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If the average (arithmetic mean) of 7 positive temperatures is x degre

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If the average (arithmetic mean) of 7 positive temperatures is x degre  [#permalink]

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New post 18 Sep 2019, 00:11
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If the average (arithmetic mean) of 7 positive temperatures is \(x\) degrees Celsius, then the sum of the 4 greatest of these temperatures, in degrees Celsius, could be which of the following?

A. \(\frac{4x}{7}\)

B. \(\frac{8x}{7}\)

C. \(\frac{7x}{4}\)

D. \(5x\)

E. \(8x\)

Source: McGraw-Hill's GMAT (1-19)

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Re: If the average (arithmetic mean) of 7 positive temperatures is x degre  [#permalink]

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New post 18 Sep 2019, 00:40
SajjadAhmad wrote:
If the average (arithmetic mean) of 7 positive temperatures is \(x\) degrees Celsius, then the sum of the 4 greatest of these temperatures, in degrees Celsius, could be which of the following?

A. \(\frac{4x}{7}\)

B. \(\frac{8x}{7}\)

C. \(\frac{7x}{4}\)

D. \(5x\)

E. \(8x\)

Source: McGraw-Hill's GMAT (1-19)


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Re: If the average (arithmetic mean) of 7 positive temperatures is x degre  [#permalink]

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New post 23 Sep 2019, 18:29
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SajjadAhmad wrote:
If the average (arithmetic mean) of 7 positive temperatures is \(x\) degrees Celsius, then the sum of the 4 greatest of these temperatures, in degrees Celsius, could be which of the following?

A. \(\frac{4x}{7}\)

B. \(\frac{8x}{7}\)

C. \(\frac{7x}{4}\)

D. \(5x\)

E. \(8x\)

Source: McGraw-Hill's GMAT (1-19)


If the temperatures are all the same, i.e., each is x degrees Celsisus, then the sum of the 4 greatest temperatures is 4x. If the temperatures are not all the same, then the sum of the 4 greatest temperatures is at least 4x. Since the sum of all 7 temperatures is 7x, we see that the sum of the 4 greatest temperatures is between 4x and 7x. Since the only quantity in the given choices that fits in this range is 5x, then 5x could be the sum of the 4 greatest temperatures.

Answer: D
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Re: If the average (arithmetic mean) of 7 positive temperatures is x degre   [#permalink] 23 Sep 2019, 18:29
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