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a, b, c, d, and e are five numbers such that a b c d e and e -

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Bunuel
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a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  15 Feb 2021, 01:15
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a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

(1) e + c = 34
(2) c = a + 10
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chetan2u
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  15 Feb 2021, 11:08
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Bunuel wrote:
a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

(1) e + c = 34
(2) c = a + 10

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The median will be c as per the given condition, so we have to find if A>c?

(1) e + c = 34
e-c=4
Two equations so we can find e and c, but nothing about a and b

(2) c = a + 10
Now e-c=4
For taking the max value of mean, let us take all unknown values b and d as maximum possible. => b=c and d=e
So mean = \(\frac{a+b+c+d+e}{5}=\frac{c-10+c+c+c+4+c+4}{5}=c-\frac{2}{5}\)<c.
Thus even the maximum possible value of mean, A, is less than c, that is M.
So A<M always
Sufficient

B
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TarunKumar1234
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  Updated on: 14 Mar 2021, 07:06
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a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

We need to check, average (arithmetic mean) > median (M), if a, b, c, d, and e are equidistant or not.

Stat1: e + c = 34
So, e= 19 and c= 15, but no idea about a and b, they can be equidistant or not. Not sufficient

Stat2: c = a + 10 or, c-a =10, given, e - c = 4. So we can saw, a, b, c, d, and e are not equidistant. So, definitely, A <M. Sufficient.

So, I think B. :)

Originally posted by TarunKumar1234 on 15 Feb 2021, 11:46.
Last edited by TarunKumar1234 on 14 Mar 2021, 07:06, edited 1 time in total.
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ravish844
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  14 Mar 2021, 06:37
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TarunKumar1234 wrote:
a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

We need to check, average (arithmetic mean) > median (M), if a, b, c, d, and e are equidistant or not.

Stat1: e + c = 34
So, e= 19 and c= 23, but no idea about a and b, they can be equidistant or not. Not sufficient

Stat2: c = a + 10 or, c-a =10, given, e - c = 4. So we can saw, a, b, c, d, and e are not equidistant. So, definitely, A <M. Sufficient.

So, I think B. :)



Hi TarunKumar1234,

A small correction here (calculation mistake),
From Statement 1, e = 19 and c = 15.

Regards,
Ravish.
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ravish844
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  14 Mar 2021, 06:43
Bunuel wrote:
a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

(1) e + c = 34
(2) c = a + 10

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Hi Bunuel,

A quick query on this question?
a, b, c, d, and e are five numbers....

Here, number means a whole number or a natural number or an integer or a decimal number or any of these?
Although I can see that this number thing doesn't matter in the final answer and doesn't affect our answer choice, I just want to understand for clarity.
TIA.

Regards,
Ravish.
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TarunKumar1234
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  14 Mar 2021, 07:07
ravish844 wrote:
TarunKumar1234 wrote:
a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

We need to check, average (arithmetic mean) > median (M), if a, b, c, d, and e are equidistant or not.

Stat1: e + c = 34
So, e= 19 and c= 23, but no idea about a and b, they can be equidistant or not. Not sufficient

Stat2: c = a + 10 or, c-a =10, given, e - c = 4. So we can saw, a, b, c, d, and e are not equidistant. So, definitely, A <M. Sufficient.

So, I think B. :)



Hi TarunKumar1234,

A small correction here (calculation mistake),
From Statement 1, e = 19 and c = 15.

Regards,
Ravish.


Thanks! It is corrected. :thumbsup:
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Bunuel
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Re: a, b, c, d, and e are five numbers such that a b c d e and e - [#permalink] New post  14 Mar 2021, 08:22
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ravish844 wrote:
Bunuel wrote:
a, b, c, d, and e are five numbers such that a ≤ b ≤ c ≤ d ≤ e and e - c = 4. A is the average (arithmetic mean) of the five numbers, and M is their median. Is A > M?

(1) e + c = 34
(2) c = a + 10

Project DS Butler Data Sufficiency (DS3)


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Hi Bunuel,

A quick query on this question?
a, b, c, d, and e are five numbers....

Here, number means a whole number or a natural number or an integer or a decimal number or any of these?
Although I can see that this number thing doesn't matter in the final answer and doesn't affect our answer choice, I just want to understand for clarity.
TIA.

Regards,
Ravish.


It means real numbers, so it can be integer, fraction, or an irrational number.
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