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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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Kudos [?]: 139512 [0], given: 12794

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:

63% (01:39) correct 37% (01:16) wrong based on 720 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. [Reveal] Spoiler: OA _________________ Kudos [?]: 139512 [0], given: 12794 Director Joined: 10 Mar 2013 Posts: 588 Kudos [?]: 512 [2], given: 200 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, 09:13 2 This post received KUDOS 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, 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 _________________ Regards , Kudos [?]: 81 [0], given: 25 Retired Moderator Joined: 29 Oct 2013 Posts: 284 Kudos [?]: 520 [2], given: 197 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, 02:06 2 This post received KUDOS 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 Kudos [?]: 520 [2], given: 197 Manager Joined: 07 Jan 2015 Posts: 91 Kudos [?]: 25 [3], given: 654 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 3 This post received KUDOS 1 This post was BOOKMARKED 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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11 Jun 2016, 23:55
1
KUDOS
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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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Senior Manager
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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
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.

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Kudos [?]: 132 [0], given: 98

Intern
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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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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?

Kudos [?]: 1 [0], given: 166

Math Expert
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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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01 Jan 2018, 07:47
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
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Kudos [?]: 6433 [0], given: 122

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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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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

10 is a big amount compared to x & Y ??? I DID NOT UNDERSTAND THIS

Kudos [?]: 1 [0], given: 166

Re: A merchant discounted the sale price of a coat and the sale price of a   [#permalink] 01 Jan 2018, 08:30
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