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A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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09 Oct 2008, 10:08
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17% (01:43) wrong based on 246 sessions
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A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio? A. $2 B. $3 C. $4 D. $5 E. $6
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Last edited by Bunuel on 18 Oct 2013, 00:26, edited 2 times in total.
Moved to PS forum and added the OA.



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Re: word prob [#permalink]
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09 Oct 2008, 10:15
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Hi guys, For me E mean price=(720*30+480*15)/1200=24 mean profit=2418=$6 OA? Cheers
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Re: word prob [#permalink]
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09 Oct 2008, 10:21
A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks![/quote]
TOTAL SALE PRICE  TOTAL COST / NO OF RADIOS SOLD = AVERAGE PROFIT /RADIO
TOTAL COST = 21,600, TOTAL SALE PRICE = 720*30+480*15 = 21600+7200 = 28800
2880021600 / 1200 = 7200/1200 = 6
E is the answer



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Re: word prob [#permalink]
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09 Oct 2008, 10:38
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FACTOR, FACTOR, FACTOR! Fractorization is your best friend (Do NOT attempt to solve equation, especially any multiplication until all the factorization is completed.) Total Cost: 1200*18 Sales1: 1200*(3/5)*30 = 1200*18 Sales2: 1200*(2/5)*15 = 1200*6 Ave profit = (Sales1 + Sales2  Cost) / 1200 = ( (1200*18)+(1200*6)(1200*18) ) / 1200 = (1200*6)/1200 = 6 The approach shows many details, but in reality all you need is the first line: "( (1200*18)+(1200*6)(1200*18) ) / 1200", which should give you '6' right away after you cross them out. The only arithmetics I had to do were "3/5 * 30 = 18" and "2/5 * 15 = 6" Do simple arithmetic as you read the question! 18 and 6 were already written on my scratch paper by the time I read the word, "average" in the last sentense 1200 was never even involved The whole process should not take more than 30 sec.



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Re: word prob [#permalink]
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09 Oct 2008, 11:31
vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Key to solve this question:  Do not multiply 1,200 with the list price. It will make much longer to solve the problem.  Try to set up basic equation to see the best possible way to solve the problem. Profit = Revenue  Cost Average Profit = (Revenue  Cost) / 1,200  (1) Cost = 18 x 1,200  (2) Revenue = (30 x 1,200 x 60%) + (15 x 1,200 x 40%) = 1,200 [(30 x 0.6) + (15 x 0.4)] = 1,200(18 + 6)  (3) (3)  (2); Revenue  Cost = Profit = 1,200 [18+6]  (1,200 x 18) = 1,200x6  (4) Put (4) in (1); Average Profit = 1,200 x 6 / 1,200 = $6 per radio. The answer is E.



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6
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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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18 Oct 2013, 00:25
VeritasPrepKarishma wrote: vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6 Thanks karishma, I was able to identify weighted average concept here,but was unable to proceed.



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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18 Oct 2013, 00:44
VeritasPrepKarishma wrote: vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6 Using scale method 15$4Average S.P630$ W1:W2 = 3:2 Average S.P = 15 + (3/5 X 15) = 24 Average profit = S.P  C.P = 24  18 = 6



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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01 Nov 2013, 22:29
I think an easy way to answer this problem is to scale it down. 1,200 @ $18 60% @ $30 40% @ $15 Right?
It doesn't matter what number you base your percent on as long as it is a counting number.
So instead of doing the calculations based on 1,200 radios, base the problem on 10 radios.
Purchase Price 10 @ $18 = $180
Sale Price 6 + 4 = 10 6 @ $30 = $180 4 @ $15 = $60 $180 + $60 = $240
Sale Price  Purchase Price = Profit $240  $180 = $60
And because we based this problem on 10 radios to find the price per unit we divide $60 by 10
$60 / 10 = $6



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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03 Nov 2013, 23:14
< 6(60%) ><4(40%)>  15 30
SO the avg will be towards 30 . Exactly 6/10 th of the line segment of 15 units (6*15)/10 = 9
So avg is 9+15 = 24 i.e $24 per radio. Profit = SPCP = 2418 = $6



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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09 Dec 2013, 00:55
((0.6.1200*30+0.4*1200*15)18*1200)/1200=(18*1200+6*120018*1200)/1200=6
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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6 60% for a profit of 12 40% for a loss of 3 Ratio is 3:2 between both Now then, 12(3)3(2)=30 So average 30/5=6 Hence answer is (E) Cheers J



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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25 Sep 2015, 08:06
VeritasPrepKarishma wrote: vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6 VeritasPrepKarishmaI approached this question using weighted average only, but a little variation. Since we need to find profit/radio. C1 = \(12 (3018)\) C2 =\(3 (15  18)\) w1 =\(.6\) w2 = \(.4\) \(Cavg\) =\((12*.6 + (3) * .4 ) / .6+.4\) \(Cavg = 6\) Please let me know if it is alright. Thank you



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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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28 Sep 2015, 02:47
earnit wrote: VeritasPrepKarishma wrote: vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6 VeritasPrepKarishmaI approached this question using weighted average only, but a little variation. Since we need to find profit/radio. C1 = \(12 (3018)\) C2 =\(3 (15  18)\) w1 =\(.6\) w2 = \(.4\) \(Cavg\) =\((12*.6 + (3) * .4 ) / .6+.4\) \(Cavg = 6\) Please let me know if it is alright. Thank you Yes, you are calculating the weighted average of the profit  that's fine.
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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink]
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25 Nov 2015, 14:58
VeritasPrepKarishma wrote: vksunder wrote: A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?
A. $2 B. $3 C. $4 D. $5 E. $6
This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks! Responding to a pm: Yes, you can use weighted average here. You want to find the average selling price. 60% of radios were sold at $30 and 40% at $15. Average selling price = (30*0.6 + 15*0.4)/1 = 24 Average cost price = $18 Average profit = $6 why do we divide by 1 to get the $24?




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