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# Missy ate m more crackers than Audrey did, from a box that originally

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Manager
Joined: 26 Dec 2015
Posts: 246
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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Updated on: 19 Apr 2017, 21:17
2
13
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:05) correct 30% (02:08) wrong based on 217 sessions

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Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?

A) $$\frac{(n+m)}{2n}$$

B) $$\frac{(m-n)}{2}$$

C) $$\frac{(n-m)}{2}$$

D) $$\frac{(m+n)}{2}$$

E) $$\frac{(n}{2+m)}$$

Originally posted by LakerFan24 on 19 Apr 2017, 19:23.
Last edited by Bunuel on 19 Apr 2017, 21:17, edited 1 time in total.
Renamed the topic.
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Joined: 02 Aug 2009
Posts: 7764
Re: Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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19 Apr 2017, 20:10
9
5
LakerFan24 wrote:
Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?

A) $$\frac{(n+m)}{2n}$$

B) $$\frac{(m-n)}{2}$$

C) $$\frac{(n-m)}{2}$$

D) $$\frac{(m+n)}{2}$$

E) $$\frac{(n}{2+m)}$$

Hi...

I. Logically..
Since Missy ate more than Audrey and both finished n crackers..
Missy has to eat MORE than half that is >$$\frac{n}{2}$$..
Only D is left..

II. Substitution..
Take total as 10 and M ate 6 and A ate 4...
So m =6-4=2 and n=10..
Substitute in choices and see which gives answer as 6..

A) $$\frac{(n+m)}{2n}....=\frac{10+2}{2*10}$$..No

B) $$\frac{(m-n)}{2}...=\frac{2-10}{2}$$..no

C) $$\frac{(n-m)}{2}...=\frac{10-2}{4}$$..no

D) $$\frac{(m+n)}{2}=\frac{10+2}{2}$$.. Yes

E) $$\frac{(n}{2+m)}=10/2+2$$..No

D

III. Algebra..
Let Missy eat x and Audrey eat y..
x-y=m and x+y=n....
Since we are looking for X, add two equations..
So x-y+x+y=m+n......2x=m+n.......x=(m+n)/2
D
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Joined: 07 Dec 2014
Posts: 1206
Re: Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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19 Apr 2017, 21:05
1
LakerFan24 wrote:
Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?

A) $$\frac{(n+m)}{2n}$$

B) $$\frac{(m-n)}{2}$$

C) $$\frac{(n-m)}{2}$$

D) $$\frac{(m+n)}{2}$$

E) $$\frac{(n}{2+m)}$$

let a=crackers A ate
a+m=crackers M ate
n=2a+m
a=(n-m)/2
a+m=(m+n)/2
D
Manager
Joined: 26 Dec 2015
Posts: 246
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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26 Jul 2017, 19:52
Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?

A) (n+m)2n(n+m)2n

B) (m−n)2(m−n)2

C) (n−m)2(n−m)2

D) (m+n)2(m+n)2

E) (n2+m)

** Sorry I don't want to waste time formatting the A/C, you can find them neater above **

What was key here for me is manipulating the Question into algebra:

M=A+m; A=?; n=total --> This translates to: A+(A+m)=n

- If you got lost: you're basically adding Missy and Audry to get "n", b/c you know they are the only 2 ppl we're talking about who are eating crackers and they finished the box, hence setting them equal to "n".

- This simplifies to: 2A+m=n

Now, let's play around with numbers. If we set n=20, A=9, m=2, M=(9+2) so M=11. NEED TO FIND 11 IN THE A/C
A) 11/20 - wrong;

B) negative # - wrong;

C) 9 - wrong

D) 11 - correct

E) 5 - wrong
Intern
Joined: 29 Jan 2017
Posts: 44
Re: Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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22 Jan 2018, 20:48
Picking numbers strategy

Mi = Missy
a = Audrey

I chose n = 5, a = 1 and left with m = 3

(given) Mi = m + a
Mi = 3 + 1
Mi = 4
n = Mi + a

Looking for an answer choice that results in 4

D

LakerFan24 wrote:
Missy ate m more crackers than Audrey did, from a box that originally contained n crackers. Together, they finished the box. Which of the following represents the number of crackers that Missy ate?

A) $$\frac{(n+m)}{2n}$$

B) $$\frac{(m-n)}{2}$$

C) $$\frac{(n-m)}{2}$$

D) $$\frac{(m+n)}{2}$$

E) $$\frac{(n}{2+m)}$$
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Joined: 09 Sep 2013
Posts: 11666
Re: Missy ate m more crackers than Audrey did, from a box that originally  [#permalink]

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12 Apr 2019, 23:17
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Re: Missy ate m more crackers than Audrey did, from a box that originally   [#permalink] 12 Apr 2019, 23:17
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