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# If m is an integer greater than 9 but less than 20, is n greater than

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Math Expert
Joined: 02 Sep 2009
Posts: 65785
If m is an integer greater than 9 but less than 20, is n greater than  [#permalink]

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06 Dec 2019, 04:36
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Difficulty:

75% (hard)

Question Stats:

49% (02:15) correct 51% (02:09) wrong based on 52 sessions

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If m is an integer greater than 9 but less than 20, is n greater than the average (arithmetic mean) of m and 20?

(1) n = 3m
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.

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Re: If m is an integer greater than 9 but less than 20, is n greater than  [#permalink]

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07 Dec 2019, 13:08
2
Bunuel wrote:
If m is an integer greater than 9 but less than 20, is n greater than the average (arithmetic mean) of m and 20?

(1) n = 3m
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.

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1) since 9 < m < 20, so the average of m and 20 will be more than 14.5 and less than 20. now when the avg is 15, m is 10 and n is 30. so for any value of m, n will be at least 18 more than m. so the average will always be lower than n. sufficient.

2) | n - 20| < |n -m|. since both 20 and m are in the right of the number line and m < 20, so n will be situated either after the mid point (average of m and 20) or after 20. so in both case n is greater than the avg of m and 20. sufficient.

D is the answer.
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Re: If m is an integer greater than 9 but less than 20, is n greater than  [#permalink]

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07 Dec 2019, 02:38
#1
n = 3m
for 9<m<20 ; we see that the avg of m+20 <n ; sufficient
#2
The distance on the number line between n and 20 is less than the distance on the number line between n and m.

(m-20)<(m-n)
20<n
value of n will always be >20 and the avg of m+20 <n sufficient
IMO D

Bunuel wrote:
If m is an integer greater than 9 but less than 20, is n greater than the average (arithmetic mean) of m and 20?

(1) n = 3m
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.

Are You Up For the Challenge: 700 Level Questions
Re: If m is an integer greater than 9 but less than 20, is n greater than   [#permalink] 07 Dec 2019, 02:38

# If m is an integer greater than 9 but less than 20, is n greater than

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