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A number p equals 3/2 the average of 10, 12, and q. What is q in terms

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Bunuel
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A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   01 Mar 2018, 00:47
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A
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C
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90% (00:57) correct 10% (01:27) wrong based on 67 sessions
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A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

(A) 2p/3 - 22

(B) 4p/3 - 22

(C) 2p - 22

(D) p/2 + 11

(E) 9p/2 - 22
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C
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Re: A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   01 Mar 2018, 00:52
Bunuel wrote:
A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

(A) 2p/3 - 22

(B) 4p/3 - 22

(C) 2p - 22

(D) p/2 + 11

(E) 9p/2 - 22



Step 1: Find the average - \(\frac{10+12+q}{3} = \frac{22+q}{3}\)

Step 2: p is 3/2 the average

p = \(\frac{3}{2}*(\frac{22+q}{3}) = \frac{22+q}{2}\) -> \(p = \frac{22+q}{2}\)

Therefore, q = 2p - 22(Option C)
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Re: A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   01 Mar 2018, 02:58
Bunuel wrote:
A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

(A) 2p/3 - 22

(B) 4p/3 - 22

(C) 2p - 22

(D) p/2 + 11

(E) 9p/2 - 22


it's given in the question that p=3/2*(10+12+q)/3
3 is both numerator and denominator. we can clear way 3 from our calculation.
p= 1/2(22+q)
2p=22+q
2p-22=q

whic is option C .
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Re: A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   02 Mar 2018, 10:37
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Bunuel wrote:
A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

(A) 2p/3 - 22

(B) 4p/3 - 22

(C) 2p - 22

(D) p/2 + 11

(E) 9p/2 - 22


We can create the equation:

p = (3/2) x (10 + 12 + q)/3

p =(22 + q)/2

2p = 22 + q

2p - 22 = q

Answer: C
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A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   14 Mar 2018, 00:55
Bunuel wrote:
A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

(A) 2p/3 - 22

(B) 4p/3 - 22

(C) 2p - 22

(D) p/2 + 11

(E) 9p/2 - 22



Given : p = 3/2 * (10 + 12 + q)/3

means 2p = 22 + q

q = 2p - 22

(C)

Testing values

Take p = 1

1 = 3/2 * (10 + 22 + q)/3

2 = 22 + q

q = 2 - 22

q = -20

Now put p = 1 in all answer choices

Only (C) will give q = -20.

Hence (C)
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Re: A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink] New post   14 Mar 2018, 01:23
P= \(\frac{3}{2}\)* \(\frac{(10+12+q)}{3}\)

P= \(\frac{3}{2}\)* \(\frac{(22+q)}{3}\)

2P= 22+q

q= 2P-22

Answer: C.
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Re: A number p equals 3/2 the average of 10, 12, and q. What is q in terms [#permalink]
14 Mar 2018, 01:23
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