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# If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1

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Joined: 02 Sep 2009
Posts: 52113
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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09 Dec 2018, 23:02
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:03) correct 14% (01:26) wrong based on 49 sessions

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If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible integer value of x ?

A) 8
B) 11
C) 20
D) 28
E) 44

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If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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Updated on: 10 Dec 2018, 02:27
1
Bunuel wrote:
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible integer value of x ?

A) 8
B) 11
C) 20
D) 28
E) 44

6<(6 + 8 + 10 + x)/4 < 12

24< 24 + x < 48

0 < x < 24

So greatest value of x is 20.

C is our answer.

Originally posted by selim on 09 Dec 2018, 23:08.
Last edited by selim on 10 Dec 2018, 02:27, edited 1 time in total.
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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09 Dec 2018, 23:18
1
$$6 < Average < 12$$
$$6 < \frac{6+8+10+x}{4} < 12$$
$$24 < 24 + x < 48$$
$$0 < x < 24$$

So from the given options, it looks like 20 should be the answer.

Hence Option (C) is our bet.

Best,

Bunuel wrote:
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible integer value of x ?

A) 8
B) 11
C) 20
D) 28
E) 44

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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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10 Dec 2018, 02:00
selim wrote:
Bunuel wrote:
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible integer value of x ?

A) 8
B) 11
C) 20
D) 28
E) 44

6<(6 + 8 + 10 + x)/4 < 12

24< 24 + x < 48

0 < x < 24

So greatest value of x is 20.

D is our answer.

selim : typo error please change D to C..
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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10 Dec 2018, 02:03
Bunuel wrote:
If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 12, what is the greatest possible integer value of x ?

A) 8
B) 11
C) 20
D) 28
E) 44

(6+8+10+x)/4 = (between 6 to 12)

(24+x)/4 = avg could be 7,8,9,10,11

for x to be greatest the avg has to be 11

and it would be at x =20 only IMO C suffices relation given
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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29 Dec 2018, 03:49
I followed the same steps as you guys did! I also reach the point where 0 < X <24

but

If there were e.g. number 23 in the OA, wouldn't that also be sufficient? I thought the OAs always yield the exact answer that we are looking for?!
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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29 Dec 2018, 03:54
gota900 wrote:
I followed the same steps as you guys did! I also reach the point where 0 < X <24

but

If there were e.g. number 23 in the OA, wouldn't that also be sufficient? I thought the OAs always yield the exact answer that we are looking for?!

gota900

if 23 is considered then the avg mean would be 11.75 ~ 12 , but in the question its given that x is between 6 to 12 so it cannot be 23 ..
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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29 Dec 2018, 04:07
Archit3110 wrote:
gota900 wrote:
I followed the same steps as you guys did! I also reach the point where 0 < X <24

but

If there were e.g. number 23 in the OA, wouldn't that also be sufficient? I thought the OAs always yield the exact answer that we are looking for?!

gota900

if 23 is considered then the avg mean would be 11.75 ~ 12 , but in the question its given that x is between 6 to 12 so it cannot be 23 ..

Hey man! Thanks for the fast reply. Well, if we consider 21 for X, wouldn't the average be 11.25, which would be less than 12, right? I can't find a hint in the prompt that the average has to be an integer, too. If that were the case, I would gladly eliminate 22 (avg 11.5, so not possible because avg>12) and 23 as mentioned by you.
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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29 Dec 2018, 04:11
gota900 wrote:
Archit3110 wrote:
gota900 wrote:
I followed the same steps as you guys did! I also reach the point where 0 < X <24

but

If there were e.g. number 23 in the OA, wouldn't that also be sufficient? I thought the OAs always yield the exact answer that we are looking for?!

gota900

if 23 is considered then the avg mean would be 11.75 ~ 12 , but in the question its given that x is between 6 to 12 so it cannot be 23 ..

Hey man! Thanks for the fast reply. Well, if we consider 21 for X, wouldn't the average be 11.25, which would be less than 12, right? I can't find a hint in the prompt that the average has to be an integer, too. If that were the case, I would gladly eliminate 22 (avg 11.5, so not possible because avg>12) and 23 as mentioned by you.

gota900

Well yes you need to choose from the given options only.. so the best option in this case is 20 :

range of x : largest answer value given within range is 20 ..
0<x<24
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1  [#permalink]

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29 Dec 2018, 04:16
Perfect! So the GMAT actually offers answers that sometimes don't include others that could also be correct? Well this is new to me but very valuable to notice! Thanks Archit3110
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Re: If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1 &nbs [#permalink] 29 Dec 2018, 04:16
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# If the average (arithmetic mean) of 6, 8, 10, and x is between 6 and 1

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