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# The average of p, q and 40 is 20 more than the average of p, q, 40 and

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Posts: 52294
The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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17 Sep 2018, 01:11
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:05) correct 28% (02:29) wrong based on 64 sessions

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The average of p, q and 40 is 20 more than the average of p, q, 40 and 60. What is the average of p and q?

(A) 95

(B) 190

(C) 220

(D) 240

(E) 380

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The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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17 Sep 2018, 01:22
1
Bunuel wrote:
The average of p, q and 40 is 20 more than the average of p, q, 40 and 60. What is the average of p and q?

(A) 95

(B) 190

(C) 220

(D) 240

(E) 380

From the question stem, we can form the basic equation: $$\frac{p+q+40}{3} - \frac{p+q+40+60}{4} = 20$$

This can be further simplified as $$4(p+q) + 160 - 3(p+q) - 300 = 20*12 = 240$$

Now, that we have $$p+q = 380$$, the average of p and q is $$\frac{p+q}{2}$$ which is 190(Option B)

P.S It is easy to fall into the trap that the answer is 380, if you don't carefully read the question(which asks for the average)
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Re: The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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17 Sep 2018, 01:30
Bunuel wrote:
The average of p, q and 40 is 20 more than the average of p, q, 40 and 60. What is the average of p and q?

(A) 95

(B) 190

(C) 220

(D) 240

(E) 380

$$\frac{p+q+40}{3}$$ - $$\frac{p +q+ 40 +60}{4}$$= 20

$$\frac{4p + 4q + 160 - 3p -3q - 120 - 180}{12}$$ = 20

p +q -140 = 240

p +q / 2 = 380/2

p + q / 2 = 190.

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Joined: 03 Sep 2018
Posts: 7
The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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18 Sep 2018, 07:37
Analysis:
I'm being given the values of $$\frac{(p + q)}{2}$$ in the answers and an equation $$\frac{(p + q + 40)}{3} = \frac{(p + q + 100)}{4} + 20$$ in the question. It's clear that if I knew $$p + q$$ then I could answer this so I'll choose to multiply the answers by 2 and plug them in. The answers are in ascending order so I'm going to choose B first, then D to find the correct value in no more than 2 attempts (eliminating lesser or greater values in the process).

Strategy:

Reframed Question:
Using the answers below, find the value for p + q that makes the equation true.

Solution:
B = 190, 2B = 380: $$\frac{420}{3}=140$$, $$\frac{480}{4} = 120 + 20 = 140$$

Time:
1:34 - just over a minute on analysis, less than 30 seconds to find the answer.

Thoughts:
Avoiding algebra made me more confident in my answer choice and helped me avoid silly mistakes that I make when I choose Algebra as the strategy.
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Re: The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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19 Sep 2018, 16:59
Bunuel wrote:
The average of p, q and 40 is 20 more than the average of p, q, 40 and 60. What is the average of p and q?

(A) 95

(B) 190

(C) 220

(D) 240

(E) 380

We can create the equation:

(p + q + 40)/3 = 20 + (p + q + 40 + 60)/4

(p + q + 40)/3 = 20 + (p + q + 100)/4

Multiplying the equation by 12, we have:

4(p + q + 40) = 240 + 3(p + q + 100)

4p + 4q + 160 = 240 + 3p + 3q + 300

p + q = 380

Thus, the average p and q is 380/2 = 190.

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Re: The average of p, q and 40 is 20 more than the average of p, q, 40 and  [#permalink]

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19 Sep 2018, 17:38
Bunuel wrote:
The average of p, q and 40 is 20 more than the average of p, q, 40 and 60. What is the average of p and q?

(A) 95

(B) 190

(C) 220

(D) 240

(E) 380

Did you recognize that the sum p+q will appear "as a block" everywhere (DATA and FOCUS)? Doing so, the following approach is absolutely "natural":

$$k = p + q$$

$$? = \frac{k}{2}$$

From the question stem, we know that:

$$\left( {{{p + q + 40} \over 3} = } \right)\,\,\,{{k + 40} \over 3}\,\,\, = 20 + {{k + 100} \over 4}\,\,\,\,\left( { = 20 + {{p + q + 40 + 60} \over 4}} \right)$$

$${{k + 40} \over 3}\,\,\, = 20 + {{k + 100} \over 4}\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,12} \,\,\,\,4\left( {k + 40} \right) = 12 \cdot 20 + 3\left( {k + 100} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,k = 12 \cdot 20 - 4 \cdot 40 + 3 \cdot 100$$



$$? = \frac{k}{2} = 6 \cdot 20 - 4 \cdot 20 + 3 \cdot 50 = 190$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: The average of p, q and 40 is 20 more than the average of p, q, 40 and &nbs [#permalink] 19 Sep 2018, 17:38
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