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M10-32

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M10-32 [#permalink]

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The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?

A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:43
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Official Solution:

The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?

A. 179 cm and 172 cm
B. 181 cm and 169 cm
C. 173 cm and 178 cm
D. 176 cm and 176 cm
E. 174 cm and 177 cm

Denote \(X\) as the sum of the heights of the two new people. From the stem it follows that \(\frac{(700 + X)}{6} \gt 175\). This reduces to \(X \gt 350\). Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.

Answer: B
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Collection of Questions:
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Re: M10-32 [#permalink]

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New post 31 May 2016, 09:30
Could you also just average the two quantities for each answer choice and identify which answer is at or below 175?

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M10-32 [#permalink]

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New post 31 May 2016, 21:29
mimisoko9 wrote:
Could you also just average the two quantities for each answer choice and identify which answer is at or below 175?


Hi,
Yes that would be the easiest approach without getting into much of calculations. In order for the overall average to increase, the combined average for two new elements should be higher than 175.

It is sort of weighted average question where you have to just figure out the appropriate side (>175) the average of new elements should reside.

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Re: M10-32 [#permalink]

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New post 12 Sep 2017, 09:47
Hello all,

Another approach to get to the answer is by using the differential method. Here, we basically see by "How much above the average is the items added. This gives us the answer quickly. Less Math, faster answers

Here's the Differential values from the average for the options

A. 179 and 172 : Differential from the current average of 175 = +4-3 = +1 => The average will be more than 175
B. 181 and 169 : Differential from the current average of 175 = +6-6 = 0 => The average will remain unchanged (Note you can stop here and pick the answer)
C. 173 and 178 : Differential from the current average of 175 = -2+3 = +1 => The average will be more than 175
D. 176 and 176 : Differential from the current average of 175 = +1+1 = +2 => The average will be more than 175
E. 174 and 177 : Differential from the current average of 175 = -1+2 = +1 => The average will be more than 175

Clearly, the required answer is B

Hope this helps!
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Re: M10-32   [#permalink] 12 Sep 2017, 09:47
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