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There are c chocolate chip cookies and r oatmeal raisin cookies in a j

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There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:14
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

82% (01:19) correct 18% (02:03) wrong based on 22 sessions

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There are c chocolate chip cookies and r oatmeal raisin cookies in a jar. If there are no other cookies in the jar, is the probability of randomly selecting an oatmeal raisin cookie greater than the probability of selecting a chocolate chip cookie?
1)\(\frac{(r^2-rc)}{(r^2-c^2)}\) > \(\frac{c(r+c)}{(r+c)^2}\)
2) If p peanut butter cookies were added to the jar then \(\frac{r}{(r+c+p)} > \frac{c}{(r+c+p)}\)


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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:20
Both are sufficient.

statement 1 can be solved using distributive law

Statement 2 is sufficient
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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:22
D:

Statement 1:
the question stem asks if r / (r+c) > c / (r+c)
Statement 1 states the same thing except LHS is multiplied by (r-c)/(r-c) and RHS is multiplied by (r+c)/(r+c)

Statement 2:
adding in a constant does not change the proportion therefore also sufficient

Therefore D
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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:23
D is sufficient

Option A, r(r-c)/(r-c)(r+c) >. c(r+c)/(r+c)^2
if (r-c) is not equal to 0 and (r+c) is not equal to 0,

r/(r+c) > c/(r+c)
which is 1/(r+c) (r-c)>0.... which gives r>c

sufficient

Option B, r/(r+c+p)> c/(r+c+p)
if r+c+p is not equal to 0,

1/(r+p+c) (r-c)>0,
which means r>c,
sufficient
Hence D is the answer
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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:23
D.

Since we can assume r and c would be positive, solving statement 1 gives r>c. The second statement introduces a constant to both sides and it can be concluded that r>c.
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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j  [#permalink]

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New post 20 Oct 2018, 09:30
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Answer choice: D. Details please see in the file attached
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Re: There are c chocolate chip cookies and r oatmeal raisin cookies in a j &nbs [#permalink] 20 Oct 2018, 09:30
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There are c chocolate chip cookies and r oatmeal raisin cookies in a j

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