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# Of the students in a school, 20 percent are in the science club and 30

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Math Expert
Joined: 02 Sep 2009
Posts: 51135
Of the students in a school, 20 percent are in the science club and 30  [#permalink]

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12 Jul 2018, 23:50
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:46) correct 34% (02:35) wrong based on 50 sessions

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Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

A) 5%
B) 20%
C) 25%
D) 60%
E) 75%

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Joined: 17 May 2018
Posts: 43
Re: Of the students in a school, 20 percent are in the science club and 30  [#permalink]

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13 Jul 2018, 02:38
It is easy to find the values with a Venn diagram.

From the 30 that are in the band, 25 are not in science, meaning that 5 are in both science and the band.
This means that the ones that are in science but not in the band are 20-5=15.

We need to find: #students that are in science but not in the band / #students that are in science = 15 / 20 = 75 / 100.

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Of the students in a school, 20 percent are in the science club and 30  [#permalink]

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13 Jul 2018, 15:29
1
Bunuel wrote:
Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

A) 5%
B) 20%
C) 25%
D) 60%
E) 75%

Attachment:

venn2018.07.13.jpg [ 25.52 KiB | Viewed 544 times ]

Agreed, a Venn diagram is easy; I drew one immediately.
Careful with the question's wording: "[W]hat percent of the students who are in the science club are not in the band?"
"S . . .but not B" means "S only" (they are only in S, and not at all in B)
This percent means $$\frac{S.Only}{S.total}*100$$

Assume 100 students. Science club = S. Band = B
S total: 20% of all students = 20
B total: 30% of all students = 30

"25 percent of the students in the school are in the band but are not in the science club"
B but not S = "B only": 25% = 25
None of those 25 students can be in the overlap,
because the overlap contains B and S.
So 25 in B only (turquoise)

Number of students in both S and B, i.e. overlap? Use B total = 30
25 of 30 are B only
The other 5 must be in the overlap (lavender). There is no other category. Thus
Overlap, the number of students who are in both: S and B = 5

Now fill in S only.
S only? = (S total - overlap)
S only: (20 - 5) = 15 (yellow)

"What percent of the students who are in the science club are not in the band?"
Percent of all S who are not B? (OR: Percent of all S who are S only? OR: "S Only" is what percent of "all S"?)
$$\frac{15}{20}=\frac{3}{4}=(.75*100)=75$$ percent

Of the students in a school, 20 percent are in the science club and 30 &nbs [#permalink] 13 Jul 2018, 15:29
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