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

 It is currently 18 Jun 2019, 20:09

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

In a certain clothing store, the most expensive pair of socks sells fo

Author Message
TAGS:

Hide Tags

Manager
Joined: 08 Sep 2017
Posts: 77
Location: Colombia
GMAT 1: 710 Q49 V39
In a certain clothing store, the most expensive pair of socks sells fo  [#permalink]

Show Tags

09 Sep 2018, 14:22
4
00:00

Difficulty:

95% (hard)

Question Stats:

51% (02:58) correct 49% (03:10) wrong based on 71 sessions

In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly $18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased? (A) 3 (B) 5 (C) 6 (D) 12 (E) 36 _________________ Kudos please if you liked my post Thanks! RC Moderator Joined: 24 Aug 2016 Posts: 804 Location: Canada Concentration: Entrepreneurship, Operations GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: In a certain clothing store, the most expensive pair of socks sells fo [#permalink] Show Tags 09 Sep 2018, 17:41 1 3 dimmak wrote: In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly$18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36

Let the Price of Cheapest pair is x . Hence price of expensive pair is 2x-1
For $18 , we get n cheapest pair & N expensive pair . Hence , n=18/x & N=18/(2x-1) As per the Q steam : $$n-N=3$$ i.e., 18/x - 18/(2x-1) =3 or, 6/x - 6/(2x-1) =1 or , $$6(2x-1)-6x=x(2x-1)$$ or ,$$2x^2 - 7x +6 =0$$ or, $$(2x-3)(x-2)=0$$ =====> $$x=2,1.5$$ When x=2, 2x-1=3 , n=9 & N=6 When x=1.5, 2x-1=2 , n=12 & N=9.......................Hence the ans is 12 (D) _________________ Please let me know if I am going in wrong direction. Thanks in appreciation. CEO Joined: 12 Sep 2015 Posts: 3783 Location: Canada Re: In a certain clothing store, the most expensive pair of socks sells fo [#permalink] Show Tags 30 Sep 2018, 10:13 1 Top Contributor dimmak wrote: In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly$18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36

Let C = price of one pair of the CHEAPEST socks
So, 2C - 1 = price of one pair of the MOST EXPENSIVE socks

A customer notices that for exactly $18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. As a word equation, we can write: (# of pairs of EXPENSIVE socks purchased with$18) = (# of pairs of CHEAP socks purchased with $18) - 3 With$18, the number of pairs of CHEAP socks we can purchase = 18/C
With $18, the number of pairs of EXPENSIVE socks we can purchase = 18/(2C - 1) So, we can write: (18/(2C - 1)) = (18/C) - 3 Multiply both sides by C to get: 18C/(2C - 1) = 18 - 3C Multiply both sides by (2C - 1) to get: 18C = 18(2C - 1) - 3C(2C - 1) Simplify: 18C = 36C - 18 - 6C² + 3C Simplify: 18C = 39C - 18 - 6C² Rearrange to get: 6C² - 21C + 18 = 0 Divide both sides by 3 to get: 2C² - 7C + 6 = 0 Factor to get: (2C - 3)(C - 2) = 0 So, EITHER 2C - 3 = 0 OR C - 2 = 0 In other words, EITHER C = 1.5 OR C = 2 Let's check each answer choice. If C =$1.5 (the price of one pair of the CHEAPEST socks), then 2C - 1 = $2 (the price of one pair of the MOST EXPENSIVE socks) So, the number of CHEAP socks purchased for$18 = 18/$1.5 = 12 And the number of EXPENSIVE socks purchased for$18 = 18/$2 = 9 Perfect, this meets the condition that the customer can buy three fewer pairs of the most expensive socks than the cheapest socks. If C =$2 (the price of one pair of the CHEAPEST socks), then 2C - 1 = $3 (the price of one pair of the MOST EXPENSIVE socks) So, the number of CHEAP socks purchased for$18 = 18/$2 = 9 And the number of EXPENSIVE socks purchased for$18 = 18/$3 = 6 This ALSO meets the condition that the customer can buy three fewer pairs of the most expensive socks than the cheapest socks. So, the customer bought EITHER 12 pairs of cheap socks or 9 pairs of cheap socks. Check the answer choices, we have 12 Answer: D Cheers, Brent _________________ Test confidently with gmatprepnow.com Senior Manager Joined: 04 Aug 2010 Posts: 420 Schools: Dartmouth College In a certain clothing store, the most expensive pair of socks sells fo [#permalink] Show Tags 28 Feb 2019, 17:43 2 dimmak wrote: In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly$18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36

We can PLUG IN THE ANSWERS, which represent the number of cheap pairs that can be purchased for $18. When the correct answer is plugged in, the number of expensive pairs that can be purchased will be 3 less than the number of cheap pairs that can be purchased. B will yield an ugly price for each cheap pair (18/5 = 3.60) and thus is unlikely to be correct. D: 12 pairs, implying that the price for each cheap pair = 18/12 =$1.50
Since each expensive pair costs $1 less than twice each cheap pair, each expensive pair = 2(1.50) - 1 = 2. Number of$2 expensive pairs that be purchased for $18 = 18/2 = 9. Success! The value in blue is 3 less than the value in red. . _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 6567 Location: United States (CA) Re: In a certain clothing store, the most expensive pair of socks sells fo [#permalink] Show Tags 04 Mar 2019, 20:13 dimmak wrote: In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly$18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36

We can let c = the price of the cheapest socks and e = the price of the expensive socks, and thus:

e = 2c - 1

Letting n = the number of pairs of the cheapest socks that she could buy, we have:

nc = 18

and

(n - 3)e = 18

Equating the second and the third equations, we have:

nc = (n - 3)e

nc = (n - 3)(2c - 1)

nc = 2nc - n - 6c + 3

18 = 2(18) - n - 6(18/n) + 3

18 = 36 - n - 108/n + 3

n - 21 + 108/n = 0

n^2 - 21n + 108 = 0

(n - 9)(n - 12) = 0

n = 9 or n = 12

We see that n is either 12 or 9, but since only 12 is one of the answer choices. 12 is the correct answer.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In a certain clothing store, the most expensive pair of socks sells fo   [#permalink] 04 Mar 2019, 20:13
Display posts from previous: Sort by