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# If a set of numbers consists of 1/4 and 1/6, what number can be added

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Math Expert
Joined: 02 Sep 2009
Posts: 50670
If a set of numbers consists of 1/4 and 1/6, what number can be added  [#permalink]

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06 Nov 2017, 21:33
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Difficulty:

25% (medium)

Question Stats:

83% (01:39) correct 17% (01:28) wrong based on 104 sessions

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If a set of numbers consists of 1/4 and 1/6, what number can be added to the set to make the average (arithmetic mean) also equal to 1/4?

A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

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Re: If a set of numbers consists of 1/4 and 1/6, what number can be added  [#permalink]

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06 Nov 2017, 23:01
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Lets say we add a number 'x'. Now average of 1/6, 1/4 and x is 1/4. This means their sum is 3* 1/4 = 3/4

So, 1/6 + 1/4 + x = 3/4 .. This gives x = 3/4 - 1/6 - 1/4 = 1/3

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Re: If a set of numbers consists of 1/4 and 1/6, what number can be added  [#permalink]

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07 Nov 2017, 04:52
On the number line we need to add a number that nullifies the distance between 1/6 and the average, 1/4

So, 1/4 - 1/6 = 3/12 - 2/12 = 1/12, which is the distance between 1/4 and 1/6

Now we need to add the distance to the average to counter the effect of 1/6:

1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3

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Re: If a set of numbers consists of 1/4 and 1/6, what number can be added  [#permalink]

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07 Nov 2017, 08:21
Bunuel wrote:
If a set of numbers consists of 1/4 and 1/6, what number can be added to the set to make the average (arithmetic mean) also equal to 1/4?

A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

The average of 3 numbers must be $$\frac{1}{4}$$

Since one of the 3 numbers is equal to the mean,
the average of the other two numbers should also be 1/4

If the third number is x, (1/6 + x)/2 = 1/4 => 1/6 + x = 1/2 => x = 1/2 - 1/6 = 2/6 = 1/3(Option D)
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Re: If a set of numbers consists of 1/4 and 1/6, what number can be added  [#permalink]

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08 Nov 2017, 16:39
Bunuel wrote:
If a set of numbers consists of 1/4 and 1/6, what number can be added to the set to make the average (arithmetic mean) also equal to 1/4?

A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

We’ll use the formula average = sum/quantity. We can let n = the added number:

(1/4 + 1/6 + n)/3 = 1/4

1/4 + 1/6 + n = 3/4

Multiplying the entire equation by 12, we have:

3 + 2 + 12n = 9

12n = 4

n = 1/3

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Re: If a set of numbers consists of 1/4 and 1/6, what number can be added &nbs [#permalink] 08 Nov 2017, 16:39
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