abhishek1990p wrote:
The table above shows the average (arithmetic mean) price per dozen eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
A. $1.08
B. $1.10
C. $1.14
D. $1.16
E. $1.18
Attachment:
2019-09-21_1453.png
1. Let's say a total of \(90\) eggs were sold during the 3 month period
Quote:
If 2/3 as many dozen were sold in April as in May
2. Let the eggs sold in May be \(x\), then the eggs sold in April were be \(\frac{2}{3}x\)
Quote:
twice as many were sold in June as in April
3. We know that the eggs sold in April were \(\frac{2}{3}x\), hence the eggs sold in June were \(\frac{4}{3}x\)
4. Now, \(x + \frac{2}{3}x + \frac{4}{3}x = 90 \)
-> \(\frac{3}{3}x + \frac{2}{3}x + \frac{4}{3}x = 90\)
-> \(9/3x = 90 \)
-> \(x = 30\)
5. Substituting \(x = 30\) we get that the eggs sold in May were \(30\), April were \(20\) and June were \(40\)
6. The average price for the 3 months is:
\(\frac{Eggs sold in April * Average price in April + Eggs sold in May * Average price in May + Eggs sold in May * Average price in June}{Eggs sold in April + Eggs sold in May + Eggs sold in June}\)
\(\frac{20 * 1.20 + 30 * 1.26 + 40 * 1.08}{20 + 30 + 40}\) \(=\) \(\frac{37.8 + 24 + 43.2}{90}\) \(=\) \(\frac{105}{90}\) \(=\) \(1.16\)
Ans.
D _________________
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