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# Out of 75 students, 17 students enrolled in a Physics class, 28 studen

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Out of 75 students, 17 students enrolled in a Physics class, 28 studen  [#permalink]

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14 Mar 2018, 00:25
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Difficulty:

45% (medium)

Question Stats:

68% (02:15) correct 32% (03:16) wrong based on 76 sessions

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[GMAT math practice question]

Out of 75 students, 17 students enrolled in a Physics class, 28 students enrolled in a Chemistry class, and 39 students enrolled in a Biology class. 5 students enrolled in both the Physics and Chemistry classes, 7 students enrolled in both the Chemistry and Biology classes, and 6 students enrolled in both the Biology and Physics classes. If 4 students enrolled in Physics, Chemistry, and Biology, how many students did not enroll in any of the three science classes?

A. 2
B. 3
C. 4
D. 5
E. 6

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Status: It always seems impossible until it's done. Joined: 16 Sep 2016 Posts: 751 GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen [#permalink] ### Show Tags 14 Mar 2018, 01:06 It is a three category Venn diagram problem. Start from the inside ( with no. Of students participating in all three being 4) and build as you go out. It all falls down to 70 students inside the circles and 5 not participating in any subjects. Certain subsets are : only physics - 10. Only chemistry - 20. Only biology - 30. Only P & B - 2. Only P & C - 1. Only B&C - 3. All three - 4. Hence none =5. Hence D. Posted from my mobile device Posted from my mobile device _________________ Regards, Gladi “Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back) Intern Joined: 06 Oct 2017 Posts: 6 Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen [#permalink] ### Show Tags 15 Mar 2018, 15:52 1 This can be solved by directly applying the formula for overlapping sets $$Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither$$ Let students who enrolled in none of the courses be x $$75 = 17 + 28 + 39 - (5 + 7 + 6) + 4 + x$$ $$75 = 70 + x$$ $$x = 5$$ Answer: D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7603 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen [#permalink] ### Show Tags 16 Mar 2018, 00:54 => Attachment: 777.png [ 10.71 KiB | Viewed 949 times ] The total number of students is given by $$a + b + c + d + e + f + g + h = 75.$$ Of these, $$a + d + f + g = 17$$ are enrolled in Physics, $$b + d + e + g = 28$$ are enrolled in Chemistry, and $$c + e + f + g = 39$$ are enrolled in Biology. Adding these three equations gives $$( a + b + c ) + 2( d + e + f ) + 3g = 84.$$ We also know that $$d + g = 5$$ study both Physics and Chemistry, $$e + g = 7$$ study both Chemistry and Biology, and $$f + g = 6$$ study both Physics and Biology. Adding these three questions yields $$( d + e + f ) + 3g = 18.$$ Since $$4$$ students are enrolled in all three classes, we have $$g = 4,$$ Plugging this value for $$g$$ into the above equation yields $$(d + e + f) + 3g = 18$$ $$(d + e + f) + 12 = 18$$ $$d + e + f = 6.$$ So, $$( a + b + c ) + 2( d + e + f ) + 3g = 84$$ yields $$(a + b + c) + 2(6) + 3(4) = 84$$ $$(a + b + c) + 12 + 12 = 84$$ $$a + b + c = 60.$$ Finally, using the equation, $$a + b + c + d + e + f + g + h = 75$$, we see that $$(a + b + c) + (d + e + f) + g + h = 75$$ $$60 + 6 + 4 + h = 75$$ $$h = 5.$$ Therefore, the answer is D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Joined: 27 Dec 2016
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Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen  [#permalink]

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07 Mar 2019, 20:08
Hi chetan2u Bunuel VeritasKarishma Gladiator59 generis,

I was wondering could one of you experts please help me solve this question via the overlap formula? If I am not mistaken, the formula for three overlap set is Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither.

Based on this we get: 75=17+28+39-18-8+x or x=17. Could one of you please help me and tell me where I am making a mistake? Would greatly appreciate it!
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen  [#permalink]

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07 Mar 2019, 20:30
JS1290 wrote:
Hi chetan2u Bunuel VeritasKarishma Gladiator59 generis,

I was wondering could one of you experts please help me solve this question via the overlap formula? If I am not mistaken, the formula for three overlap set is Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither.

Based on this we get: 75=17+28+39-18-8+x or x=17. Could one of you please help me and tell me where I am making a mistake? Would greatly appreciate it!

Hi,
you are going wrong in formula..
It is Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three)+all three + Neither.... 75 = 17+28+39-18+4+x or x=5..

Logic is when you add Group 1, 2 and 3... all three portion gets added 3 times, and when you subtract 'two together', you are subtracting 'all three' thrice, so finally your solution is without the group ' all three', that is why we have to add 'all three' once..
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Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen  [#permalink]

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07 Mar 2019, 21:07
JS1290 wrote:
Hi chetan2u Bunuel VeritasKarishma Gladiator59 generis,

I was wondering could one of you experts please help me solve this question via the overlap formula? If I am not mistaken, the formula for three overlap set is Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither.

Based on this we get: 75=17+28+39-18-8+x or x=17. Could one of you please help me and tell me where I am making a mistake? Would greatly appreciate it!

Check out this post: https://www.veritasprep.com/blog/2015/1 ... ping-sets/
It discusses the various formulas you can use to solve overlapping sets questions.
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Re: Out of 75 students, 17 students enrolled in a Physics class, 28 studen   [#permalink] 07 Mar 2019, 21:07
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