guerrero wrote:X is the average price of 10 items of which no two cost the same. If each of the cheapest 5 items loses 10% in price while each of the most expensive 5 items gains 10% in price, which of the following is possible about X?
I. X will decrease
II. X will not change
III. X will increase
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
OA A
Brent's solution is great.
Some test-takers might find it easier to plug in values.
Average = sum/number.
Thus, if the SUM increases, so does the AVERAGE.
Let L = the total cost of the 5 least expensive items and E = the total cost of the 5 most expensive items.
Case 1:
Old sum:
Let L = 10 and E = 100.
Old sum = 10+100 = 110.
New sum:
L reduced by 10% = 10 - .1(10) = 9.
E increased by 10% = 100 + 10 = 110.
New sum = 9 + 110 = 119.
The new sum is greater, implying that the value of X -- the new average -- also will be greater.
Case 2:
Old sum:
Let L = 10 and E = 11.
Old sum = 10+11 = 21.
New sum:
L reduced by 10% = 10 - .1(10) = 9.
E increased by 10% = 11 + 1.1 = 12.1.
New sum = 9 + 12.1 = 21.1.
The new sum is greater, implying that the value of X -- the new average -- also will be greater.
When L and E are far apart, the value of X increases.
When L and E are very close together, the value of X increases.
Thus, we can be reasonably certain that the value of X will increase in every case.
The correct answer is
A.
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