DS OG 13th 105 problem

[sohailmbaprep]

Material A costs $3 /kg ,and MAterial B costs $5/kg .If 10Kg of material K consists of X kilograms of Material A and y Kg of Material B,is x>y ?
1) y>4
2) the cost of the 10kg of material K is less than $40.

[GMATGuruNY]

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.

Since statement 1 is in terms of y, we should rephrase the question stem in terms of y.

x = the number of kilograms of A.
y = the number of kilograms of B.
Since a total of 10 kilograms are purchased:
x + y = 10.
x = 10-y.

Substituting x=10-y into the question stem (Is x>y?), we get:
10-y > y?
10 > 2y?
5 > y?

Question rephrased: Is y < 5?

Statement 1: y>4.
Since it's possible that y=4.5 or that y=6, no way to determine whether y<5.
INSUFFICIENT.

Statement 2: The cost of the 10 kilograms of material K is less than $40.
Since the cost of each of the x kilograms is $3 and the cost of each of the y kilograms is $5, we get:
3x + 5y < 40.

Substituting x=10-y into 3x+5y<40, we get:
3(10-y) + 5y < 40
30 - 3y + 5y < 40
2y < 10
y < 5.
SUFFICIENT.

The correct answer is B.

[GMATGuruNY]

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.

One more approach.

Since 10 kilograms are purchased, x+y = 10.

Statement 1: y>4
It's possible that y=5 and that x=5, in which case x=y.
It's possible that y=4.5 and that 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.

[sarawutc]

Hi Experts,
I have one question as for this question.
The two statements are contradictory right ?
I thought we wouldn't confront this situation in GMAT though.

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Hi sarawutc,

The two Facts/statements in DS questions will NOT be contradictory, but one of them may contain "options" that the other does not.

In this question:

Fact 1 tells us that y > 4
Fact 2 tells us that y < 5

While your first reaction might be to call these two Facts contradictory, they're not....

IF you were dealing with a DS question that required you to Combine Facts, then there will be at least one possible answer (it's just that sometimes there's more than 1 answer and you're responsible to find those possibilities).

In this case, y could = 4.01, 4.5, 4.999999, etc.

GMAT assassins aren't born, they're made,
Rich