Data Sufficiency

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

Please explain..

Thanks.

Ans is c.

Ref : from 1 (15x + 25y)/)x+y) = 21

not sufficient since two unknows

From 2 : 15x+25y=420, again two unknows hence insufficient

by combining both we can get the values of x and y.
So, ans is C.

I think the answer should be A.

Equation from 1) can give us the ratio of shirts to sweaters, thus it can be determined what sold more(pls note we dont have to find out how many were each items sold)

(15x + 25y)/(x+y) = 21
=> 15x + 25y = 21x + 21y
=> 4y = 6x
=> x:y = 6:4
or x:y = 3:2

Hence X(Shirt) sold more that Y(Sweater) SUFFICIENT

2) Can be written as
15x + 25y = 420

Possible values, X=3, Y=15
X=23, Y=3

Hence not possible to say what sold more. INSUFFICIENT


Cheers!
Aks

dferm wrote: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

Please explain..

Thanks.

This question is much simpler if we think of concepts rather than specific arithmetic.

(1) Well, $21 is closer to $25 than it is to $15. Therefore, $25 must have more "weight" in the weighted average equation. The only way that $25 could have more weight is if there were more items sold at $25 than at $15: sufficient.

(2) We still have too many variables (2) and not enough equations (1): insufficient.

(1) is sufficient and (2) isn't: choose (A).

Sorry to unearth an old thread..In akshatsingh's explanation

15x + 25y = 420

Possible values, X=3, Y=15
X=23, Y=3

Is there a shortcut to identify the possible values like X=3 & Y=15 and X=23, Y=3. In a rush I had assumed that there's only one possible value

Guys - is there a shortcut to decode this equation: 15x + 25y = 420. It takes me over a minutes to evaluate statements of this nature. So if you have any suggestions to speed up the evaluation process, please share them. Thanks!

beater wrote:Guys - is there a shortcut to decode this equation: 15x + 25y = 420. It takes me over a minutes to evaluate statements of this nature. So if you have any suggestions to speed up the evaluation process, please share them. Thanks!

15x + 25y = 420

3x +5y = 84

We know 5y can end up with only 5 or 0 as units digit.

therefore find out what could end up as 4 when added with 5 or 0.

9 or 4.

75 and 9

45 and 39

15 and 69

many such solutions pop up.. practice should make it easier!

kamu wrote:

beater wrote:Guys - is there a shortcut to decode this equation: 15x + 25y = 420. It takes me over a minutes to evaluate statements of this nature. So if you have any suggestions to speed up the evaluation process, please share them. Thanks!

15x + 25y = 420

3x +5y = 84

We know 5y can end up with only 5 or 0 as units digit.

therefore find out what could end up as 4 when added with 5 or 0.

9 or 4.

75 and 9

45 and 39

15 and 69

many such solutions pop up.. practice should make it easier!

Kamu - U lost me after, "We know 5y can end up with only 5 or 0 as units digit.". Can u please explain how to solve for x & y. thanks!

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?

We know that the prices are integer values and we sell shirts and sweater so they also come in integers




(1) The average (arithmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21.
This is sufficient : we know the ratio of shirts to sweaters is 2:3 so more sweaters must have been sold



(2) The total of the prices of all the shirts and sweaters that the store sold during the sale was $420

Total price = 420 = 15*number of shirts +25*number of sweaters

when we simplify we get

84 = 3*number of shirts +5*number of sweaters

But there are a lot of values which satisfy this equation so we don't have a specific value , Hence its insufficient

Answer is A