A neighborhood bakery owner selected some pastries to feature in

Question

A neighborhood bakery owner selected some pastries to feature in a weekend display case. Was the number of selected pastries that were fruit-filled but not topped with glaze less than the number of selected pastries that were topped with glaze but not fruit-filled?

(1) Every selected pastry that was fruit-filled was also topped with glaze.

(2) Every selected pastry that was not fruit-filled was also not topped with glaze.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A neighborhood bakery owner selected some pastries to feature in a weekend display case. Was the number of selected pastries that were fruit-filled but not topped with glaze less than the number of selected pastries that were topped with glaze but not fruit-filled?

(1) Every selected pastry that was fruit-filled was also topped with glaze.

If every fruit-filled pastry was also topped with glaze, then the number of pastries that were fruit-filled but not topped with glaze is 0.

The question thus becomes: is 0 less than the number of pastries that were topped with glaze but not fruit-filled?

That could be YES if that number (the number of pastries that were topped with glaze but not fruit-filled) is positive, or NO if that number is also 0.

Not sufficient.

(2) Every selected pastry that was not fruit-filled was also not topped with glaze.

If every pastry that was not fruit-filled was also not topped with glaze, then the number of pastries that were topped with glaze but not fruit-filled is 0.

The question thus becomes: is the number of pastries that were fruit-filled but not topped with glaze less than 0?

Since that number cannot be negative, the answer to the question is NO.

Sufficient.

Answer: B.

ankushsambare · Answer

Good word problem,

Let
F = fruit-filled pastries
G = glazed pastries
We compare:
number of (F and not G) versus number of (G and not F)

Statement (1): 
Every fruit-filled pastry is also glazed.
So F is a subset of G.

This means there are no pastries that are fruit-filled but not glazed.
 So (F and not G) = 0. 
 But (G and not F) could be 0 or positive.

We cannot tell if 0 is less than that or equal to that.
Not sufficient.

Statement (2):
Every pastry that is not fruit-filled is also not glazed.
So if something is glazed, it must be fruit-filled.

This means G is a subset of F.
So there are no pastries that are glazed but not fruit-filled.
So (G and not F) = 0.
But (F and not G) could be 0 or positive.
We cannot determine the comparison.
 Not sufficient.
 
Now combine (1) and (2):
From (1): F ⊆ G
From (2): G ⊆ F
So F = G.
Thus:
(F and not G) = 0
(G and not F) = 0
So the question becomes: is 0 < 0? No.
So answer is definite.
 Final answer: C

Adit_ · Answer

Statement 1:
Drawing a venn diagram we see that fruit filled is inside the glaze circle. We dont know about pastries that is glaze but not fruit filled here.
INSUFFICIENT.

Statement 2:
Here we see that not fruit filled is also not glaze.
We still dont know what proportion has fruit filled but not glaze.
INSUFFICIENT.

Combining both:
Using venn diagram it becomes evident that from 1, fruit is inside glaze completely.
From 2, we see that the portion between fruit ans glaze is also eliminated as it says those are NOT fruit filled, also DONT have glaze.
So basically, fruit filled and glaze become just 1 circle and are subsets of each other.
Both are equal in number.
Answer is NO.
SUFFICIENT.

Answer:  Option C

A neighborhood bakery owner selected some pastries to feature in

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