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# A merchant discounted the sale price of a coat and the sale price of a

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Math Expert
Joined: 02 Sep 2009
Posts: 47200
A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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26 Oct 2015, 09:41
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55% (hard)

Question Stats:

63% (01:37) correct 37% (01:18) wrong based on 1003 sessions

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A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. Kudos for a correct solution. _________________ Director Joined: 10 Mar 2013 Posts: 562 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 26 Oct 2015, 10:13 4 Bunuel wrote: A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount? (1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater. (2) Before the discounts, the sale price of the coat was$10 less than the sale price of the sweater.

Kudos for a correct solution.

(1) not sufficient; we dont't have dollar amounts
(2) Sweter: P dollars, Coat P-10 clearly not sufficient, as no info about %of a discount
(1+2) Still not sufficient Price could be 20$or 1000000$ which will give us differnt results....
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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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27 Oct 2015, 02:43
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. Kudos for a correct solution. St 1 -> actual discount percent not given . Also price of two items not given ... Hence not possible to cal which article is given greater discount . St 2 -> price of sweater =x price of coat = x - 10 not possible to calculate the which article is given greater discount .As actual prices and discount not given. Together not possible also . Hence E _________________ Regards , Retired Moderator Joined: 29 Oct 2013 Posts: 272 Concentration: Finance GPA: 3.7 WE: Corporate Finance (Retail Banking) A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 13 Dec 2015, 03:06 2 Let Pc and Ps, Dc and Ds be prices, percentage discounts for Coat and Sweater respectively. So the question is Pc*Dc>Ps*Ds or Pc*Dc<Ps*Ds? It’s a clever question but if we get rid of all the verbiage it could be stripped down to: Is Pc*Dc>Ps*Ds St1) Dc>Ds St2) Pc<Ps Since two statements put together don’t give us a certain direction of inequality we cant answer the question. Ans E For details see below- St1) Dc=Ds+2--> Pc*(Ds+2)>Ps*Ds? INSUF as we dont know the values of Pc and Ps. To be precise we need to know if Pc>Ps*Ds/(Ds+2)? St2) Pc=Ps-10 --> (Ps-10)*Dc>Ps*Ds? INSUF as we dont know the values of Dc and Ds. To be precise we need to know if Dc>Ds*Ps/(Ps-10)? St1+St2) since Dc=Ds+2 doesnt help us answer Dc>Ds*Ps/(Ps-10)? or Pc=Ps-10 doesnt help us answer if Pc>Ps*Ds/(Ds+2)? INSUF Ans E _________________ Please contact me for super inexpensive quality private tutoring My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876 Current Student Joined: 08 Jan 2015 Posts: 85 Location: Thailand GMAT 1: 540 Q41 V23 GMAT 2: 570 Q44 V24 GMAT 3: 550 Q44 V21 GMAT 4: 660 Q48 V33 GPA: 3.31 WE: Science (Other) A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 14 Feb 2016, 20:48 3 1 A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount? (1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater. (2) Before the discounts, the sale price of the coat was$10 less than the sale price of the sweater.

Statement 1 and 2 are clearly insufficient.

Combine both statement, we have

Price for coat = C
Percent discount for coat = X

Price for sweater = C+2
Percent discount for sweater = X-2

$$\frac{(X-2)(C+10)}{100} > \frac{XC}{100}$$

Multiply both side by 100

$$(X-2)(C+10) > XC$$

Simplify the equation, we get

Is $$10X > 2C + 20$$ ?

Since it depends on 2 variables, we cannot conclude which of the two articles was discounted by greater dollar amount.

Am I doing it right?
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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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12 Jun 2016, 00:55
2
1
Bunuel wrote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. Kudos for a correct solution. Clearly both statements alone are insuff.. So needed to check 2 different values of sweater with very much difference for getting a quick answer. I will check for a price of$20 and another for $1000 for a given discount of 10% (check easy number for fast calculation) for sweater @$20 discount is $2 thus price of coat is$10 less=$10 and discount is 12 %( as discount on the coat was 2 percentage points greater) of it is$1.2.
discount amount of sweater > discount amount of Coat.
similarly for a sweater price of $1000 will have a discount$100
And discount of coat is 12% of 990 =118.....
discount amount of sweater < discount amount of Coat.

Ans E.
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A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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21 Jul 2017, 21:21
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. The question is asking about the exact dollar amount (1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater. --- From percentage point different absolute value cannot be calculated. So clearly it's insufficient. (2) Before the discounts, the sale price of the coat was$10 less than the sale price of the sweater. --- Here it doesn't specify any discount amount. So clearly it's insufficient.

(1) + (2)
Generally discount is calculated on the cost price of the product. Cost price is unknown here.
Besides,
Let's say

Sc = 100 and Ss = 110 (according to statement-2)
and Dc=12% and Ds=10% (according to statement-1)
difference in dollar value = 110(1 - 10%) - 100 (1-12%) = 11

Sc = 100 and Ss = 110 (according to statement-2)
and Dc=7% and Ds=5% (according to statement-1)
difference in dollar value = 110(1 - 5%) - 100 (1-7%) = 11.5

So it's also insufficient.

So ans (E).
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Joined: 06 Jul 2016
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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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22 Jul 2017, 04:54
1
Bunuel wrote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. Kudos for a correct solution. Coat = C -> Discount by a% Sweater = S -> Discount by b% Is $$\frac{C*a}{100}$$ > or < $$\frac{S*b}{100}$$? 1) x = y + 2 We do not know the price. Insufficient. 2) C = S - 10 We do not know the discount %. Insufficient. 1+2) x = y +2 C = S - 10 x = 10% and y = 8% C = 10, S = 20 $$\frac{S*b}{100}$$ = 1.6 $$\frac{C*a}{100}$$ = 1 But if x = 52%, y = 50% C = 1000, S = 1010 $$\frac{S*b}{100}$$ = 505 $$\frac{C*a}{100}$$ = 520 2 different values. Insufficient. E is the answer. _________________ Put in the work, and that dream score is yours! Intern Joined: 23 Jul 2016 Posts: 25 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 01 Jan 2018, 08:40 c=s-10 x=y+2 case 1: c=90 s=100 x=4% y 2% discount on coat = 90*4%=3.6 discount on sweater = 100*2%=2 coat>sweater case 2: c= 490 s =500 x=12% y=10% discount on coat = 490*12%=58.8 discount on sweater=500*10%=50 coat >sweater why am i getting same scenarios are there any constraints on taking the sample values? Math Expert Joined: 02 Aug 2009 Posts: 6286 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 01 Jan 2018, 08:47 Psk13 wrote: c=s-10 x=y+2 case 1: c=90 s=100 x=4% y 2% discount on coat = 90*4%=3.6 discount on sweater = 100*2%=2 coat>sweater case 2: c= 490 s =500 x=12% y=10% discount on coat = 490*12%=58.8 discount on sweater=500*10%=50 coat >sweater why am i getting same scenarios are there any constraints on taking the sample values? Take scenarios where 10 is a big amount as compared to x and y.. say x = 5 and y =15... 4% 0f 5 = 0.2 and 2% of 15 = 0.3, so s>c.. similarly there will be many other values _________________ 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 Intern Joined: 23 Jul 2016 Posts: 25 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 01 Jan 2018, 09:30 chetan2u wrote: Psk13 wrote: c=s-10 x=y+2 case 1: c=90 s=100 x=4% y 2% discount on coat = 90*4%=3.6 discount on sweater = 100*2%=2 coat>sweater case 2: c= 490 s =500 x=12% y=10% discount on coat = 490*12%=58.8 discount on sweater=500*10%=50 coat >sweater why am i getting same scenarios are there any constraints on taking the sample values? Take scenarios where 10 is a big amount as compared to x and y.. say x = 5 and y =15... 4% 0f 5 = 0.2 and 2% of 15 = 0.3, so s>c.. similarly there will be many other values can you please elaborate 10 is a big amount compared to x & Y ??? I DID NOT UNDERSTAND THIS Study Buddy Forum Moderator Joined: 04 Sep 2016 Posts: 1109 Location: India WE: Engineering (Other) Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 28 Jan 2018, 17:24 niks18 amanvermagmat chetan2u Quote: A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount? (1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater. (2) Before the discounts, the sale price of the coat was$10 less than the sale price of the sweater.

Is my interpretation correct that the Q is basically asking for ABSOLUTE change in SP and
to correctly solve it , I either need earlier and discounted SP or only % change in SP and original SP?
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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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28 Jan 2018, 23:09
niks18 amanvermagmat chetan2u

Quote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was \$10 less than the sale price of the sweater.

Is my interpretation correct that the Q is basically asking for ABSOLUTE change in SP and
to correctly solve it , I either need earlier and discounted SP or only % change in SP and original SP?

Hi

Yes, which of the two articles of clothing was discounted by the greater dollar amount? means that we have to compare the ABSOLUTE discount values for coat and sweater.
Re: A merchant discounted the sale price of a coat and the sale price of a &nbs [#permalink] 28 Jan 2018, 23:09
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