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# If a, b, and c are positive integers, a > b > c, and a + b + c < 27

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
If a, b, and c are positive integers, a > b > c, and a + b + c < 27  [#permalink]

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21 Jan 2019, 01:36
00:00

Difficulty:

35% (medium)

Question Stats:

56% (01:00) correct 44% (00:45) wrong based on 22 sessions

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If a, b, and c are positive integers, a > b > c, and a + b + c < 27, what is the maximum value for a?

A 23
B 24
C 25
D 26
E 27

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VP
Joined: 31 Oct 2013
Posts: 1138
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If a, b, and c are positive integers, a > b > c, and a + b + c < 27  [#permalink]

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21 Jan 2019, 02:03
Bunuel wrote:
If a, b, and c are positive integers, a > b > c, and a + b + c < 27, what is the maximum value for a?

A 23
B 24
C 25
D 26
E 27

** all are positive integers***

a>b>c*****

*** a + b + c<27.

(a + b + c ) max = 26.

a is the largest among a,b,c.

i must use back solving here.

Option A: 23

23 + 2 + 1.

Note: In order to get the max value of a , we must assume the max value of a + b + c.

SVP
Joined: 18 Aug 2017
Posts: 1880
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a, b, and c are positive integers, a > b > c, and a + b + c < 27  [#permalink]

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21 Jan 2019, 08:31
Bunuel wrote:
If a, b, and c are positive integers, a > b > c, and a + b + c < 27, what is the maximum value for a?

A 23
B 24
C 25
D 26
E 27

questions say +ve integers
so
c cannot be 0 ; it has to be 1
so
max value of a can be 23 and b = 2 , a =1
so
IMO A is correct
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VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: If a, b, and c are positive integers, a > b > c, and a + b + c < 27  [#permalink]

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21 Jan 2019, 08:39
Bunuel wrote:
If a, b, and c are positive integers, a > b > c, and a + b + c < 27, what is the maximum value for a?

A 23
B 24
C 25
D 26
E 27

If a, b, and c are positive integers, a > b > c, and a + b + c < 27

For value of a to be maximum and satisfy the aboverelationship

One can realize that c != b and c = 1, as they are +ive integers

23 + 2 + 1 < 27

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Re: If a, b, and c are positive integers, a > b > c, and a + b + c < 27   [#permalink] 21 Jan 2019, 08:39
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