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

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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