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If the average (arithmetic mean) of five distinct positive integers is

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If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46
[Reveal] Spoiler: OA

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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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Since the average of 5 numbers is 10, the total must be 50.
The numbers, must be consecutive for the greatest number to be least (8,9,10,11,12)

The least possible value of the greatest number(as it has been given that the numbers are distinct) has to be 12(Option B)
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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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New post 03 Jul 2017, 05:15
Ans :A
9,10,10,10,11

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New post 03 Jul 2017, 05:18
Anannt wrote:
Ans :A
9,10,10,10,11

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It cannot be 9,10,10,10,11 because it has been given that the integers are distinct.
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Bunuel wrote:
If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46

\(a + ( a + 1 ) + ( a + 2 ) + ( a + 3 ) + (a + 4) = 50\) ( As the numbers are distinct )

Or, \(5a + 10 = 50\)

Or, \(5a = 40\)

Or, \(a = 8\)

So, The least value of the greatest of the five numbers is 8 + 4 = 12, answer , must be (B) 12
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New post 15 Nov 2017, 20:51
Hi,

I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.

Thank you!

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shamsm wrote:
Hi,

I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.

Thank you!


If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46

Given: \(0<a < b < c< d< e\) and \(a + b + c + d + e = 10*5\).

We want to minimise e.

General rule for such kind of problems, when the sum is fixed:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So, here we should maximize a, b, c, and d. Since the integers are distinct, then the max value of d is e - 1, the max value of c is e - 2, the max value of b is e - 3 and the max value of a is e - 4.

Thus, \((e - 4) + (e - 3) + (e - 2) + (e - 1) + e = 50\);
e = 12.

Answer: B.


14. Min/Max Problems



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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If the average (arithmetic mean) of five distinct positive integers is   [#permalink] 15 Nov 2017, 22:31
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