A manufacturer makes and sells 2 products, P and Q. The revenue from t

Revenue last year from the sale of P is 20*1 = 20
Revenue last year from the sale of Q is 17*2 = 34

Total Revenue from the sale of P and Q last year is 54

Average Revenue from the sale of P and Q last year is \(\frac{54}{2+1} = 18\)

Hence, answer will be (E) 18

If the weights were the same we would get an average of (17 + 20) / 2 = 18.5.

But we have more of the product that costs 17$, so the average would be less than 18.5, only 18 works - E

GMATPrepNow

I often get the below logic wrong. Could you please help?

Last year the manufacturer sold twice as many units of Q as P.
So, let's say the manufacturer sold 1 P and 2 Q's

This kind of wording can be tricky at times.

Last year the manufacturer sold TWICE as many units of Q as P = the number of Q's sold is TWICE the number of P's sold = = the number of Q's sold = 2(the number of P's sold)

Likewise, Joe has TWICE as many dogs as cats = the number of dogs is TWICE the number of cats = = the number of dogs = 2(the number of cats)

Does that help?

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley
^^ this is the actual question. What if the question is modified a bit? Could you help me by removing other choices with the EASIEST way in the new version that i modified?
A manufacturer makes and sells 2 products, P and Q. The revenue from the sale of each unit of P is $20.00 and the revenue from the sale of each unit of Q is $17.00. Last year the manufacturer sold twice as many units of P as Q. What was the manufacturer’s average (arithmetic mean) revenue per unit sold of these 2 products last year?

A. $28.50
B. $27.00
C. $19.00
D. $18.50
E. $18.00
Thanks__

Asad

The average revenue cant go beyond 17 and 20 so two options A and B eliminated

twice as many units of P as Q

i.e Average should be twice as close to price of P than to the price of Q i.e. Options D and E eliminated because the price is either midpoint 18.5 or close to Q

P = 20, Q = 17

i.e. Answer will be Option C

Hi Asad,

The Answer choices to this question are really helpful - and they're "spread out" in a way that creates a great 'concept shortcut' so that we really don't have to do much math to answer this question.

To start, in simple terms we're taking the average of a certain number of 17s and a certain number of 20s.... so the average MUST be between 17 and 20. Next, IF we had the SAME number of 17s and 20s, then the average would be (17+20)/2 = 37/2 = 18.5..... However, we do NOT have the same number of each. In your example, we have MORE 20s, which will INCREASE the average to something GREATER than 18.5 (but not greater than 20, since that's not mathematically possible here). There's only one answer that makes sense....


GMAT assassins aren't born, they're made,
Rich

It doesn't matter what the question is. Think this way:
P - Selling price is $20
Q - Selling price is $17

If equal quantities of the two are sold, the average selling price would be right in the middle, i.e. 18.5.

Now, if you sell P more, avg selling price will move toward 20.
But if you sell Q more, avg selling price will move toward 17.

So if Q are more than P in number, avg will lie between 17 and 18.5 (exclusive if both are sold)
If P are more in number than Q, avg will lie between 18.5 and 20 (exclusive if both are sold)

Answer: Option E

Video solution by GMATinsight

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

"manufacturer’s average (arithmetic mean) revenue per unit sold " can be considered same as combined avg of P and Q ?
got confused with COMBINED AVG

Since we are asked for "manufacturer’s average (arithmetic mean) revenue per unit sold" and a single number is given in the options, it means we are looking for combined average for P and Q, not the average of each. Anyway, since each unit of P is sold at $20, its average is simply $20. Similarly for Q. The question tests your understanding of weighted averages.

Check here: https://www.youtube.com/watch?v=_GOAU7moZ2Q

Given:
Revenue: P = 20 $/unit Q = 17 $/unit
Sales: Q = 2P

Average = Total revenue / Total sales = P(20) + 2P(17)/(P+2P) = 54/3 = 18

Hi Scott,

Why does the statement "sold twice as many units of Q as P" mean 2Q = P in this case?
I saw this old thread with the same statement, but the meaning is Q = 2P.
https://gmatclub.com/forum/twice-as-man ... 04188.html

This is a question of weighted average

Q=2P (Reading this correct from the statement is the most trickiest key to unlock this question)

WA= (20*P+17*2P)/(P+2P)
Answer is 18. P in denominator and numerator cancels out.

This is not taking more than 90 seconds ONLY IF YOU DO TAKE Q=2P.

Even in this question it means Q = 2P,

That's why we are assuming if 1 unit of P was sold, then 2 units of Q were sold, i.e. if P = 1, then Q = 2P => Q = 2(1) => Q = 2.

by weighted average method, the average should be less than average of the prices. Average is 18.5. Only 18 is a suitable value from the options