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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 20 May 2019, 21:48
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FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres


M36-121

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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 16 Nov 2021, 03:53
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres


M36-121
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Official Solution:


Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.

The heights of the three musketeers in ascending order are \(x\), \(x+1\), and \(x+10\). The median is \(x+1\) and the mean is \(\frac{x+(x+1)+(x+10)}{3}=x+2.something\). Obviously the mean (\(x+2.something\)) is greater than the median (\(x+1\)). Sufficient.

(2) Porthos height is 190 centimetres.

Clearly insuficient.


Answer: A
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 20 May 2019, 21:57
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres
Show more

We have to find the relation between mean and median of theses three heights.

Statement 2, gives us only th height of one person clearly insufficient.

Statement 1

Athos, Aramis, Porthos
x, (x+1), (10+x) , X>0 as it's height.

Median is= x+1 and mean is clearly greater than median height. So A.
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 21 May 2019, 02:43
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres
Show more

#1 Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
let P = x
so Athos = x-10
Aramis = x-9
so avg ; x+x-9+x-10/3 ; 3x-19/3
median ; x-9
value of x is not know ; insufficient
#2
P = 190
but relation and value with other 2 are not given; insufficient
from 1 & 2
x=190
so
we get
551>543
sufficient
IMO C
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 21 May 2019, 03:30
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres

#1 Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
let P = x
so Athos = x-10
Aramis = x-9
so avg ; x+x-9+x-10/3 ; 3x-19/3
median ; x-9
value of x is not know ; insufficient
#2
P = 190
but relation and value with other 2 are not given; insufficient
from 1 & 2
x=190
so
we get
551>543
sufficient
IMO C
Show more

Archit3110 The median x-9 has to be a positive number because it's height of a person. Also for any value of x (here x>9) we can compare mean and median of the list. Please correct me if I'm wrong.
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 19 Oct 2019, 06:36
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres
Show more

Porthos = p, Athos = t, Aramis = r;

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis. sufic.

\(p=t+10…p=r+9…average=sum/num=\frac{p+t+r}{3}=\frac{p+p-10+p-9}{3}…median=p-9\)
\(Question:\frac{p+p-10+p-9}{3}>p-9…3p-19>3p-27…19<27?…Answer:yes\)

(2) Porthos height is 190 centimetres insufic.

Answer (A)
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 04 Jun 2022, 13:59
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Bunuel

FRESH GMAT CLUB TESTS QUESTION



Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?

(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres

#1 Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
let P = x
so Athos = x-10
Aramis = x-9
so avg ; x+x-9+x-10/3 ; 3x-19/3
median ; x-9
value of x is not know ; insufficient
#2
P = 190
but relation and value with other 2 are not given; insufficient
from 1 & 2
x=190
so
we get
551>543
sufficient
IMO C
Show more


Using Statement 1, your working out was spot on, the only thing is you walked past the answer, you actually had enough info in your solution to determine that A was sufficient alone.

As you correctly mentioned, x-9 is the median, in addition to this, the average height can be expressed as (3x-19)/3 (as you all correctly noted). We can rewrite this average height as x - 19/3

But the thing you walked past was that these two values are indeed comparable (also bear in mind that heights can never be negative).

We can compare the median of x-9 to the average of x-19/3. 19/3 is approx 6.33

X-9 is clearly going to be LESS than x-6.33, therefore, the average is indeed greater than the median and (1) is sufficient alone. The key point is, it does NOT matter what the value of 'x' is, x will always be positive, and the other heights can never be negative either, so x must be 9 at the very least.
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis 04 Sep 2025, 08:58
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