GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 May 2019, 15:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55188
A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

### Show Tags

26 Oct 2015, 09:41
3
40
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:49) correct 37% (01:49) wrong based on 1537 sessions

### HideShow timer Statistics

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 CEO Joined: 12 Sep 2015 Posts: 3717 Location: Canada Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 11 Aug 2018, 08:20 4 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
_________________
Test confidently with gmatprepnow.com
Current Student
Joined: 08 Jan 2015
Posts: 80
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
7
2
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 Joined: 10 Mar 2013 Posts: 495 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 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....
_________________
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: 162
Location: United States
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, 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: 257 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 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 Director Joined: 05 Mar 2015 Posts: 998 Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 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. Intern 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 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). Senior Manager Joined: 06 Jul 2016 Posts: 364 Location: Singapore Concentration: Strategy, Finance Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 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: 24
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: 7681
Re: A merchant discounted the sale price of a coat and the sale price of a  [#permalink]

### Show Tags

01 Jan 2018, 08:47
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
_________________
Intern
Joined: 23 Jul 2016
Posts: 24
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
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1333
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? _________________ It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!! Retired Moderator Joined: 22 Aug 2013 Posts: 1443 Location: India Re: A merchant discounted the sale price of a coat and the sale price of a [#permalink] ### Show Tags 28 Jan 2018, 23:09 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.
Re: A merchant discounted the sale price of a coat and the sale price of a   [#permalink] 28 Jan 2018, 23:09
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.