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Apr 2808:00 AM PDT
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22 Oct 2019, 00:03
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E
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Difficulty:
25%
(medium)
Question Stats:
73% (01:14) correct
27%
(01:14)
wrong
based on 164
sessions
History
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Last year, the average price of eight different products sold by Company X was $245. What is the average price of those same eight products this year?
(1) For 5 of the 8 products, the price is 10% higher this year than last.
(2) For 3 of the products, the price remained unchanged.
(1) For 5 of the 8 products, the price is 10% higher this year than last.
(2) For 3 of the products, the price remained unchanged.
22 Oct 2019, 08:49
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The Answer is E
It is clear that each of statement (1) and (2) alone is insufficient.
let the sum of the 5 items whose price increased = x , so after the increase, the price is \(\frac{11}{10}\)x
and let the sum of the 3 items whose price remained = y
The sum of the eight items = \(x + y = 245*8\)
the sum of the eight items after change of price = \(\frac{11}{10}x + y = \frac{1}{10}x + x + y = \frac{1}{10}x + 245*8\)
and the average of the eight items this year = \(\frac{1}{80}x + 245\)
so it is clear that we can't know the average without knowing the value of x
It is clear that each of statement (1) and (2) alone is insufficient.
let the sum of the 5 items whose price increased = x , so after the increase, the price is \(\frac{11}{10}\)x
and let the sum of the 3 items whose price remained = y
The sum of the eight items = \(x + y = 245*8\)
the sum of the eight items after change of price = \(\frac{11}{10}x + y = \frac{1}{10}x + x + y = \frac{1}{10}x + 245*8\)
and the average of the eight items this year = \(\frac{1}{80}x + 245\)
so it is clear that we can't know the average without knowing the value of x
22 Oct 2019, 11:59
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The sum of the eight prices is 8*245 = $1960. Using both Statements, maybe the three products that didn't change in price were all free, and the five products that went up 10% cost a total of $1960. Then the total price will increase by 10% of $1960, or by $196. Or maybe the five products that went up 10% each cost 10 cents and the other (much higher) prices didn't change. Then the total price will increase by only $0.05. So the answer is E.
