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# A carton contains 30 pens, of which 20 are blue ink pens and 10 are

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
A carton contains 30 pens, of which 20 are blue ink pens and 10 are  [#permalink]

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27 Dec 2017, 01:15
00:00

Difficulty:

25% (medium)

Question Stats:

86% (01:16) correct 14% (01:29) wrong based on 34 sessions

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A carton contains 30 pens, of which 20 are blue ink pens and 10 are black ink pens. If 9 of the pens are removed, what is the new ratio of blue ink pens to black?

(1) Of the pens removed, the ratio of the number of black ink pens removed to the number of blue ink pens is 2 : 1.
(2) Of the first 7 pens that are removed, 5 are black.

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Joined: 07 Dec 2017
Posts: 1061
Re: A carton contains 30 pens, of which 20 are blue ink pens and 10 are  [#permalink]

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27 Dec 2017, 02:09
Bunuel wrote:
A carton contains 30 pens, of which 20 are blue ink pens and 10 are black ink pens. If 9 of the pens are removed, what is the new ratio of blue ink pens to black?

(1) Of the pens removed, the ratio of the number of black ink pens removed to the number of blue ink pens is 2 : 1.
(2) Of the first 7 pens that are removed, 5 are black.

To solve this we'll look for options which give a specific number of blue or black ink pens.
This is a Logical approach.

(1) We have a total number of pens (9) and the ratio inside these 9 (2:1).
This is sufficient to calculate the exact ratio of pens by why bother?
Sufficient.

(2) We have information only on 7 of the 9 pens removed.
Insufficient.

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Re: A carton contains 30 pens, of which 20 are blue ink pens and 10 are  [#permalink]

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27 Dec 2017, 04:36
Imo A
St1: 2x+x=9
We can find value of x and hence find the new ratio.

Sufficient

St2: don't have any information about remaining 2 pens
Insufficient

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Joined: 24 Nov 2016
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Re: A carton contains 30 pens, of which 20 are blue ink pens and 10 are  [#permalink]

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27 Dec 2017, 18:30
Bunuel wrote:
A carton contains 30 pens, of which 20 are blue ink pens and 10 are black ink pens. If 9 of the pens are removed, what is the new ratio of blue ink pens to black?

(1) Of the pens removed, the ratio of the number of black ink pens removed to the number of blue ink pens is 2 : 1.
(2) Of the first 7 pens that are removed, 5 are black.

(1) Of the pens removed, the ratio of the number of black ink pens removed to the number of blue ink pens is 2 : 1.

If removed ratio is $$black:blue=2x:1x$$ (where x is a multiplier), then $$2x+x=9$$, and $$x=9/3=3$$.
So, removed ratio is $$black:blue=2x:1x=6:3$$ and new ratio $$blue:black=20-6:10-3=14:7$$; sufficient.

(2) Of the first 7 pens that are removed, 5 are black. So out of 9 we know that 5 are black and 2 are blue, but we don't know the remaining 2; insufficient.

Re: A carton contains 30 pens, of which 20 are blue ink pens and 10 are   [#permalink] 27 Dec 2017, 18:30
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