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A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 09 Oct 2008, 09:08 9 This post was BOOKMARKED 00:00 Difficulty: 5% (low) Question Stats: 83% (02:52) correct 17% (01:43) wrong based on 240 sessions ### HideShow timer Statistics 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 [Reveal] Spoiler: OA Last edited by Bunuel on 17 Oct 2013, 23:26, edited 2 times in total. Moved to PS forum and added the OA. Senior Manager Joined: 21 Apr 2008 Posts: 497 Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon Followers: 9 Kudos [?]: 52 [2] , given: 13 Re: word prob [#permalink] ### Show Tags 09 Oct 2008, 09:15 2 This post received KUDOS Hi guys, For me E mean price=(720*30+480*15)/1200=24 mean profit=24-18=$6

OA?

Cheers
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09 Oct 2008, 09:21
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

28800-21600 / 1200 = 7200/1200 = 6

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09 Oct 2008, 09:38
5
KUDOS
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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09 Oct 2008, 10:31
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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7060 Location: Pune, India Followers: 2082 Kudos [?]: 13241 [9] , given: 221 Re: A wholesaler bought 1,200 radios for$18 each. The [#permalink]

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17 Oct 2013, 20:45
9
KUDOS
Expert's post
3
This post was
BOOKMARKED
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 01 Jan 2013 Posts: 67 Location: India Followers: 0 Kudos [?]: 27 [0], given: 131 Re: A wholesaler bought 1,200 radios for$18 each. The [#permalink]

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17 Oct 2013, 23:25
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] ### Show Tags 17 Oct 2013, 23:44 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 = $6 Using scale method 15$----4-----Average S.P-----6-----30$W1:W2 = 3:2 Average S.P = 15 + (3/5 X 15) = 24 Average profit = S.P - C.P = 24 - 18 = 6 Intern Joined: 19 Nov 2012 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 2 Re: A wholesaler bought 1,200 radios for$18 each. The [#permalink]

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01 Nov 2013, 21:29
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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08 Dec 2013, 23:55
((0.6.1200*30+0.4*1200*15)-18*1200)/1200=(18*1200+6*1200-18*1200)/1200=6
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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 16 Dec 2013, 13:29 1 This post received KUDOS 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 GMAT Club Legend Joined: 09 Sep 2013 Posts: 12852 Followers: 559 Kudos [?]: 157 [0], given: 0 Re: A wholesaler bought 1,200 radios for$18 each. The [#permalink]

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Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 25 Sep 2015, 07:06 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 VeritasPrepKarishma I approached this question using weighted average only, but a little variation. Since we need to find profit/radio. C1 = $$12 (30-18)$$ 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 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7060 Location: Pune, India Followers: 2082 Kudos [?]: 13241 [0], given: 221 Re: A wholesaler bought 1,200 radios for$18 each. The [#permalink]

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28 Sep 2015, 01:47
Expert's post
1
This post was
BOOKMARKED
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

VeritasPrepKarishma

I approached this question using weighted average only, but a little variation.

Since we need to find profit/radio.

C1 = $$12 (30-18)$$
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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25 Nov 2015, 13:58
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? Re: A wholesaler bought 1,200 radios for$18 each. The   [#permalink] 25 Nov 2015, 13:58
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