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# The average (arithmetic mean) weight of two men is x, which is twice

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Math Expert
Joined: 02 Sep 2009
Posts: 52442
The average (arithmetic mean) weight of two men is x, which is twice  [#permalink]

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08 Jan 2018, 06:25
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:39) correct 38% (01:41) wrong based on 44 sessions

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The average (arithmetic mean) weight of two men is x, which is twice the average weight of three different men. Which of the following expresses the average weight of all five men in terms of x?

A. x/2
B. 3x/5
C. 7x/2
D. 7x/10
E. 8x/5

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Location: India
Re: The average (arithmetic mean) weight of two men is x, which is twice  [#permalink]

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08 Jan 2018, 10:04
Bunuel wrote:
The average (arithmetic mean) weight of two men is x, which is twice the average weight of three different men. Which of the following expresses the average weight of all five men in terms of x?

A. x/2
B. 3x/5
C. 7x/2
D. 7x/10
E. 8x/5

Since average weight of first two men is 'x', their total weight = 2x.

Also 'x' is twice the average weight of last three men. That means average weight of last three men = x/2, thus total weight of last three men = 3x/2.

So, total weight of these five men = 2x + 3x/2 = 7x/2. And so their average weight = (7x/2) / 5 = 7x/10.

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Joined: 22 May 2016
Posts: 2376
The average (arithmetic mean) weight of two men is x, which is twice  [#permalink]

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08 Jan 2018, 14:31
Bunuel wrote:
The average (arithmetic mean) weight of two men is x, which is twice the average weight of three different men. Which of the following expresses the average weight of all five men in terms of x?

A. x/2
B. 3x/5
C. 7x/2
D. 7x/10
E. 8x/5

Another approach: smart numbers. Have the men in each group (2 men, 3 men) weigh the same. Then each man's weight is also his group's average weight.

The men are A, B, C, D, and E

Let A and B each weigh 10.
10 = x
($$\frac{10+10}{2}=10$$)

x = 10 is twice the average of the other three men. Their average is 5.
Let C, D, and E each weigh 5.
($$\frac{5+5+5}{3}=5$$)

Average of all five men?
$$\frac{SumOfWeights}{NumberOfMen} = \frac{10+10+5+5+5}{5} = 7$$ average

With x = 10, find the answer that yields 7.

A. x/2 = 5 NO
B. 3x/5 = 6 NO
C. 7x/2 = 35 NO
D. 7x/10 = 7 YES
E. 8x/5 = 16 NO

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I was alive then.

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The average (arithmetic mean) weight of two men is x, which is twice &nbs [#permalink] 08 Jan 2018, 14:31
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