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Math Expert V
Joined: 02 Sep 2009
Posts: 58442
A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 64% (01:47) correct 36% (01:48) wrong based on 1540 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 Expert Reply GMAT Club Legend  V Joined: 12 Sep 2015 Posts: 4009 Location: Canada Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] Show Tags 8 Top Contributor 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.

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

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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. 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 So, the question asks whether $$\frac{(X-2)(C+10)}{100} > \frac{XC}{100}$$ 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 Senior Manager  B Joined: 10 Mar 2013 Posts: 465 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A) 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 4 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.

(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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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: 250 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 3 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 VP  D Joined: 05 Mar 2015 Posts: 1000 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] Show Tags 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. Intern  B Joined: 04 Jun 2012 Posts: 5 Concentration: General Management, Marketing GPA: 3.8 WE: Information Technology (Computer Software) A merchant discounted the sale price of a coat and the sale price of a [#permalink] Show Tags 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). Senior Manager  G Joined: 06 Jul 2016 Posts: 358 Location: Singapore Concentration: Strategy, Finance Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] Show Tags 2 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.
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Intern  B
Joined: 23 Jul 2016
Posts: 23
Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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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 V
Joined: 02 Aug 2009
Posts: 7988
Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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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
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Joined: 23 Jul 2016
Posts: 23
Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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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
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

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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? _________________ It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!! Retired Moderator P Joined: 22 Aug 2013 Posts: 1428 Location: India Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] Show Tags adkikani wrote: 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.
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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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