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# The average (arithmetic mean) of y numbers is x. If 30 is added to the

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Math Expert
Joined: 02 Sep 2009
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The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 03:32
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The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 03:56
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Let sum of y numbers by S(y)

$$So Average = \frac{S(y)}{y}= x => S(y) = x*y$$

Now 30 is added to the list.
=> Sum = S(y)+30
No. of terms = y+1

$$So average = \frac{S(y) +30}{y+1}= x-5$$
=> S(y)+30 = (x-5)(y+1)
=> xy+30 = xy+x-5y-5
=> x-5y=35
=>5y=x-35
=>$$y= \frac{x}{5} -7$$

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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 03:57
Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

Since mean of "y" numbers is "x"...sum of these no. = mean (or average)* number of nos=x*y
again..if a no 30 is added..sum will be (xy+30) and no of numbers will be y+1;

reapplying same formula... (xy+30)=(x-5)(y+1) as new mean is (x-5) as per question stem;

so...solving we get (xy+30)=xy+x-5y-5
35=x-5y
5y=x-35
or y=x/5-7 hence (D)

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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 04:03
Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

AVG of y Numbers is x, so SUM is yx..
Add 30 to it yx+30..
So new avg = $$\frac{yx+30}{1+y}=x-5.....yx+30=x-5+xy-5y.....35=x-5y......y=\frac{x-35}{5}=\frac{x}{5}-7$$

D
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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 05:43
Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

Sum =Average *Number
Sum of y numbers is xy
Sum of y+1= (x-5)*y+1

xy+30 =(x-5)*(y+1)
xy+30=xy-5y+x-5
30+5=x-5y
x=5(y+7);
y=x/5-7

So Ans:D
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The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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13 Sep 2017, 10:19
Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

If the equation is hard to set up, a simple A*n = S table can help.

The key is that one occurrence of a numeric value added or subtracted to the set of numbers gets its own row; then add column "n" to get total number and column "S" to get total sum (averages CANNOT be added).

__A__|__n__|___S____|
__x__|__y__|___xy____|
_30__|__1__|___30___|
-------|_y+1_|_xy+30__|

The new average is (x - 5). That doesn't get written in the table anywhere. It's the RHS of the equation.

LHS = $$\frac{Total Sum}{Total Number}$$

$$\frac{(xy + 30)}{(y+1)} = (x - 5)$$

$$xy + 30 = (x - 5)(y + 1)$$
$$xy + 30 = xy + x - 5y - 5$$
$$5y = x - 35$$

$$y = \frac{x}{5} - 7$$

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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

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01 Jan 2019, 04:41
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Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the   [#permalink] 01 Jan 2019, 04:41
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