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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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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.
Answer is D.
Bunuel
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
Posts: 31
The answer is D.
Sum of 4 number is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
Sum of 4 number is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
Sum of 4 no is 16x+12
Sum of 3 no except x is 15x+12
=> mean is 5x+4
The answer is D.
Sum of 3 no except x is 15x+12
=> mean is 5x+4
The answer is D.
Posts: 735
\(Average = \frac{(Sum of Items)}{(Number of Items)}\)
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
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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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
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
Posts: 32
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
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
Given that ,
Sum of three no +x=4(4x+3)
Sum of three no = 15x+12
Mean of the three =5x+4
Answer D
Sum of three no +x=4(4x+3)
Sum of three no = 15x+12
Mean of the three =5x+4
Answer D
Bunuel
The correct answer is D.
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(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
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
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)
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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Bunuel
\(\frac{4( 4x + 3 ) - x}{3}\)
\(= \frac{16x + 12 - x}{3}\)
\(= \frac{15x + 12}{3}\)
\(= 5x + 4\)
Hence, answer will be (D) 5x + 4
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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
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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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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Bunuel
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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Expert reply
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Bunuel
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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