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26 Dec 2023, 23:55
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If the prices of four of the five books that Ann bought are $4, $6, $10, and $12, what is the price of the fifth book that Ann bought?
(1) The price of the fifth book that Ann bought is greater than $8.
(2) The median price of the five books that Ann bought is equal to the average (arithmetic mean) price of 5 books.
(1) The price of the fifth book that Ann bought is greater than $8.
(2) The median price of the five books that Ann bought is equal to the average (arithmetic mean) price of 5 books.
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27 Dec 2023, 00:12
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If the prices of four of the five books that Ann bought are $4, $6, $10, and $12, what is the price of the fifth book that Ann bought?
(1) The price of the fifth book that Ann bought is greater than $8.
This information alone is clearly insufficient.
(2) The median price of the five books that Ann bought is equal to the average (arithmetic mean) price of 5 books.
Assuming the price of the fifth book is $x, the average price would be (4 + 6 + 10 + 12 + x)/5.
Our set of values is {4, 6, 10, 12, x}. Note that the given set can have only three possible medians:
When the median is 6, equating the average and the median gives us (4 + 6 + 10 + 12 + x)/5 = 6, resulting in x = -2. Discard this value because a price cannot be negative.
When the median is x, equating the average and the median gives (4 + 6 + 10 + 12 + x)/5 = x, resulting in x = 8.
When the median is 10, equating the average and the median gives (4 + 6 + 10 + 12 + x)/5 = 10, resulting in x = 18.
Hence, we have two possible prices for the fifth book: $8 and $18.
Not sufficient.
(1)+(2) Since from (1) x > 8, we are left with only x = 18 from (2). Sufficient.
Answer: C.
(1) The price of the fifth book that Ann bought is greater than $8.
This information alone is clearly insufficient.
(2) The median price of the five books that Ann bought is equal to the average (arithmetic mean) price of 5 books.
Assuming the price of the fifth book is $x, the average price would be (4 + 6 + 10 + 12 + x)/5.
Our set of values is {4, 6, 10, 12, x}. Note that the given set can have only three possible medians:
- 6, when \(x \leq 6\)
- x, when \(6 \leq x \leq 10\)
- 10, when \(10 \leq x\)
When the median is 6, equating the average and the median gives us (4 + 6 + 10 + 12 + x)/5 = 6, resulting in x = -2. Discard this value because a price cannot be negative.
When the median is x, equating the average and the median gives (4 + 6 + 10 + 12 + x)/5 = x, resulting in x = 8.
When the median is 10, equating the average and the median gives (4 + 6 + 10 + 12 + x)/5 = 10, resulting in x = 18.
Hence, we have two possible prices for the fifth book: $8 and $18.
Not sufficient.
(1)+(2) Since from (1) x > 8, we are left with only x = 18 from (2). Sufficient.
Answer: C.
05 Jun 2024, 04:07
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Vanshikakataruka
In an evenly spaced set (arithmetic progression), the median is equal to the mean, although the reverse isn't necessarily true. For example, consider the set {0, 1, 1, 2} where the median and mean are both 1, yet the set is not evenly spaced.
