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Joined: 10 Jun 2017
Posts: 5
A pen was sold at 10% loss. If the selling price was $6 more then the [#permalink] ### Show Tags Updated on: 15 Oct 2017, 20:57 00:00 Difficulty: 35% (medium) Question Stats: 71% (01:48) correct 29% (02:51) wrong based on 37 sessions ### HideShow timer Statistics A pen was sold at 10% loss. If the selling price was$6 more then the seller could have made a profit of 5%. What was the purchase price of the pen?

(A) 45
(B) 40
(C) 30
(D) 25
(E) None of these.

Originally posted by RockySinha on 15 Oct 2017, 20:52.
Last edited by Bunuel on 15 Oct 2017, 20:57, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: A pen was sold at 10% loss. If the selling price was $6 more then the [#permalink] ### Show Tags 15 Oct 2017, 21:42 1 RockySinha wrote: A pen was sold at 10% loss. If the selling price was$6 more then the seller could have made a profit of 5%. What was the purchase price of the pen?

(A) 45
(B) 40
(C) 30
(D) 25
(E) None of these.

Hi...

You can make the Q very simple if you realize that both loss% and profit % are on cost or purchase price..
So an addition of $6 gets it from -10% to +5%, so a change of 15% in purchase price (P). So 15%of P=6....... P=$$6*\frac{100}{15}=40$$ B _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Senior SC Moderator Joined: 22 May 2016 Posts: 2210 A pen was sold at 10% loss. If the selling price was$6 more then the  [#permalink]

### Show Tags

16 Oct 2017, 03:51
1
RockySinha wrote:
A pen was sold at 10% loss. If the selling price was $6 more then the seller could have made a profit of 5%. What was the purchase price of the pen? (A) 45 (B) 40 (C) 30 (D) 25 (E) None of these. Algebra Let purchase price (cost) = P A pen sold at 10 percent loss means it was sold at 90 percent of P = .90P If sold at 5 percent profit = 1.05P It was sold at .90P IF sold for$6 more: 90P + 6...
It would make a 5% profit: 1.05P

.90P + 6 = 1.05P
6 = .15P
P = $$\frac{6}{.15}= 40$$

At a 10 percent loss, it sold for:
($30)(.9)=$27

IF sold at 5 percent profit:
(1.05)($30) =$31.50

The difference between loss price and 5% profit price should be $6:$31.50 - 27 = $4.50 Too low. That means the base, 30, from which percentages are drawn, is too low (greater number yield greater difference between percentages). But:$4.50 is 3/4 of $6.00.$30 is 3/4 of $40. Try B) 40 Sold at 10 percent loss: (.90)($40) = $36 IF sold at 5 percent profit: (1.05)($40) = $42 ($42 - $36) =$6

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Re: A pen was sold at 10% loss. If the selling price was $6 more then the [#permalink] ### Show Tags 17 Oct 2017, 10:42 RockySinha wrote: A pen was sold at 10% loss. If the selling price was$6 more then the seller could have made a profit of 5%. What was the purchase price of the pen?

(A) 45
(B) 40
(C) 30
(D) 25
(E) None of these.

We can let r = revenue and c = cost. Since the pen was sold at a 10% loss:

r - c = -0.1c

r = 0.9c

Since if the selling price was $6 more then the seller could have made a profit of 5%: r + 6 - c = 0.05c r + 6 = 1.05c Thus: 0.9c + 6 = 1.05c 6 = 0.15c 40 = c Answer: B _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: A pen was sold at 10% loss. If the selling price was$6 more then the &nbs [#permalink] 17 Oct 2017, 10:42
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