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If the average (arithmetic mean) height of Bob, John and Tom is 180 cm

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If the average (arithmetic mean) height of Bob, John and Tom is 180 cm  [#permalink]

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New post 01 Aug 2018, 23:39
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[Math Revolution GMAT math practice question]

If the average (arithmetic mean) height of Bob, John and Tom is 180 cm, what is their median height?

1) Bob’s height is 175cm.
2) John’s height is 180cm.

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Re: If the average (arithmetic mean) height of Bob, John and Tom is 180 cm  [#permalink]

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New post 02 Aug 2018, 01:26
1
To find the median height of John, Tom and Bob

The average (arithmetic mean) height of Bob, John and Tom is 180 cm

=> Sum of heights of Bob, John and Tom = 180 * 3 = 540

Statement 1

Bob’s height is 175cm

=> Sum of heights of John and Tom = \(540 - 175 = 365\)

The height of John and Tom can be 178 and 187 making the median height 178 OR

The height of John and Tom can be 170 and 195 making the median height 175

Statement 1 is not sufficient

Statement 2

John’s height is 180cm

=> Sum of heights of Bob and Tom = \(540 - 180 = 360\)

Now only two cases are possible

Case 1)

Heights of John, Bob and Tom are equal to 180 and the median height = 180

Case 2)

The height of Bob/Tom can be < 180 and height of Tom/Bob can be > 180 making the median height 180

The median height in both cases is 180

Statement 2 is sufficient

Hence option B
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If the average (arithmetic mean) height of Bob, John and Tom is 180 cm  [#permalink]

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New post 02 Aug 2018, 02:35
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If the average (arithmetic mean) height of Bob, John and Tom is 180 cm, what is their median height?

1) Bob’s height is 175cm.
2) John’s height is 180cm.


1) Bob’s height is 175cm.
it means that Bob is either the median or the least !!

insufficient

2) John’s height is 180cm
In this case John cannot be highest or lowest
given J= 180
B+T=360
even if B/T =179.9 (highest value) , T/B >180

which leaves us with
1.all of them are 180 cm - in this case median = 180
2.John's height =180 - median = 180

sufficient
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Re: If the average (arithmetic mean) height of Bob, John and Tom is 180 cm  [#permalink]

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New post 05 Aug 2018, 18:02
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

When we have 3 numbers, if one of them is equal to their average, then it is also equal to their median.

Thus, condition 2) is sufficient.

Therefore, B is the answer.
Answer: B
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Re: If the average (arithmetic mean) height of Bob, John and Tom is 180 cm &nbs [#permalink] 05 Aug 2018, 18:02
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If the average (arithmetic mean) height of Bob, John and Tom is 180 cm

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