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# If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2

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Re: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2 [#permalink]
AbdurRakib wrote:
If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
A. $$\frac{1}{3}$$
B. $$\frac{7}{13}$$
C. 1
D. 3
E. 8

We can create the equation:

(j + j + 5 + 2j - 1 + 4j - 2 + 5j - 1)/5 = 8

13j + 1 = 40

13j = 39

j = 3

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Re: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2 [#permalink]
AbdurRakib wrote:
If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
A. $$\frac{1}{3}$$
B. $$\frac{7}{13}$$
C. 1
D. 3
E. 8

We can create the equation:

(j + j + 5 + 2j - 1 + 4j - 2 + 5j - 1)/5 = 8

13j + 1 = 40

13j = 39

j = 3

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If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2 [#permalink]
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AbdurRakib wrote:
If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
A. $$\frac{1}{3}$$
B. $$\frac{7}{13}$$
C. 1
D. 3
E. 8

GIVEN: he average (arithmetic mean) of 5 numbers $$j$$, $$j + 5$$, $$2j – 1$$, $$4j – 2$$, and $$5j – 1$$ is $$8$$

We can write: $$\frac{j + (j+5) + (2j-1) + (4j-2)+ (5j-1)}{5}=8$$

Multiply both sides of the equation by $$5$$ to get: $$j + (j+5) + (2j-1) + (4j-2)+ (5j-1) = 40$$

Simplify to get: $$13j + 1 = 40$$

Subtract $$1$$ from both sides to get: $$13j = 39$$

Divide both sides by $$13$$ to get: $$j = \frac{39}{13}=3$$

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Originally posted by BrentGMATPrepNow on 07 Apr 2020, 11:00.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:24, edited 1 time in total.
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Re: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j 1, 4j 2 [#permalink]
AbdurRakib wrote:
If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
A. $$\frac{1}{3}$$
B. $$\frac{7}{13}$$
C. 1
D. 3
E. 8

Take a look at the answer choices. Most of them look really easy to work with. Maybe we can just use PITA (Plugging in the Answers).
Let's try C. Our numbers are 1, 6, 1, 2, 4. Is the average 8? Nope! Do we need something bigger or smaller? Bigger.
Okay, let's try D. Our numbers are now 3, 8, 5, 10, and 14. That sure looks close. Do we even really need to add them up and divide by 5, or can we just tell that E is going to be way too big.

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If the average (arithmetic mean) of 5 numbers j, j + 5, 2j 1, 4j 2 [#permalink]
Top Contributor
Given that the Average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8 and we need to find the value of j

================================================================

Theory
‣‣‣ Mean or Average = Sum Of All The Numbers) / (Total Number Of Numbers)

================================================================

Average = $$\frac{Sum}{5}$$ = $$\frac{j + (j+5) + (2j-1) + (4j-2) + (5j-1)}{8}$$ = $$\frac{13j + 1}{5}$$ = 8 (given)

=> 13j + 1 = 5*8 = 40
=> 13j = 40 - 1 = 39
=> j = $$\frac{39}{13}$$ = 3

Hope it helps!

Watch the following video to Learn the Basics of Statistics

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If the average (arithmetic mean) of 5 numbers j, j + 5, 2j 1, 4j 2 [#permalink]
Quick solution:

j+j+2j+4j+5j+5-1-2-1=8*5=40
13j+1=40
13j=39
j=3

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Re: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j 1, 4j 2 [#permalink]
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Re: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j 1, 4j 2 [#permalink]
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