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# If the average (arithmetic mean) of a and b is 50 and the average (ari

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If the average (arithmetic mean) of a and b is 50 and the average (ari  [#permalink]

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01 Jan 2018, 10:38
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Difficulty:

25% (medium)

Question Stats:

81% (00:59) correct 19% (00:54) wrong based on 46 sessions

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If the average (arithmetic mean) of a and b is 50 and the average (arithmetic mean) of b and c is 70, what is the value of c – a ?

A. 10
B. 20
C. 40
D. 60
E. It cannot be determined from the information given.

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If the average (arithmetic mean) of a and b is 50 and the average (ari  [#permalink]

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01 Jan 2018, 13:45
Bunuel wrote:
If the average (arithmetic mean) of a and b is 50 and the average (arithmetic mean) of b and c is 70, what is the value of c – a ?

A. 10
B. 20
C. 40
D. 60
E. It cannot be determined from the information given.

If $$\frac{a + b}{2} = 50$$, then
$$a + b = 100$$, and similarly
$$c + b = 140$$

Subtract first equation from second equation.

$$c + b = 140$$
$$a + b = 100$$
··························
$$c - a = 40$$

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If the average (arithmetic mean) of a and b is 50 and the average (ari  [#permalink]

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02 Jan 2018, 00:30
Bunuel wrote:
If the average (arithmetic mean) of a and b is 50 and the average (arithmetic mean) of b and c is 70, what is the value of c – a ?

A. 10
B. 20
C. 40
D. 60
E. It cannot be determined from the information given.

$$\frac{(a + b)}{2}$$ = 50

a + b = 100

b = 100 - a -----> (I)

$$\frac{(b + c)}{2}$$ = 70

b + c = 140 ------> (II)

Using equation I & II we get c - a = 40 (C)
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Re: If the average (arithmetic mean) of a and b is 50 and the average (ari  [#permalink]

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20 Jan 2018, 23:12
(a + b)/2 = 50
Hence, a + b = 100 Equation 1

(b + c)/2 = 70
Hence, b + c = 140 Equation 2

Subtract Equation 1 from Equation 2:
(b + c) - (a + b) = 140 - 100
c - a = 40 (Answer C)
Re: If the average (arithmetic mean) of a and b is 50 and the average (ari   [#permalink] 20 Jan 2018, 23:12
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