GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 May 2020, 09:51

### 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

# Amy's sells kale at x dollar per pound for the first 20 pounds and .8x

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64242
Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

13 Feb 2020, 06:46
00:00

Difficulty:

75% (hard)

Question Stats:

62% (02:12) correct 38% (03:16) wrong based on 52 sessions

### HideShow timer Statistics

Amy's sells kale at x dollar per pound for the first 20 pounds and 0.8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and 0.9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?

A. 24
B. 25
C. 26
D. 27
E. 28

Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2084
Re: Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

13 Feb 2020, 07:01
1
For the six pounds between the 14th and 20th pound, you save 0.1x dollars by buying from Lucia. But after the 20th pound, you save 0.1x dollars by buying from Amy. So for the prices to be equal buying from either person, you'd need to buy six pounds beyond the first 20, and the answer is 26 pounds.

The wording of the question is confusing though -- when it asks for "the minimum number of pounds over 15", I think you could legitimately interpret the question to be asking how many pounds we would need to add to a 15 pound purchase to arrive at equal prices (in which case the answer would be 11). That's not the intended meaning though.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Director
Joined: 25 Jul 2018
Posts: 712
Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

13 Feb 2020, 08:42
1
Amy’s price — 20x+ 0.8x*a
Lucy’s price — 14x + 0.9x*b
—> 20x+ 0.8x*a ≥ 14x+ 0.9x*b

Let’s find the minimum number of (20 + a ) :

20x + 0.8x*a = 14x + 0.9x*b
6x = x( 0.9b —0.8a)
—> $$a = \frac{(9b —60)}{8}$$— must be integer

If $$b= 12$$ , then $$a = \frac{(108–60)}{8 }= 6$$
—> $$20 + a = 26$$

The answer is C

Posted from my mobile device
GMATWhiz Representative
Joined: 07 May 2019
Posts: 709
Location: India
Re: Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

14 Feb 2020, 10:47
1
Bunuel wrote:
Amy's sells kale at x dollar per pound for the first 20 pounds and 0.8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and 0.9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?

A. 24
B. 25
C. 26
D. 27
E. 28

Are You Up For the Challenge: 700 Level Questions

Solution

• Let us assume that the number of pounds over 15 is n.
o So, the total number of pounds $$= 15+ n$$
• So, the total price at which Amy's sells (15 +n) pounds of kale $$= 20*x + (15+n-20) *0.8*x …. Eq.(i)$$
• Now, the total price at which Lucia's sells (15 +n) pounds of kale $$= 14 *x + (15+n -14) *0.9*x …………. Eq. (ii)$$
• From Eq.(i) and Eq.(ii) we can say that deal offered by Amy’s to become a equal or better than Lucia’s:
o $$20x + (15+n-20) * 0.8x ≤ 14 x + (15+n -14) *0.9x$$
o Or, $$20x + (n-5) *0.8x ≤ 14x + (1+n) *0.9x$$
o Or, $$6x + 0.8nx – 4x ≤ 0.9nx+ 0.9x$$
o Or, $$1.1x ≤ 0.1nx$$
o Or, $$11 ≤ n$$
So, for minimum 11 pounds over 15, Amy’s will be a better deal.
Hence total number of pounds = 15 +11 = 26
Thus, the correct answer is Option C.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10590
Location: United States (CA)
Re: Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

21 Feb 2020, 08:04
1
1
Bunuel wrote:
Amy's sells kale at x dollar per pound for the first 20 pounds and 0.8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and 0.9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?

A. 24
B. 25
C. 26
D. 27
E. 28

Are You Up For the Challenge: 700 Level Questions

We can create the inequality:

20x + 0.8x(T - 20) ≤ 14x + 0.9x(T - 14)

20 + 0.8(T - 20) ≤ 14 + 0.9(T - 14)

6 + 0.8T - 16 ≤ 0.9T - 12.6

2.6 ≤ 0.1T

26 ≤ T

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 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.

Manager
Joined: 09 Nov 2015
Posts: 191
Amy's sells kale at x dollar per pound for the first 20 pounds and .8x  [#permalink]

### Show Tags

16 Feb 2020, 00:04
The question is confusing on two counts:
The first, as explained by IanStewart, is that it can be logically interpreted to mean the solver has to find the minimum number of pounds that a buyer has to buy IN EXCESS OF 15 POUNDS so that he gets an equal or better deal from Amy than from Lucia.
The second is the condition in the stem which states that "Amy's becomes an equal OR better deal". According to this, the correct answer could be either C (26 lbs) (the buyer spends the same amount of money whether he buys from Amy or Lucia) or D (27 lbs) ( where he spends less money when he buys from Amy).

Corrigendum: Sorry, my second point is incorrect - I overlooked the "minimum number of pounds" stipulation. First point stands though.
Amy's sells kale at x dollar per pound for the first 20 pounds and .8x   [#permalink] 16 Feb 2020, 00:04

# Amy's sells kale at x dollar per pound for the first 20 pounds and .8x

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne