Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 02:38

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# During a sale, a clothing store sold each shirt at a price

Author Message
Intern
Joined: 10 Jun 2009
Posts: 7
Followers: 0

Kudos [?]: 6 [1] , given: 0

During a sale, a clothing store sold each shirt at a price [#permalink]

### Show Tags

30 Aug 2009, 07:01
1
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

80% (01:59) correct 20% (01:41) wrong based on 206 sessions

### HideShow timer Statistics

During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25. Did the store sell more sweaters than shirts during the sale?
(1) The average (arithmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21. (2) The total of the prices of all the shirts and sweaters that the store sold during the sale was$420.

In the xy-plane, does the line with equation y=3x+2 contain the point(r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0
Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [2] , given: 11602

Re: During a sale, a clothing store sold each shirt at a price [#permalink]

### Show Tags

28 Mar 2012, 09:04
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
In the XY plane, does the line with equation y=3x+2 contain the point (r,s)?

Line with equation $$y=3x+2$$ contains the point $$(r,s)$$ means that when substituting $$r$$ ans $$s$$ in line equation: $$s=3r+2$$ (or $$3r+2-s=0$$) holds true.

So basically we are asked to determine whether $$3r+2-s=0$$ is true or not.

(1) $$(3r+2-s)(4r+9-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r+9-s=0$$ OR both. Not sufficient.

(2) $$(4r-6-s)(3r+2-s)=0$$ --> either $$3r+2-s=0$$ OR $$4r-6-s=0$$ OR both. Not sufficient.

(1)+(2) Both $$4r+9-s=0$$ and $$4r-6-s=0$$ can not be true (simultaneously), as $$4r-s$$ can not equal to both -9 and 6, hence $$3r+2-s=0$$ must be true. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [1] , given: 11602

### Show Tags

28 Mar 2012, 09:04
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
dchow23 wrote:
from statement 2,

shirts x
sweaters y

15x +20y = 420

Can we say that since 60 is a common multiple between the 15 and 20, there will be more than one answer that can satisfy the equation?
If there is a common multiple for

Not sure that I understand your question correctly but generally for such kind of question it's always better to check whether an equation whose solution must be integers only has one or more set of variables satisfying it.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

As for the question.

During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25. Did the store sell more sweaters than shirts during the sale?

(1) The average (arithmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21 --> since the average sale price of$21 is closer to $25 than to$15 then store sold more sweaters than shirts (sweaters have more weight in the weighted average and thus pulled it closer to $21). Sufficient. (2) The total of the prices of all the shirts and sweaters that the store sold during the sale was$420 --> 15x + 25y =420 --> 3x+5y=84. If x=8 and y=12 then x<y but if x=13 and y=5 then x>y. Not sufficient.

_________________
Manager
Joined: 25 Aug 2009
Posts: 175
Followers: 1

Kudos [?]: 91 [0], given: 12

### Show Tags

30 Aug 2009, 08:05
Let number of shirts he bought = Sh
and,number of sweaters he bought = Sw

total price of all shirts and sweaters = Sh*15 + Sw*25

1.) Average price = 21

=> (15*Sh + 25*Sw)/(Sh + Sw) = 21 ----[ Av = total price/total quantity]

=> Sw = 3Sh/2

=> Sh is less than Sw( 3/2 is greater than 1)

Hence, sufficient..

2.) total price = 420

=> Sh*15 + Sw*25 = 420

=> 3Sh + 5Sw = 84

This is possible when

Sh = 18 , Sw = 6

and

Sh = 8 , Sw = 12

In one case, Sh is greater than Sw and vice versa..

Hence, insufficient..

Manager
Joined: 25 Aug 2009
Posts: 175
Followers: 1

Kudos [?]: 91 [0], given: 12

### Show Tags

30 Aug 2009, 08:11
2) In the xy plane, does the line with the equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r + 6 - s)(3r + 2 - s) = 0

The line y = 3x + 2 contains the point means it passes through (r,s)

=> it should satisfy the equation.

=> s = 3r +2
or, 3r + 2 - s = 0 --- equation 1st...

1.) (3r + 2 - s)(4r + 9 - s) = 0

It is possible when
(3r + 2 - s) = 0 or (4r + 9 - s) = 0
if (3r + 2 - s) = 0, then , (r,s) satisfies the equation ( from 1st)
but if, (4r + 9 - s) = 0 then, we can not be sure that (r,s) satisfies the equation ( from 1st)
Hence, insufficient..

2.) Same as 1

Combining both,

both are possible only when
(3r + 2 - s) = 0 ..Hence, (r,s) lies on the line..

Hence, sufficient.. C is the answer..
Manager
Joined: 10 Aug 2009
Posts: 130
Followers: 3

Kudos [?]: 69 [0], given: 10

### Show Tags

30 Aug 2009, 09:08
First question.

Without any equations and thinking logically, it can be shown that the stmt 1 is sufficient.
The average price is 21. Price per shirt =15, price per sweater = 25. If the equal quantity of shirts and sweater was sold, then the average would be 20. Since average is greater than 20, the store sold more items with higher price - sweaters.
Manager
Joined: 24 Aug 2009
Posts: 149
Followers: 5

Kudos [?]: 108 [0], given: 46

### Show Tags

22 Nov 2009, 18:54
gmate2010 wrote:
2) In the xy plane, does the line with the equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r + 6 - s)(3r + 2 - s) = 0

The line y = 3x + 2 contains the point means it passes through (r,s)

=> it should satisfy the equation.

=> s = 3r +2
or, 3r + 2 - s = 0 --- equation 1st...

1.) (3r + 2 - s)(4r + 9 - s) = 0

It is possible when
(3r + 2 - s) = 0 or (4r + 9 - s) = 0
if (3r + 2 - s) = 0, then , (r,s) satisfies the equation ( from 1st)
but if, (4r + 9 - s) = 0 then, we can not be sure that (r,s) satisfies the equation ( from 1st)
Hence, insufficient..

2.) Same as 1

Combining both,

both are possible only when
(3r + 2 - s) = 0 ..Hence, (r,s) lies on the line..

Hence, sufficient.. C is the answer..

I have the question

the question stem itself gives us the info that 3r+2-s = 0

so from statement 1, applying question stem, the equation statisfies irrespective of of what (4r + 9 - s) is.

same for statement 2 as well, so i chose D
Manager
Joined: 24 Aug 2009
Posts: 149
Followers: 5

Kudos [?]: 108 [0], given: 46

### Show Tags

14 Dec 2009, 20:17
ISBtarget wrote:
gmate2010 wrote:
2) In the xy plane, does the line with the equation y = 3x + 2 contain the point (r,s)?
1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r + 6 - s)(3r + 2 - s) = 0

The line y = 3x + 2 contains the point means it passes through (r,s)

=> it should satisfy the equation.

=> s = 3r +2
or, 3r + 2 - s = 0 --- equation 1st...

1.) (3r + 2 - s)(4r + 9 - s) = 0

It is possible when
(3r + 2 - s) = 0 or (4r + 9 - s) = 0
if (3r + 2 - s) = 0, then , (r,s) satisfies the equation ( from 1st)
but if, (4r + 9 - s) = 0 then, we can not be sure that (r,s) satisfies the equation ( from 1st)
Hence, insufficient..

2.) Same as 1

Combining both,

both are possible only when
(3r + 2 - s) = 0 ..Hence, (r,s) lies on the line..

Hence, sufficient.. C is the answer..

I have the question

the question stem itself gives us the info that 3r+2-s = 0

so from statement 1, applying question stem, the equation statisfies irrespective of of what (4r + 9 - s) is.

same for statement 2 as well, so i chose D

I think from statement one 3r+2-s may be 0 or second part may be zero...similarly for statement 2, combining both will prove that 3r+2-s is zero
Manager
Joined: 16 May 2011
Posts: 72
Followers: 0

Kudos [?]: 12 [0], given: 2

### Show Tags

28 Mar 2012, 07:53
from statement 2,

shirts x
sweaters y

15x +20y = 420

Can we say that since 60 is a common multiple between the 15 and 20, there will be more than one answer that can satisfy the equation?
If there is a common multiple for
Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 960
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 171

Kudos [?]: 1611 [0], given: 229

Re: During a sale, a clothing store sold each shirt at a price [#permalink]

### Show Tags

09 Sep 2013, 07:58
Dear Bunuel,

For following statement, you provided two different sets of values for x,y. I tried to identify these values by simply plugging multiples of one variable, but this approach is taking more than 2min, is there any method or trick related to lcm or any thing which we can use to quickly identify all possible values for the equation? I am really struggling with this hit and trial approach, what we should look for while selecting these values.

(2) The total of the prices of all the shirts and sweaters that the store sold during the sale was \$420 --> 15x + 25y =420 --> 3x+5y=84. If x=8 and y=12 then x<y but if x=13 and y=5 then x>y. Not sufficient.

Thanks
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: During a sale, a clothing store sold each shirt at a price   [#permalink] 09 Sep 2013, 07:58
Display posts from previous: Sort by