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Re: The positive difference between the greatest and least value [#permalink]
sandy wrote:
Explanation

The first thing you need to do is to clean up these expressions. You have 15th, 50th, and decimals, so it is very difficult to compare values.

\(\frac{6n}{15}\) can be reduced to \(\frac{2n}{5}\).
\(0.3n\) is the same as \(\frac{3n}{10}\).

Change your first expression from \(\frac{2n}{5}\) to \(\frac{4n}{10}\).

\(\frac{19n}{50}\) is pretty close to \(\frac{20n}{50}\) or \(\frac{2n}{5}\), the first expression, but a bit smaller.

Because \(\frac{n}{4}\) is clearly the smallest expression and you need only concern yourself with the smallest, the second smallest, and the biggest, you can ignore \(\frac{19n}{50}\).

Convert\(\frac{n}{4}\) to \(\frac{5n}{20}\), and convert your other expressions to 20ths as well.

You now have \(\frac{8n}{15}\), \(\frac{6n}{20}\) and \(\frac{5n}{20}\).

The difference between the smallest and largest is \(\frac{3n}{20}\). Three times the difference between the two smallest is also 3.


The answer is choice C.



I am confused that what if n=0 or -1?
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Re: The positive difference between the greatest and least value [#permalink]
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sandy wrote:
Explanation

The first thing you need to do is to clean up these expressions. You have 15th, 50th, and decimals, so it is very difficult to compare values.

\(\frac{6n}{15}\) can be reduced to \(\frac{2n}{5}\).
\(0.3n\) is the same as \(\frac{3n}{10}\).

Change your first expression from \(\frac{2n}{5}\) to \(\frac{4n}{10}\).

\(\frac{19n}{50}\) is pretty close to \(\frac{20n}{50}\) or \(\frac{2n}{5}\), the first expression, but a bit smaller.

Because \(\frac{n}{4}\) is clearly the smallest expression and you need only concern yourself with the smallest, the second smallest, and the biggest, you can ignore \(\frac{19n}{50}\).

Convert\(\frac{n}{4}\) to \(\frac{5n}{20}\), and convert your other expressions to 20ths as well.

You now have \(\frac{8n}{15}\), \(\frac{6n}{20}\) and \(\frac{5n}{20}\).

The difference between the smallest and largest is \(\frac{3n}{20}\). Three times the difference between the two smallest is also 3.


The answer is choice C.


The value of n is not specifically indicated.
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Re: The positive difference between the greatest and least value [#permalink]
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Answer: C
6n/15 , 3/10n , 19n/50. , n/4
Their order sequence is: n/4, 3n/10, 19n/50, 6n/15

The positive difference between the greatest and least values above:
The smallest number above is n/4 and biggest is 6n/15 and difference between them is 6n/15 - n/4 = 9n/60 = 3n/20

Three times the positive difference between the two least values above:
3 * (3n/10 - n/4) = 3 * n/20 = 3n/20

Both are the same and answer is C.
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Re: The positive difference between the greatest and least value [#permalink]
I got the answer by assuming n = 1 which made the over all computation to be easy.

Please correct my supposition If I am wrong.
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Re: The positive difference between the greatest and least value [#permalink]
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For negative values of n the ans is not c
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Re: The positive difference between the greatest and least value [#permalink]
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I was more comfortable doing it by converting them all into decimals. But, I think others do raise a valid point of n being negative. DIdn't think of it
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Re: The positive difference between the greatest and least value [#permalink]
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Hi, why is this answer not D) ?

6n/15, 0.3n ,19n/50,n/4

120n/300 , 90n/300 , 114n/300 , 75n/300

Quote:
Quantity A : The positive difference between the greatest and least values above
Quantity B : Three times the positive difference between the two least values above


If n is a positive number, like 1,
A is 120/300- 75/300 = 45/300
B is 3*(90/300 - 75/300) = 45/300
So A=B

But if n is a negative number, like -1,
A is - 75/300 -(-120/300 ) = 45/300
B is 3*(-114/300 - (-120/300)) = 18/300
So A is not equal to B,

So I thought answer should be D), do I miss something?

Best,
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Re: The positive difference between the greatest and least value [#permalink]
For a negative value, OA seems to be wrong. can anyone please clarify?
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Re: The positive difference between the greatest and least value [#permalink]
what if n is 0 or negative ?
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Re: The positive difference between the greatest and least value [#permalink]
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Re: The positive difference between the greatest and least value [#permalink]
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