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

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26 Oct 2015, 08:41
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Difficulty:

55% (hard)

Question Stats:

64% (01:49) correct 36% (01:48) wrong based on 1232 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. _________________ ##### Most Helpful Community Reply Current Student Joined: 07 Jan 2015 Posts: 82 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, 19:48 4 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?
##### General Discussion
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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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26 Oct 2015, 09:13
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.... Answer (E) _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Manager Joined: 13 Mar 2013 Posts: 164 Location: United States Concentration: Leadership, Technology GPA: 3.5 WE: Engineering (Telecommunications) Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 27 Oct 2015, 01:43 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
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A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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13 Dec 2015, 02:06
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
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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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11 Jun 2016, 23:55
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, 20:21
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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Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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22 Jul 2017, 03:54
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, 07:40 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: 7099 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 01 Jan 2018, 07:47 1 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, 08:30 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: 1268 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, 16:24 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, 22:09
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. CEO Joined: 11 Sep 2015 Posts: 3231 Location: Canada Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 11 Aug 2018, 07:20 2 Top Contributor 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.

Target question: Which of the two articles of clothing was discounted by the greater dollar amount?

Let's jump straight to....

Statements 1 and 2 combined
Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT

Let x = price of SWEATER before discount
Let x - 10 = price of COAT before discount

Now let's calculate the discount for each item.

Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)

Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)

So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?

Let's test some values.

Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is the SWEATER has the greater discount

Case a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is the COAT has the greater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: A merchant discounted the sale price of a coat and the sale price of a &nbs [#permalink] 11 Aug 2018, 07:20
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