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Seventy percent of the 800 students in School T are male. At

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Seventy percent of the 800 students in School T are male. At  [#permalink]

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Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

A. 216
B. 383
C. 384
D. 416
E. 417

Originally posted by kidderek on 08 Nov 2006, 19:41.
Last edited by Bunuel on 17 Jun 2014, 10:48, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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New post 08 Nov 2006, 22:36
B it is 383.......when we take into account fewer than 30% male . if we take exactly 30% then it is 384
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New post 08 Nov 2006, 22:40
gmacvik wrote:
B it is 383.......when we take into account fewer than 30% male . if we take exactly 30% then it is 384


Fewer then 30% don't participate, so at least 70% participate. This makes it B :)
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New post 09 Nov 2006, 01:44
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1
# of male students = 560
# of female students = 240

10% female participate in sport = 24
Fewer than 30% of male students do not participate in sport = 168
# of female studnets who do not pariticpate in sport = 216
Total = 384
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Re: sports participants  [#permalink]

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New post 09 Nov 2006, 02:04
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kidderek wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

216
383
384
416
417


Female students = 30% of 800 =240
90% of female students = 216 (do not participate)
30% of male students = 30% of 70% of 800 = 168
The questions says fewer than 30% of male students did not participate, hence the number of males students who did not participate is 167.

The maximum possible number of students who did not participate = 216 + 167 = 383
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New post 09 Nov 2006, 06:22
I got the question wrong, chose C. OA is B b/c the question stem clearly says FEWER, therefore if you added 30% of males students, you did not go LESS than 30%, but rather exactly 30%.

I guess since there are two answer choices so close (384, 383) you should second guess why there is an answer choice just 1 number less.
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Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 14 Mar 2011, 04:15
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

A. 216
B. 383
C. 384
D. 416
E. 417
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Re: Sets  [#permalink]

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New post 14 Mar 2011, 04:32
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Please see the attached answer image.
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Re: Sets  [#permalink]

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New post 14 Mar 2011, 18:00
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AnkitK wrote:
70 percent of the 800 students in school T are male.At least 10 percent of the female students in school T participate in sport.Fewer than 30 percent of the male students in school T do not participate in a sport .What is the maximum possible number of students in school T who do not participate in a sport?
A.216
B.383
C.384
D.416
E.417


pls expalin with diagramatic explanation.


You can also use a Venn diagram (with a twist) to assimilate the given information. Note that the male and female sets will obviously not overlap and the sports set will be completely made up of male and female sets.
Male students: 70% of 800 = 560
Female students = 800 - 560 = 240
Male students not participating in sports < 30% of 560 = 168
Female students participating in sports >= 10% of 240 = 24

Attachment:
Ques3.jpg
Ques3.jpg [ 7.95 KiB | Viewed 11862 times ]

We have to maximize the students not participating in sports i.e. the shaded red and green regions.
Maximum value of shaded red region is 167 (to make it less than 168)
Maximum value of shaded green region will be obtained when females playing sports is minimized i.e. taken to be 24. Then females not playing sports = 240 - 24 = 216
Sum of red and green regions = 167+216 = 383
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Re: Sets  [#permalink]

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New post 14 Mar 2011, 21:07
From question, 560 students are male and 240 students are female


To get the max # of people who do not partipate in sports, maximize the number for both males and females.

At least 10% of Females participate in sports so Max # of non-participants(we need to keep participants at minimum) = 90% of females = 0.9 * 240 = 216


< 30% of the male students in school T do not participate in a sport => so Max # of male non-participants = greatest integer value of male participant < (30% of males = 0.3 * 560 = 168)

So the nearest value of male students not participating in sports = 167

So total = 167 + 216 = 383

Answer is B.
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Re: Sets  [#permalink]

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New post 15 Mar 2011, 04:27
m=800*.70=560
f=800*.30= 240
female not participate = 240*.90= 216
male not participate = 560*.30 = <168 or 167

216+167= 383
Ans. B.
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Re: Seventy percent of the 800 students in School T are male  [#permalink]

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New post 26 Aug 2013, 22:06
alphabeta1234 wrote:
Hey Guys,

I have been recently trying to study answer choice patterns. I have noticed this pattern on a couple of GMAT questions. Notice how (b) and (c) are 1 apart. Same with (d) and (e). Has anyone found any useful clues about such questions?

Seventy percent of the 800 students in School T are male. At least ten percent of the female students in
School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate
in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

a) 216 b) 383 c) 384 d) 416 e)417


Does it imply a wording trick by GMAC. I went for answer (c) having missed "FEWER" in the question.


Not necessarily but you must be mindful in such cases. If you got 384, you should take a step back and review once whether the correct answer could be 383 because you missed something. There will be trick options. The other 4 options are not put in blindly. The question setter makes frequently made mistakes and follows up to get an incorrect answer. These answers are then put as options.
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 21 Oct 2013, 02:52
Damn.I solved for the number of players who play sports. :(
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 18 Jun 2014, 00:07
1
Refer diagram below:

30% of 560 = 168

Fewer than 30%, so just substract 1

= 168 - 1 = 167

167 + 216 = 383

Answer = B
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Seventy percent of the 800 students in School T are male. At least ten  [#permalink]

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New post 01 Sep 2014, 09:33
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in
School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate
in a sport. What is the maximum possible number of students in School T who do not participate in a sport?
A. 216
B. 383
C. 384
D. 416
E. 417
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Re: Seventy percent of the 800 students in School T are male. At least ten  [#permalink]

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New post 01 Sep 2014, 09:39
AmoyV wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in
School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate
in a sport. What is the maximum possible number of students in School T who do not participate in a sport?
A. 216
B. 383
C. 384
D. 416
E. 417


Number of male students = 70% of 800 = 560
Number of females students = 30% of 800 = 240

At least 10% of female students participate in sports => at most 90% of female students do NOT participate in sports => 0.9*240 = 216
Fewer than 30% of male students do NOT participate=> less than 0.3*560 => less than 168 => 167 (max)

So, maximum number of students who do not participate = 216 + 167 = 383
So, Answer will be B

Hope it helps!
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 01 Sep 2014, 09:47
AmoyV wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in
School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate
in a sport. What is the maximum possible number of students in School T who do not participate in a sport?
A. 216
B. 383
C. 384
D. 416
E. 417


Merging topics. Please refer to the discussion above.

Can you please try searching before posting? Thank you.
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 01 Sep 2014, 10:01
Bunuel wrote:
AmoyV wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in
School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate
in a sport. What is the maximum possible number of students in School T who do not participate in a sport?
A. 216
B. 383
C. 384
D. 416
E. 417


Merging topics. Please refer to the discussion above.

Can you please try searching before posting? Thank you.


I have a doubt here. Question says " at least 10 percent of the female student participate in sport", I thought it meant 10 or more than 10%. Minimum is 10% and it can go higher as well.
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 14 Mar 2016, 17:16
kidderek wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

A. 216
B. 383
C. 384
D. 416
E. 417


ok, so 70% are males, or males = 560
females = 240
at least 24 females practice sport.
30% of 560 = 168. since we need fewer, the next maximum number we can have is 167. this is clearly fewer than 30%.
now females.
at least 24 practice, that means that the maximum number of females who do not practice is 216.

total max # of people who do not practice = 216+167=383.
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Re: Seventy percent of the 800 students in School T are male. At  [#permalink]

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New post 29 May 2017, 15:55
kidderek wrote:
Seventy percent of the 800 students in School T are male. At least ten percent of the female students in School T participate in a sport. Fewer than thirty percent of the male students in School T do not participate in a sport. What is the maximum possible number of students in School T who do not participate in a sport?

A. 216
B. 383
C. 384
D. 416
E. 417



This problem can best be tackled via the max/min principle. To wit, if you want to maximize a value, you should minimize some other value or constraint. In this case, we want to maximize the number of students who do not play a sport, so we should minimize the number of students who do play a sport.

We know that at least 10% of female students out of 240 total female students play a sport. So the minimum value here is 24. Thus, 240-24 = 216 female students do not play a sport at most.

We know that fewer than 30% of male students do not play a sport, so we want to maximize this value. Since students are humans and thus must be integers, the smallest value here is 167<3/10*560 -1. If we did not reduce by 1, then the number of male students who do not play a sport would be equal to 30% of male students, not less than 30% of male students. It plays a role in the answer choices.

240+ 167 = 383, the maximum number of students who do not play a sport.
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Re: Seventy percent of the 800 students in School T are male. At &nbs [#permalink] 29 May 2017, 15:55

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