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The positive difference between the greatest and least value

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The positive difference between the greatest and least value [#permalink] New post 28 Dec 2016, 15:12
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Question Stats:

52% (01:01) correct 47% (02:07) wrong based on 23 sessions
\(\frac{6n}{15}, 0.3n, \frac{19n}{50}, \frac{n}{4}\)

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


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Drill 2
Question: 10
Page: 316
[Reveal] Spoiler: OA

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Re: The positive difference between the greatest and least value [#permalink] New post 28 Dec 2016, 15:33
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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.
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Re: The positive difference between the greatest and least value [#permalink] New post 27 Mar 2018, 23:13
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] New post 27 Mar 2018, 23:14
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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] New post 28 Mar 2018, 10:47
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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] New post 20 May 2018, 01:29
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] New post 06 Jun 2018, 03:47
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For negative values of n the ans is not c
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: The positive difference between the greatest and least value [#permalink] New post 07 Jun 2018, 20:48
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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
Re: The positive difference between the greatest and least value   [#permalink] 07 Jun 2018, 20:48
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