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# The average (arithmetic mean) of 13 numbers is 70. If the average of

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Math Expert
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The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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29 Aug 2018, 23:31
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5% (low)

Question Stats:

91% (00:58) correct 9% (01:21) wrong based on 41 sessions

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The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

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Posts: 12
The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 00:21
total sum of 13 numbers= 13*70=910

sum of 10 numbers =10* 90=900

AVG of remaining numbers =(910-900)/3= 10/3

ANS:B
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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 00:25
1
avg 70 for 13 numbers : total = 70 * 13 = 910
avg 90 for 10 numbers : total = 90*10 = 900

Remaining 3 numbers total = 910-900
Avg for the three numbers 10/3
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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 01:39
Let a to m be the 13 #
Subtract
a+b+c+... +m=70(13) = 910
- a+b+c+...+j = 90(10)= - 900
k+l+m= 10
Thus, the average is 10/3
B

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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 03:12
Bunuel wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

Look at the deviations of the numbers from the average.

The average is 70.
10 numbers are 20 more than average so have a total deviation of +200.
The 3 numbers will make up for it with a deficit of 200/3 each i.e. their average will be 70 - 200/3 = 10/3

For more on this topic, check: https://www.veritasprep.com/blog/2012/0 ... eviations/
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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 05:24
Bunuel wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

Total age of 13 people = 13*90 = 910

Total age of 10 people = 10*90 = 900

Difference of ages = 910 -900 = 10..........Total age of 3 people.

Average age of 3 people = 10 / 3.

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The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 05:26
Bunuel wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

$$?\,\,\, = \,\,\mu \,\left( {3\,\,{\text{left}}} \right)$$

By the homogeneity nature of the average, we proceed as follows:

$$\sum\nolimits_{\,13} {\, = } \,\,\,13 \cdot 70$$

$$\sum\nolimits_{\,10} {\, = } \,\,\,10 \cdot 90$$

$$\sum\nolimits_{\,13} { - \sum\nolimits_{\,10} \, } = \,\,\,700 + 210 - 900 = 10$$

$$? = \frac{{\sum\nolimits_{\,13} { - \sum\nolimits_{\,10} \, } }}{3} = \frac{{10}}{3}$$

The above follows the notations and rationale taught in the GMATH method.
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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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30 Aug 2018, 05:32
Bunuel wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

$$\frac{13*70 - 10*90}{3}$$

$$= \frac{10}{3}$$ , Answer must be (B)
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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of  [#permalink]

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04 Sep 2018, 03:40
Bunuel wrote:
The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?

(A) $$-130$$

(B) $$\frac{10}{3}$$

(C) $$30$$

(D) $$90$$

(E) $$290$$

We use the formula for the average: average = sum/number. We re-express the formula as sum = average x number.

The sum of the 13 numbers is 13 x 70 = 910, and the sum of 10 of the these numbers is 10 x 90 = 900. Thus the sum of the other 3 numbers is 910 - 900 = 10 and hence the average of these 3 numbers is 10/3.

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Re: The average (arithmetic mean) of 13 numbers is 70. If the average of   [#permalink] 04 Sep 2018, 03:40
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