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Updated on: 18 Oct 2013, 00:26
1
12
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Difficulty:

5% (low)

Question Stats:

85% (01:47) correct 15% (01:49) wrong based on 325 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

Originally posted by vksunder on 09 Oct 2008, 10:08.
Last edited by Bunuel on 18 Oct 2013, 00:26, edited 2 times in total.
Moved to PS forum and added the OA.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8189
Location: Pune, India
Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 17 Oct 2013, 21:45 12 3 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 _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 09 Oct 2008
Posts: 22

### Show Tags

09 Oct 2008, 10:38
6
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.
##### General Discussion
Senior Manager
Joined: 21 Apr 2008
Posts: 456
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon

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09 Oct 2008, 10:15
2
Hi guys,

For me E

mean price=(720*30+480*15)/1200=24

mean profit=24-18=$6 OA? Cheers _________________ mates, please visit my profile and leave comments http://gmatclub.com/forum/johnlewis1980-s-profile-feedback-is-more-than-welcome-80538.html I'm not linked to GMAT questions anymore, so, if you need something, please PM me I'm already focused on my application package My experience in my second attempt http://gmatclub.com/forum/p544312#p544312 My experience in my third attempt http://gmatclub.com/forum/630-q-47-v-28-engineer-non-native-speaker-my-experience-78215.html#p588275 Retired Moderator Joined: 05 Jul 2006 Posts: 1731 Re: word prob [#permalink] ### Show Tags 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 28800-21600 / 1200 = 7200/1200 = 6 E is the answer Senior Manager Joined: 04 Jan 2006 Posts: 276 Re: word prob [#permalink] ### Show Tags 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.

Manager
Joined: 01 Jan 2013
Posts: 54
Location: India
Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 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. Manager Joined: 01 Jan 2013 Posts: 54 Location: India Re: A wholesaler bought 1,200 radios for$18 each. The  [#permalink]

### Show Tags

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$----4-----Average S.P-----6-----30$

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
Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 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.

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 Intern Joined: 21 Dec 2012 Posts: 1 Re: A wholesaler bought 1,200 radios for$18 each. The  [#permalink]

### Show Tags

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 = SP-CP = 24-18 =$6
Senior Manager
Joined: 23 Oct 2010
Posts: 361
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38

### Show Tags

16 Dec 2013, 14:29
1
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

Cheers
J
Current Student
Joined: 06 Mar 2014
Posts: 256
Location: India
GMAT Date: 04-30-2015
Re: A wholesaler bought 1,200 radios for $18 each. The [#permalink] ### Show Tags 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 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: 8189 Location: Pune, India Re: A wholesaler bought 1,200 radios for$18 each. The  [#permalink]

### Show Tags

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

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.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Manager Joined: 28 Dec 2013 Posts: 68 Re: A wholesaler bought 1,200 radios for$18 each. The  [#permalink]

### Show Tags

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? Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2727 Re: A wholesaler bought 1,200 radios for$18 each. The  [#permalink]

### Show Tags

17 Jul 2018, 16:43
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% of 1,200 is 0.6 x 1,200 = 720. If these 720 radios are sold for $30 each, they will generate a profit of 720 x (30 - 18) = 720 x 12 =$8,640.

The rest of 1,200 - 720 = 480 radios are sold for $15 each, but they will generate a loss of 480 x (18 - 15) = 480 x 3 =$1,440.

Therefore, the total net profit is 8,640 - 1,440 = $7,200, and thus the average profit per radio is 7,200/1,200 =$6.

_________________

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