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At a certain high school there 20 more female sophomores

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At a certain high school there 20 more female sophomores  [#permalink]

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New post Updated on: 29 Sep 2014, 23:57
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Question Stats:

69% (01:22) correct 31% (01:28) wrong based on 396 sessions

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At a certain high school, there are 20 more female sophomores than male sophomores. How many of the female sophomores are studying geometry?

(1) 20 percent of all the sophomores are studying geometry
(2) 15 percent of the male sophomores are studying geometry

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Originally posted by NoHalfMeasures on 08 Jun 2014, 04:53.
Last edited by Bunuel on 29 Sep 2014, 23:57, edited 3 times in total.
Edited the question.
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jun 2016, 01:11
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NoHalfMeasures wrote:
At a certain high school, there are 20 more female sophomores than male sophomores. How many of the female sophomores are studying geometry?

(1) 20 percent of all the sophomores are studying geometry
(2) 15 percent of the male sophomores are studying geometry


Refer following grid:


Attachment:
Female Sophomores.JPG
Female Sophomores.JPG [ 69.1 KiB | Viewed 3159 times ]


It can be seen that both from statement (1) and (2) separately we do not get the number of female sophomores who are studying geometry.

Even after we combine, we can only get an expression for female sophomores who are studying geometry. We cannot get exact number.

Note that the unknown "m" does not cancel out. So unless we know the number of total students / male students / female students, we cannot get desired answer.

E is the answer.
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jun 2014, 06:04
f=20+m (a)
Call x is the percent the female sophomores are studying geometry.
(1)&(2)
15%m + x%f = 0.2 (m+f) (b)
We have 2 equations (a,b) for 3 variables (x, m, f). Can't solve for x! --> Answer is E
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 29 Sep 2014, 16:07
for such kind of Problems , Grid method is of utmost useful.
i am unable to attach the grid, sorry for that.
By drawing grid for the above problem ,we can see that the number of female sophomores studying geometry can be different values.
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jan 2015, 06:16
Can anyone help further to approach this problem.

Any expert/ moderator ?

Bunuel : Can you suggest a fast way to approach this problem.
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jan 2015, 07:17
Given:
m = number of males, hence
m+20 = number of females
Question:
determine x%(m+20) (the number of females studying geometry).

1) 20 percent of all the sophomores are studying geometry -> tells you nothing about the females, spec -> not suff
2) 15 percent of the male sophomores are studying geometry -> again, have nothing on the females, spec-> not suff
1,2) means that 15% of the male and some of the female (an x percentage) make up to 20% of total
15%m+x%(m+20) = 20%(2m+20)
x%(m+20)=25%m+4; still indefinite -> not suff.

hope this helps.
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jan 2015, 13:02
Hi All,

By TESTing VALUES, you can prove the answer to this question changes.

We're told that there are 20 MORE female sophomores than male sophomores. We're asked how MANY female sophomores study geometry.

From the prompt, we can create the equation...

F = M + 20

Fact 1: 20% of all sophomores study geometry.

This provides a minor restriction - since 20% of ALL sophomores study geometry, the total number of sophomores has to be a MULTIPLE of 5. For example 20% of 8 is 1.6 and you can't have "0.6" students, so there CAN'T be 8 total students.

IF....
M = 5
F = 25
We know that 20%(30) = 6 students study geometry, BUT we don't know how many of those 6 are female.
Fact 1 is INSUFFICIENT

Fact 2: 15% of the male sophomores study geometry.

This gives us NO information on the number of females studying geometry.
Fact 2 is INSUFFICIENT

Combined, we know...
F = 20 + M
F + M is a multiple of 5
20%(F+M) study geometry
15%(M) study geometry

By extension, the number of males MUST be a multiple of 20, since 15% of the males study geometry and multiples of 20 are the ONLY values that give us an INTEGER number of males.

eg. 15%(20) = 3 students
eg. 15%(21) = 3.15 students which is NOT possible

While this might appear to be a lot of information, it's still not enough to get us a consistent answer. Here's proof:

M = 20
F = 40
(F+M) = 60
15%(20) = 3 males study geometry
20%(60) = 12 students study geometry
12 - 3 = 9 females study geometry

As we increase the total number of students, the total number of females and males who study geometry WILL increase...

M = 40
F = 60
(F+M) = 100
15(40) = 6 males study geometry
20%(100) = 20 students study geometry
20 - 6 = 14 females study geometry
Combined, INSUFFICIENT

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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 15 Jan 2015, 01:09
EMPOWERgmatRichC wrote:
Hi All,

By TESTing VALUES, you can prove the answer to this question changes.

We're told that there are 20 MORE female sophomores than male sophomores. We're asked how MANY female sophomores study geometry.

From the prompt, we can create the equation...

F = M + 20

Fact 1: 20% of all sophomores study geometry.

This provides a minor restriction - since 20% of ALL sophomores study geometry, the total number of sophomores has to be a MULTIPLE of 5. For example 20% of 8 is 1.6 and you can't have "0.6" students, so there CAN'T be 8 total students.

IF....
M = 5
F = 25
We know that 20%(30) = 6 students study geometry, BUT we don't know how many of those 6 are female.
Fact 1 is INSUFFICIENT

Fact 2: 15% of the male sophomores study geometry.

This gives us NO information on the number of females studying geometry.
Fact 2 is INSUFFICIENT

Combined, we know...
F = 20 + M
F + M is a multiple of 5
20%(F+M) study geometry
15%(M) study geometry

By extension, the number of males MUST be a multiple of 20, since 15% of the males study geometry and multiples of 20 are the ONLY values that give us an INTEGER number of males.

eg. 15%(20) = 3 students
eg. 15%(21) = 3.15 students which is NOT possible

While this might appear to be a lot of information, it's still not enough to get us a consistent answer. Here's proof:

M = 20
F = 40
(F+M) = 60
15%(20) = 3 males study geometry
20%(60) = 12 students study geometry
12 - 3 = 9 females study geometry

As we increase the total number of students, the total number of females and males who study geometry WILL increase...

M = 40
F = 60
(F+M) = 100
15(40) = 6 males study geometry
20%(100) = 20 students study geometry
20 - 6 = 14 females study geometry
Combined, INSUFFICIENT

Final Answer:

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


This is great explanation indeed. Can really well relate to it.

Thank you EMPOWERgmatRichC
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 12 Jun 2016, 04:40
I arrived to the correct answer through the grid method. Still, I found it a bit confusing. Anyone is kind enough to post the grid method?

Best,
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Re: At a certain high school there 20 more female sophomores  [#permalink]

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New post 14 Jun 2016, 00:09
2
IgnacioDeLoyola wrote:
I arrived to the correct answer through the grid method. Still, I found it a bit confusing. Anyone is kind enough to post the grid method?

Best,


Kindly check the attachment, and please excuse the handwriting. Hope it helps
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File comment: Excuse the handwriting
Gmat res.png
Gmat res.png [ 69.94 KiB | Viewed 3161 times ]

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Re: At a certain high school there 20 more female sophomores  [#permalink]

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Re: At a certain high school there 20 more female sophomores &nbs [#permalink] 23 Oct 2018, 07:40
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