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# The average (arithmetic mean) of the body weights of John, Jack, Bill

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Math Expert
Joined: 02 Sep 2009
Posts: 60549
The average (arithmetic mean) of the body weights of John, Jack, Bill  [#permalink]

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10 Dec 2019, 01:53
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Difficulty:

25% (medium)

Question Stats:

77% (01:55) correct 23% (01:24) wrong based on 31 sessions

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The average (arithmetic mean) of the body weights of John, Jack, Bill, Mark, and Tom is at least 170 pounds. John, Jack, and Bill weigh 140, 160, and 180 pounds, respectively. If Mark weighs between 160 and 180 pounds, inclusive, what is the least possible weight, in pounds, of Tom?

A. 180

B. 190

C. 200

D. 210

E. 220

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Joined: 16 Feb 2015
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Location: United States
Concentration: Finance, Operations
Re: The average (arithmetic mean) of the body weights of John, Jack, Bill  [#permalink]

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10 Dec 2019, 04:03
Bunuel wrote:
The average (arithmetic mean) of the body weights of John, Jack, Bill, Mark, and Tom is at least 170 pounds. John, Jack, and Bill weigh 140, 160, and 180 pounds, respectively. If Mark weighs between 160 and 180 pounds, inclusive, what is the least possible weight, in pounds, of Tom?

A. 180

B. 190

C. 200

D. 210

E. 220

Explanation :

The average weight of 5 at least = 170
John= 140 (less than by 30 from Average Weight)........1
Jack=160 (less than by 10 from Average Weight)........2
Bill=180 (More than by 10 from Average Weight)......3
Mark (we have to take highest, so Tom Will be having the least weight)i.e. 180 (More than by 10 from Average Weight).....4
From 1,2 3 & 4, we know that
Total we have 20 less than from Average Weight)
So Tom will have at least = 170+20 =190

IMO-B
CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 353
Re: The average (arithmetic mean) of the body weights of John, Jack, Bill  [#permalink]

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17 Dec 2019, 00:46
1
From the first statement in the question, we can deduce that the sum of the weights of the five persons should be at least 850 pounds. Remember,

Average Weight = $$\frac{Sum of weights }{ Number of persons.}$$

We know that there are 5 persons and the average weight is at least 170 i.e. ≥ 170. Substituting in the equation above, we can say that Sum of weights = 5 * (≥170) ≥850.

The sum of John, Jack and Bill gives us 480 pounds; this means that the weights of Mark and Tom should be adding up to at least 370 pounds. Since we are trying to minimize the weight of Tom, we can consider the least possible sum for Mark and Tom i.e. 370 pounds.

Therefore, Mark + Tom = 370. If we want to minimize the weight of Tom, we maximise the weight of Mark which is 180 (remember both 160 and 180 are inclusive). Therefore, the least possible weight for Tom should be 190 pounds.

The correct answer option is B.

Hope that helps!
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Re: The average (arithmetic mean) of the body weights of John, Jack, Bill   [#permalink] 17 Dec 2019, 00:46
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