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A certain list has 5 entries and each entries is an integer between 55

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Bunuel
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A certain list has 5 entries and each entries is an integer between 55 [#permalink] New post   23 Nov 2022, 11:30
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E

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55% (hard)

Question Stats:

61% (02:17) correct 39% (02:02) wrong based on 28 sessions
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A certain list has 5 entries and each entries is an integer between 55 and 70, inclusive. The median of the 5 entries is 60. If m is the average (arithmetic mean) of the 5 entries, which of the following must be true?

A. 54 ≤ m ≤ 60
B. 55 ≤ m ≤ 61
C. 56 ≤ m ≤ 62
D. 57 ≤ m ≤ 63
E. 58 ≤ m ≤ 64
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E
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sumit99kr
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A certain list has 5 entries and each entries is an integer between 55 [#permalink] New post   23 Nov 2022, 11:43
If median of 5 terms is 60, it means 3rd term is 60.
Terms 1st and 2nd can be anything from 55 to 60 and terms 3rd and 4th can be anything from 60 to 70.

Thus mean will be minimum when the terms are (55,55,60,60,60) and maximum when (60,60,60,70,70).

Thus, mean lies between
(55+55+60+60+60)/5 and (60+60+60+70+70)/5.

i.e, between (290/5) and (320/5)
i.e, between 58 and 64.

Hence E is the the correct choice.

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divyadna
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Re: A certain list has 5 entries and each entries is an integer between 55 [#permalink] New post   23 Nov 2022, 11:54
For the least value of m, the entries will be 55,55,60,60,60.
m= (55*2+60*3)/5= (110+180)/5= 290/5= 58
For the greatest value of m, the entries will be 60,60,60,70,70.
m= (60*3+70*2)/5= (180+140)/5= 320/5= 64

So, m should be between 58 and 64, both inclusive.
Answer should be option E IMO

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SaquibHGMATWhiz
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Re: A certain list has 5 entries and each entries is an integer between 55 [#permalink] New post   23 Nov 2022, 11:58
Expert Reply
Bunuel wrote:
A certain list has 5 entries and each entries is an integer between 55 and 70, inclusive. The median of the 5 entries is 60. If m is the average (arithmetic mean) of the 5 entries, which of the following must be true?

A. 54 ≤ m ≤ 60
B. 55 ≤ m ≤ 61
C. 56 ≤ m ≤ 62
D. 57 ≤ m ≤ 63
E. 58 ≤ m ≤ 64


Solution:

  • The median of 5 entries is 60. This means the 3rd entry is 60
  • The mean m will be least when the sum of entries is minimum i.e., in case of {55, 55, 60, 60, 60}
    • Mean in this case \(m_{min}=\frac{55+55+60+60+60}{5}=\frac{290}{5}=58\)
  • No need to check further. We can mark option E
  • Still for learning purposes: the mean m will be greatest when the sum of entries is maximum i.e., in case of {60, 60, 60, 70, 70}
    • Mean in this case \(m_{max}=\frac{60+60+60+70+70}{5}=\frac{320}{5}=64\)

Hence the right answer is Option E
GMAT Club Bot
gmatclubot
Re: A certain list has 5 entries and each entries is an integer between 55 [#permalink]
23 Nov 2022, 11:58
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