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# a,b and c are distinct natural numbers less than 20. What is the maxim

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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
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In this question make sure not to consider 0 as one of the natural numbers less than 20.

To solve make sure value of c-a is the least. Such as, c=1, and a = 2 or vice versa and b's value is maximum = 19.

|a-b| + |b-c| - |c-a| = |1-19|+|19-2|-|2-1| = 18+17-1 = 34
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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
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This is a moderately difficult question on maximization and minimization.

In this question, to maximize the value of the expression, we need to maximize the first two parts and minimize the third part, since it is negative.

To maximize |a-b|, the best way is to take the biggest possible value for a, and the smallest possible value for b. This means we take a = 19 and b = 1.
So, maximum value of |a-b| = 18.

The value of b is fixed now. In order to maximize the second part, we need to maximize c, so that the difference is maximized. The maximum possible value for c = 18.
Maximum value of |b-c| = 17.

From these values, |c-a| = 1. This is also the minimum value of |c-a|.

So, the maximum possible value of the given expression = 18 + 17 – 1 = 34.
The correct answer option is B.

Hope this helps!
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a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
To answer this question I use a a number line

---------0--c---b------------a--

If you want to maximize the result of the expression you have to put the number so that the differences between ab and bc are maximised

---------0--b--------------c-a--

---------0--1--------------18-19--
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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
CrackVerbalGMAT wrote:
This is a moderately difficult question on maximization and minimization.

In this question, to maximize the value of the expression, we need to maximize the first two parts and minimize the third part, since it is negative.

To maximize |a-b|, the best way is to take the biggest possible value for a, and the smallest possible value for b. This means we take a = 19 and b = 1.
So, maximum value of |a-b| = 18.

The value of b is fixed now. In order to maximize the second part, we need to maximize c, so that the difference is maximized. The maximum possible value for c = 18.
Maximum value of |b-c| = 17.

From these values, |c-a| = 1. This is also the minimum value of |c-a|.

So, the maximum possible value of the given expression = 18 + 17 – 1 = 34.
The correct answer option is B.

Hope this helps!

Since, a,b,c are positive natural numbers, the sign of a,b,c will always be positive.
So if we open the brackets,
a-b-b+c-c+a = 2(a-c)

To maximise this we can put a = 19 and c =1 , so the maximum value would come out to be 36.
What is wrong with this solution? Please explain and clarify
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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
Prerana94 wrote:
Since, a,b,c are positive natural numbers, the sign of a,b,c will always be positive.
So if we open the brackets,
a-b-b+c-c+a = 2(a-c)

To maximise this we can put a = 19 and c =1 , so the maximum value would come out to be 36.
What is wrong with this solution? Please explain and clarify

You can't open a module like that. There are always two signs of module irrespective it contains positive, negative, rational or irrational number.

So, |a-b| + |b-c| - |c-a|
Will be ±(a-b) + ±(b-c) - ±(c-a)
There will be more than just 2(a-c) values.

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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
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Re: a,b and c are distinct natural numbers less than 20. What is the maxim [#permalink]
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