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

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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.

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[Reveal] Spoiler: OA

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

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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.

Answer is 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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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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New post 24 Nov 2014, 08:37
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The answer is D.
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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New post 24 Nov 2014, 09:21
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Sum of 4 no is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
The answer is 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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New post 24 Nov 2014, 10:21
\(Average = \frac{(Sum of Items)}{(Number of Items)}\)

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 = \(\frac{(A+B+C)}{3}\) \(=\) \(\frac{(15X+12)}{3}\) \(=\) = \(5X+4\)

Answer: 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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New post 24 Nov 2014, 19:34
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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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

Answer 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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New post 25 Nov 2014, 05:02
Given that ,
Sum of three no +x=4(4x+3)

Sum of three no = 15x+12

Mean of the three =5x+4

Answer 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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New post 25 Nov 2014, 07:11
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


The correct answer is D.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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New post 05 Dec 2016, 08:49
(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

Answer: 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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New post 05 Dec 2016, 09:07
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

Answer (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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New post 05 Dec 2016, 09:18
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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New post 10 Dec 2016, 05:22
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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New post 01 Feb 2017, 23:10
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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New post 02 Feb 2017, 07:57
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 \(\frac{( 15x + 12 )}{3} => 5x + 4\)

Thus, answer will be (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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New post 08 Feb 2017, 10:23
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.

Answer: D
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Re: The average (arithmetic mean) of four numbers is 4x + 3. If one of the   [#permalink] 08 Feb 2017, 10:23
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