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

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by BTGmoderatorLU » Tue Nov 12, 2019 4:38 am
Source: Economist GMAT Tutor

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
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by deloitte247 » Fri Nov 15, 2019 2:20 pm
Let the number of cat pictures drawn with pencil = C
Total pictures = c + 39
Let the number of flower pictures drawn with charcoal = f

Statement 1: There are 7 flower pictures drawn in pencil in the nootbook.
Total = total flower + total cats
Let cat pictures drawn with charcoal = x
Let flower pictures drawn with pencil = y = 7
Total flower = y + f = 7 + f
Total cats = x + c
c + 39 - x -c -7 = f
f = 32 - x
Variable x is unknown, hence, statement 1 is NOT SUFFICIENT.

Statement 2: There are 11 cat pictures drawn in charcoal in the notebook.
Total = total flower + total cats
Total cat = x + c where x = 11
c + 3a = (y+f) + (11+c)
f = 39 + c - y - 11 - c
f = 28 - y
Variable y is also unknown, hence, statement 2 is NOT SUFFICIENT

Combining both statement together:
y = 7 and x = 11
Total = total flower + total cats
(c + 39) = (y + f) + (x + c)
(c + 39) = (7 + f) + (11 + c)
c + 39 - 11 - c - 7 = f
f = 39 - 11 - 7
f = 21
Conclusively, both statements combined together are SUFFICIENT. Hence, option C is the correct answer.

Thanks
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