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a, b and c are three distinct positive integers less than 25. If |a-c|

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nick1816
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a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   21 Nov 2019, 21:04
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a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19
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nick1816
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   22 Nov 2019, 18:55
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|a-c|+|b-a|=|c-b|

Sum of distance between a and c and distance between a and b is equal to distance between b and c; Hence,on number line, 'a' lies somewhere in between b and c.

\(a_{min}=2\)
\(a_{max}=23\)

Range= 23-2=21


nick1816 wrote:
a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19
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p20p
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   31 Dec 2019, 07:24
nick1816 wrote:
|a-c|+|b-a|=|c-b|

Sum of distance between a and c and distance between a and b is equal to distance between b and c; Hence,on number line, 'a' lies somewhere in between b and c.

\(a_{min}=2\)
\(a_{max}=23\)

Range= 23-2=21


nick1816 wrote:
a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19


When you do solve the question this way you are not including 2 in your answer. But 2 is a legit solution to the question. Answer should be 22.
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Sparta_750
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a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   08 Jan 2020, 04:54
The question asks about the range of possible values and not the number of possible values. Range, in this case, is nothing but the number of integer values excluding 23 and 2. Thus 21 is correct.

Hope this clarifies.

p20p wrote:
nick1816 wrote:
|a-c|+|b-a|=|c-b|

Sum of distance between a and c and distance between a and b is equal to distance between b and c; Hence,on number line, 'a' lies somewhere in between b and c.

\(a_{min}=2\)
\(a_{max}=23\)

Range= 23-2=21


nick1816 wrote:
a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19


When you do solve the question this way you are not including 2 in your answer. But 2 is a legit solution to the question. Answer should be 22.
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ManjariMishra
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   20 Jan 2020, 13:07
can you please explain how you calculated minand max value
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Inc3pti0n
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   04 Feb 2020, 21:39
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ManjariMishra wrote:
can you please explain how you calculated minand max value


Since Value of ‘a’ must be between ‘b’ and ‘c’ (where b<c)and a,b,c all are distinct integers, the minimum value that ‘a’ can have is 2, since one of ‘b‘ could be 1.

Similarly, maximum value of ‘a’ can have is 23, since ‘c’ could be 24.

Hence A(min)=2 and A(max)=23

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hadimadi
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   14 Jan 2022, 03:15
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Hi,

let the following represent a number line:

a---b---c

The distance ac and ba added will always be greater than cb, we have to put a in the middle in order to satisfy the equation, so we can have c<a<b or b<a<c. Minimum value is 1, maximum is 24, which means that 2<=a<=23 -> 23-2=21
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ThatIndianGuy
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   14 Jan 2022, 22:31
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nick1816 wrote:
a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19



Solution:

Let us consider cases to validate the answer:

1st case: When a<b<c
In this case,
|a-c|+|b-a|=|c-b| is -a+c+b-a = c-b
2b-2a=0
b=a
This case is not possible, since we are given all are distinct integers.

2nd case: When b<a<c
In this case,
|a-c|+|b-a|=|c-b| is -a+c-b+a = c-b
0=0
Hence, this case is valid.

So, now we have b<a<c
min. value of a can be 2
max. value of a can be 23

Therefore, range = max. - min.
23-2 = 21
:)
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charlie-23
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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink] New post   31 Aug 2023, 07:12
nick1816 wrote:
a, b and c are three distinct positive integers less than 25. If |a-c|+|b-a|=|c-b|, then the range of the all possible values of a is

A. 23
B. 22
C. 21
D. 20
E. 19


a,b,c are distinct positive integers less than 25. So they can be 1,2..,24

|a-c|+|b-a|=|c-b|

What this means is
On a number line, b and c are the furthest points and a is in between them.
When b = 1, c = 24,
a can be anything from 2,3,4...,23.

Range of possible values of a = 23-2 = 21

So, C is the answer.

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Re: a, b and c are three distinct positive integers less than 25. If |a-c| [#permalink]
31 Aug 2023, 07:12
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