:35
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 14431 = 113 So answer must be C. 113
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 06:16
cutegirlsimran wrote: 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 14431 = 113
So answer must be C. 113 Since no of students who took Biology =119 ,greatest = 119 greatest  smallest = 11931 = 88 Hence D



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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 08:04
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). 11988=31
11931=88
Answer: D



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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 11:12
Greatest possible # = 119 (as all the bio will be studies by 144 geo students) Least possible #= 31 (119+144232) Therefore Difference between greatest and lease possible #= 11931=88 Hence answer is D
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 17:40
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
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 19:56
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 11931 = 88 So the answer is D



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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 22:24
Bunuel wrote: 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
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, 263232=31 so the difference is 11931=88
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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13 May 2015, 22:49
Yes I got it Now I Swapped the Numbers to calculate the both
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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14 May 2015, 08:40
D88
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



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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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18 May 2015, 07:55
Bunuel wrote: 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. OFFICIAL SOLUTION:First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119. {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. The greatest possible number of students that could have taken both geometry and biology, is 119. Thus, the answer is 119  31 = 88. Answer: D.
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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19 May 2015, 04:52
EMPOWERgmatRichC wrote: 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 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
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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19 May 2015, 05:41
reto wrote: EMPOWERgmatRichC wrote: 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 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 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?
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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19 May 2015, 07:33
Bunuel wrote: reto wrote: EMPOWERgmatRichC wrote: 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 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 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? 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 ...
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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20 May 2015, 00:06
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
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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08 Oct 2016, 22:24
Bunuel wrote: 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. 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 = (144x) + x + (119x) = 232 (Given) i.e. 263x = 232 i.e. x = 31 The required difference = 119  31 = 88 Answer: Option D
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Re: In a graduating class of 232 students, 144 took geometry and 119 took
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