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# The positive difference between the greatest and least value

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Joined: 07 Jun 2014
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The positive difference between the greatest and least value [#permalink]  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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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4722
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1630 [1] , given: 390

Re: The positive difference between the greatest and least value [#permalink]  28 Dec 2016, 15:33
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Expert's post
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]  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?
Manager
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Re: The positive difference between the greatest and least value [#permalink]  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]  28 Mar 2018, 10:47
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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]  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]  06 Jun 2018, 03:47
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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]  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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