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Paul, a painter, paints only flowers or cats in his notebook

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Paul, a painter, paints only flowers or cats in his notebook

by Vincen » Mon Oct 23, 2017 7:11 pm
Paul, a painter, paints only flowers or cats in his notebook. The pictures are drawn in either regular pencil or in charcoal (but not in both.) The total number of pictures in Paul's notebook is 39 greater than the number of cat pictures painted in pencil. How many flower pictures drawn in charcoal are there in the notebook?

(1) There are 7 flower pictures drawn in pencil in the notebook.

(2) There are 11 cat pictures drawn in charcoal in the notebook.

The OA is C.

Is there a easy way to solve this DS question? Please, give me some help.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Oct 24, 2017 1:37 am
Vincen wrote:Paul, a painter, paints only flowers or cats in his notebook. The pictures are drawn in either regular pencil or in charcoal (but not in both.) The total number of pictures in Paul's notebook is 39 greater than the number of cat pictures painted in pencil. How many flower pictures drawn in charcoal are there in the notebook?

(1) There are 7 flower pictures drawn in pencil in the notebook.

(2) There are 11 cat pictures drawn in charcoal in the notebook.

The OA is C.

Is there a easy way to solve this DS question? Please, give me some help.
Say, the total number of paintings = T, the total number of cat paintings = C, and the total number of flower paintings = F

Thus, T = C + F

Again, say, the total number of cat paintings in pencil = CP, and the total number of cat paintings in charcoal = CC

Thus, C = CP + CC

Again, say, the total number of flower paintings in pencil = FP, and the total number of flower paintings in charcoal = FC

Thus, F = FP + FC

=> T = FP + FC + CP + CC

We are given that T = 39 + CP

Thus, 39 + CP = FP + FC + CP + CC

=> 39 = FP + FC + CC ---(1)

We need the value of FC.

Statement 1: There are 7 flower pictures drawn in pencil in the notebook.

=> FP = 7. Insufficient

Statement 2: There are 11 cat pictures drawn in charcoal in the notebook.

=> CC = 11. Insufficient

Statement 1 & 2 together:

From (1), we have FP = 7 and from (2), we have CC = 11.

By keying-in the values, in equation (1), we get

39 = 7 + FC + 11 => FC = 21. Sufficient.

The correct answer: C

Hope this helps!

-Jay

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