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If there are x men and y women in a choir, and there are z more men

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If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post Updated on: 03 Oct 2014, 07:24
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If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?

(1) x^2 – 2xy + y^2 – 9 = 0

(2) x^2 + 2xy + y^2 – 225 = 0

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Originally posted by him1985 on 03 Oct 2014, 04:37.
Last edited by Bunuel on 03 Oct 2014, 07:24, edited 1 time in total.
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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 03 Oct 2014, 05:49
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him1985 wrote:
I tried to search this question but did not found. If this question has already been posted then please point me in right direction. Thanks

Ques: If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?

(1) x2 – 2xy + y2 – 9 = 0

(2) x2 + 2xy + y2 – 225 = 0


A.

we know, x = y+z

1) (x-y)^2 = 3^2
or (x-y) = 3
x = y+3
so z=3

2) (x+y)^2 = 15^2
or x+y=15
insufficient.
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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 26 Apr 2015, 18:48
Is there an easier way to solve this question? When I see long equations I get so intimidated and I am terrible at factoring. Like every question that requires factoring makes me cringe. The numbers never come naturally to me and I usually blindly guess until too much time has passed and I have to guess the answer anyways!
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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 27 Apr 2015, 15:26
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Hi sabineodf,

Many Quant questions on Test Day are pattern-based, so instead of looking at a prompt and thinking "what is this?", try thinking "what does this REMIND ME of?" In that way, you'll probably be less intimidated by the structure of the questions.

The prompt is worded in a 'quirky' way, but the information isn't that complex. From the two Facts, you should recognize that we're meant to be thinking about Classic Quadratics. If you're familiar with the 3 Classic Quadratics, then the bulk of the work in this question is just about re-writing information (and not about hard-core math skills).

For example, you are expected to know that....

X^2 -2XY + Y^2 can be re-written as....

(X-Y)(X-Y) =

(X-Y)^2

If you're not familiar enough with those ideas/rules yet, then that's okay, but you DO have to have to become familiar and practice them. Algebra is a BIG category in the Quant section, so you have to make sure that you're familiar enough with the broad concepts (and can do the specific calculations when required).

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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 27 Apr 2015, 18:02
That was very helpful, thanks!
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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 10 Sep 2017, 13:52
him1985 wrote:
If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?

(1) x^2 – 2xy + y^2 – 9 = 0

(2) x^2 + 2xy + y^2 – 225 = 0



This question is just testing quadratic templates

St 1

(x-y)(x-y) =9

Since this question is basically asking for the difference between a certain amount of people the answer can't necessarily be negative so x-y =2

suff

St 2

(x +y)(x+y) =225

insuff

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Re: If there are x men and y women in a choir, and there are z more men  [#permalink]

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New post 07 Oct 2018, 10:25
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Re: If there are x men and y women in a choir, and there are z more men   [#permalink] 07 Oct 2018, 10:25
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