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by Deepthi Subbu » Tue May 24, 2011 3:08 am
Eunice sold several cakes. If each cake sold for either exactly 17 or exactly 19 dollars, how many 19 dollar cakes did Eunice sell?

1.Eunice sold a total of 8 cakes.
2.Eunice made 140 dollars in total revenue from her cakes.
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Source: — Data Sufficiency |
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by Frankenstein » Tue May 24, 2011 3:27 am
Hi,

From(1): We do not know the number of cakes of each of the two varities frm this
Not sufficient

From(2) : Let a and b be the number of cakes of 17$ and 19$ respectively
So. 17.a + 19.b =140
As a>=0 and b>=0, we get a <9 and b<8
Now, 17a+19b=140 =>17a+17b=140-2b =>17.(a+b) = 140-2b.
As b <8, 140-2b > 140-2(8) = 124. So 124 <140-2b <=140.
140-2b = 17.(a+b). So, 140-2b has to be a mulitple of 17. 136 is the only value of (140-2b) to satisfy the conditions. So, 140-2b=136 => b=2. From this we get 17(a+2) = 136 =>a=6.
Sufficient

Hence, answer is B .

Cheers!
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by GMATGuruNY » Tue May 24, 2011 3:31 am
Deepthi Subbu wrote:Eunice sold several cakes. If each cake sold for either exactly 17 or exactly 19 dollars, how many 19 dollar cakes did Eunice sell?

1.Eunice sold a total of 8 cakes.
2.Eunice made 140 dollars in total revenue from her cakes.
Statement 1: 8 cakes sold
No way to determine the number of $19 cakes.

Statement 2: Revenue = 140.
Multiples of 19 = 19,38,57,76,95,114,133
Multiples of 17 = 17,34,51,68,85,102,119,136
Only one combination -- highlighted in red above -- adds up to 140: 38+102 = 140.
Since 38 = 2*19, two $19 cakes were sold.
Sufficient.

The correct answer is B.
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