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# The average (arithmetic mean) of four numbers is 4x + 3. If one of the

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The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 07:35
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Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 07:59
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If the average of four numbers is 4x + 3, then the sum of all four numbers if 4 * (4x + 3) = 16x + 12. If one of the numbers is x, then the average of the remaining three numbers would be: (16x + 12 - x)/3 = (15x + 12)/3 = 5x + 4.

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 08:39
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Bunuel wrote:

Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

Kudos for a correct solution.

Sum of all the four numbers = (4x+3)*4----> 16x+12
one of the number is x so the sum of the other three numbers will be 16x+12-x---> 15x+12
average = sum/3----> (15x+12)/3 = 5x+4. D
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 09:37
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Sum of 4 number is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 10:21
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Sum of 4 no is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 11:21
$$Average = \frac{(Sum of Items)}{(Number of Items)}$$

One of the number is $$X$$
Let us say other numbers are $$A$$,$$B$$,$$C$$

$$Average$$ $$=$$ $$\frac{(X+A+B+C)}{4}$$ = $$4X+3$$
$$A+B+C= 4(4X+3) -X = 15X+12$$

$$Average$$ of three numbers(A,B,C) is = $$\frac{(A+B+C)}{3}$$ $$=$$ $$\frac{(15X+12)}{3}$$ $$=$$ = $$5X+4$$

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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24 Nov 2014, 20:34
Answer = D) 5x + 4

Say x = 1, so average = 7 & total = 28 [For 4 numbers]

Total of remaining 3 numbers = 28-1 = 27

Average$$= \frac{27}{3} = 9$$

Only option D fits in = 5*1 + 4 = 9
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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25 Nov 2014, 05:50
1
Sum of all the four numbers = (4x+3)*4 => 16x+12
one of the number is x so the sum of the other three numbers will be 16x+12-x =>15x+12
average = sum/3 => (15x+12)/3 => 5x+4

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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25 Nov 2014, 06:02
Given that ,
Sum of three no +x=4(4x+3)

Sum of three no = 15x+12

Mean of the three =5x+4

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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25 Nov 2014, 08:11
Bunuel wrote:

Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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05 Dec 2016, 09:49
(A+b+c+ x) / 4 = 4x+3
A+b+c+x = 16x+12
A+b+c = 15x+12. This is the sum.

To find the average:
(15x + 12) / 3 = 5x+4

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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05 Dec 2016, 10:07
sum of 4 numbers/4 = 4x+3
x+sum of three numbers/4 = 4x+3
Sum of three numbers = 4(4x+3) -x = 15x+12
Average of three numbers = Sum of three numbers/3 = 5x+4

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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05 Dec 2016, 10:18
Bunuel wrote:

Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

$$\frac{4( 4x + 3 ) - x}{3}$$

$$= \frac{16x + 12 - x}{3}$$

$$= \frac{15x + 12}{3}$$

$$= 5x + 4$$

Hence, answer will be (D) 5x + 4
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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10 Dec 2016, 06:22
Here is my solution to this one -->

Sum (4)=mean*4 => $$16x+12$$
Hence sum(3) => $$16x+12-x => 15x+12$$
New Mean = $$\frac{15x+12}{3}=> 5x+4$$

Hence D

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The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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02 Feb 2017, 00:10
This question has to do with number properties A generic formula can be applied to multiple instances of the same questions. In general multiply one of the given formula by the amount of numbers N(5x + 8) for example. ----> 25X + 8 - x = 24x - x = 24/4 + 2 --> Solution
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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02 Feb 2017, 08:57
Bunuel wrote:

Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

Kudos for a correct solution.

Source: Chili Hot GMAT

Sum of the 4 numbers is 16x + 12
One of the number is x

So, sum of the other 3 numbers is 15x + 12

Hence, average of the 3 numbers will be $$\frac{( 15x + 12 )}{3} => 5x + 4$$

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the  [#permalink]

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08 Feb 2017, 11:23
Bunuel wrote:

Tough and Tricky questions: Number Properties.

The average (arithmetic mean) of four numbers is 4x + 3. If one of the numbers is x, what is the average of the other three numbers?

A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 15x + 12

We are given that the mean of four numbers is 4x + 3 and that one of the numbers is x.

Thus, the sum of of the 4 numbers is 4(4x + 3) = 16x + 12. Since one of those numbers is x, the sum of the other 3 numbers is:

16x + 12 - x = 15x + 12

Finally, the average of the other 3 numbers is (15x + 12)/3 = 15x/3 + 12/3 = 5x + 4.

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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the &nbs [#permalink] 08 Feb 2017, 11:23
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