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

Question

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

nick1816 · Accepted Answer

|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

p20p · Answer

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.

Sparta_750 · Answer

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.

ManjariMishra · Answer

can you please explain how you calculated minand max value

Inc3pti0n · Answer

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 · Answer

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

ThatIndianGuy · Answer

Solution: Let us consider cases to validate the answer: 1st case : When a

charlie-23 · Answer

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.

Posted from my mobile device

BrushMyQuant · Answer

Theory: |a - b| always means the distance between the points a and b on the number line. (Irrespective of the signs of a and b)

=> |a - b| -> Distance between a and b
=> |b - c| -> Distance between b and a
=> |c - a| -> Distance between c and a

|a-c|+|b-a|=|c-b|
This means that, distance between a and c + distance between b and a = distance between c and b
=> a lies between b and c

Attachment:

abs-p1.jpg [ 16.29 KiB | Viewed 1537 times ]

And we know that a, b, c are distinct positive integers less than 25 and the distance between a and c + distance between b and a = distance between c and b
=> Max a can be 23 making b or c as 24 and other number can be 22
=> Min a can be 2 making b or c as 1 and the other number as 3

=> Range of a = Max a - Min a = 23 - 2 = 21

So, Answer will be C
Hope it helps!

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

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

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