Dissect the stem first.
We're told that 10kg of K consists of xA and yB therefore 10=x+y
We can see that A costs $3/kg and B costs $5/kg. We could write this as TC (Total Cost 10KGs)=3x+5y.
is X>Y? = Yes No question so determine if we have a range where X is either definitely larger than Y or definitely lower.
(1) Y>4
We can only use our equation y+x=10. Using numbers then y could be 4.5 and x be 5.5. Or y could be 6 and x be 4. Therefore x may be larger or it may be smaller than y. We can eliminate (1) alone and Each answer options from potential answers.
(2) We're told that TC < 40 so can substitute this to earlier analysis where 3x + 5y must be < 40.
Here picking numbers if y is 4.5 and x is 5.5 then TC =3(5.5)+5(4.5) = 16.5 + 22.5 = 39 which works.
If y is 6 and x is 4 then TC = 3(4)+5(6) = 12 + 30 = 42 which doesn't work.
This looks like we might be sufficient as we know X works when it is 5.5 > Y which is 4.5.
We can confirm by making x and y equal.
If X is 5 and y is 5 then TC = 3(5)+5(5) = 15 + 25 = 40 which again doesn't work. (We also note the range here where x=y TC=40, where x<y TC>40 and where x>y TC<40 )
3x + 5y must be < 40 and where x=y and x<y this statement does not hold true.
We can then confirm that x must be > y and so (2) alone is sufficient.
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Since 10 kilograms are purchased, x+y = 10.Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms
of material K consists of x kilograms of material A and y kilograms of material B, is x > y?
(1) y > 4
(2) The cost of the 10 kilograms of material K is less than $40.
Statement 1: y>4
It's possible that y=5 and x=5, in which case x=y.
It's possible that y=4.5 and x=5.5, in which case x>y.
INSUFFICIENT.
Statement 2: The cost of the 10 kilograms of material K is less than $40.
If 10 kilograms are purchased at a total cost of $40, the average cost per kilogram = 40/10 = $4.
Since the total cost here is actually LESS than $40, the average cost per kilogram is less than $4 -- LESS THAN HALFWAY between x ($3) and y ($5).
For the average cost to be LESS THAN HALFWAY between x and y, more of x must be purchased, implying that x>y.
SUFFICIENT.
The correct answer is B.
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Please notice that, for statement 2, Mitch is using an important concept regarding weighted averages to conclude that this statement is sufficient WITHOUT resorting to lengthy calculations.
If anyone is interested, we have a free and comprehensive video that covers this concept (and others) when it comes to questions involving weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805
Cheers,
Brent
If anyone is interested, we have a free and comprehensive video that covers this concept (and others) when it comes to questions involving weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Hi,
Nowhere in the question is it mentioned that x and y are equal, so we can have this scenario too :
if x=1 and y =2....then the total price will be
3x+5y
=3(1)+5(2)
=13, which is less than 40 and makes the statement 2 true.
Hence you can have both the cases to be true
when x >y (when x= 5.5 and y =4.5)
and when x<y (when x=1 and y =2)
So according to me option B is not the correct choice.
Nowhere in the question is it mentioned that x and y are equal, so we can have this scenario too :
if x=1 and y =2....then the total price will be
3x+5y
=3(1)+5(2)
=13, which is less than 40 and makes the statement 2 true.
Hence you can have both the cases to be true
when x >y (when x= 5.5 and y =4.5)
and when x<y (when x=1 and y =2)
So according to me option B is not the correct choice.
Amitmj,amitmj wrote:Hi,
Nowhere in the question is it mentioned that x and y are equal, so we can have this scenario too :
if x=1 and y =2....then the total price will be
3x+5y
=3(1)+5(2)
=13, which is less than 40 and makes the statement 2 true.
Hence you can have both the cases to be true
when x >y (when x= 5.5 and y =4.5)
and when x<y (when x=1 and y =2)
So according to me option B is not the correct choice.
You're told in the question that "10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B"
Therefore it is not possible for x=1 and y=2, if x=1 then y must =9, conversely if y=9 then x must =1. Breaking down the stem would lead to getting the equation x+y=10 which leads to determining that (2) is sufficient.
