Material A costs $3 per kilogram, and Material B costs $5 per kilogram

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?

Given: x + y = 10.
Question: is x > y ?

(1) y > 4.

Clearly insufficient: if (y = 4.5) < (x = 5.5), the answer will be YES but if (y = 6) > (x = 4), the answer will be NO.

(2) The cost of the 10 kilograms of material K is less than $40:

3x + 5y < 40

Since y = 10 - x then we'd have:

3x + 5(10 - x) < 40;
2x > 10;
x > 5, so x > y.

Sufficient.

Answer: B.
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The answer has to be B.

Let's setup the weighted average equation for this question:

\(x\) kilograms at 3$ per Kilogram
\(y\) kilograms at 5$ per Kilogram
Yields \(10\) kilograms at z$ per Kilogram
We also know that \(x+y=10\)
So Equation would be : \(3(x)+5(y)=10(z)\)

Now let's look at the statements:

Statement 1: \(y>4\)

Remember: \(x+y=10\)
So: \(x\) could range between 0 and 6. Insufficient

Statement 2: Cost is \(<40\)

So \(3(x)+5(y)<40\)
But \(x+y=10\) so \(x=10-y\)
So \(3(10-y)+5(y)<40\)
So \(30-2y+5y<40\)
So \(2y<10\)
So \(y<5\)

If \(y<5\) then \(x>5\) so \(x>y\) Sufficient

Hence B

Hi...If in the question it is mentioned that x and y are integers, then will the answer be D? because it will lead to contradiction that 'x is not greater than y' or will still answer be b because (there is no clarity whether x may be equal to y or may be less than y'?

If we were told that x and y are integers then y > 4 (5, 6, 7, ...) together with x + y = 10, would be sufficient to say that x is NOT greater than y. But in this case the question would be flawed because the statements would contradict each other which never happens in proper GMAT DS questions.

Hope it's clear.
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Responding to a pm:



To be honest, I am not sure what your question means.
40 < 40 is not correct and neither is x < x since both are equal.
And no, x > x doesn't work either.
If they are the same number, one cannot be greater than the other. You might want to show me the steps of where you come across this problem.
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The question can solved using weighted average concept easily without pen and paper calculation i.e can be solved within 30 seconds.

10kg of mixture uses x kg of Material A and y kg of Material B. If both X and Y are equal, the cost of the 10kg of material K will be right in the middle of $30 and $50 i.e. at $40.

But using stmt B, 10kg of K costs less than $40 dollars i.e. the cost shift towards $30. Hence clearly the quantity of X is more and Y. Hence B is sufficient.

I hope that helps.
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It's clear what the correct answer choice is and how to solve this problem. I think this question is odd though. Typically the 2 DS statements do not contrast each other; whereas, in this question, the two statements cannot both be right. Interesting.

And as Bunuel pointed out here below, this rule was actually not violated since the two statements can both be right as x and y do not have to be integers.

Actually the statements do not contradict each other. Consider x = 5.5 and y = 4.5. The would contradict if we assume that a and y are integers but we are not told that they are.
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Given: Material A costs $3 per kilogram, and Material B costs $5 per kilogram. 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B
We can write: x + y = 10
We can also say the COST of 10 kg of Material K = 3x + 5y

Target question: Is x > y?

Statement 1: y > 4
How does this information work with the fact that x + y = 10?
We'll, there are several possible cases that satisfy statement 1 (and satisfy the equation x + y = 10). Here are two:
Case a: y = 4.5 and x = 5.5. In this case, the answer to the target question is YES, x IS greater than y
Case b: y = 6 and x = 4. In this case, the answer to the target question is NO, x in NOT greater than y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The cost of the 10 kilograms of Material K is LESS THAN $40.
We already know that the COST of 10 kg of Material K = 3x + 5y
So, we can now write: 3x + 5y < 40
Let's reduce this inequality to ONE variable by taking x + y = 10 and rewriting it to get: x = 10 - y
Now replace the x in the inequality with 10-y to get: 3(10-y) + 5y < 40
Expand: 30 - 3y+ 5y < 40
Simplify: 30 + 2y < 40
Subtract 30 from both sides: 2y < 10
Divide both sides by 2 to get: y < 5
Since y is LESS THAN 5, and since x and y add to 10, we know that x is GREATER THAN 5
In other words: y < 5 < x
We can clearly see that the answer to the target question is YES, x IS greater than y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

This is really a weighted averages problem. The giveaway is that we have something made up of two different materials, with different properties (in this case, cost). It's a sort of mixture (and in fact, mixture problems are another type of weighted average). So, we can treat this one like a weighted average if we'd like, and it might actually be easier.

Jot down the given info:

A costs $3/kg
B costs $5/kg

10 kg = x kg A + y kg B

The question is whether there is more of material A, or more of material B, in the mixture. If you're savvy about weighted averages, you'll know that you can figure this out based on the average cost of the mixture. If it costs closer to $3/kg, then there must be more of material A. If it costs closer to $5/kg, there must be more of material B. And if the cost is exactly $4/kg, then the mixture must be exactly equal between A and B.

(1) y > 4 No info about cost here, so that won't help us. Also, y could still make up less than half of the 10kg. For instance, y = 4.5 and x = 5.5. Or, alternatively, it could be more than half: y = 9 and x = 1. Insufficient.

(2) The cost of the 10 kilograms of Material K is less than $40. In other words, the average cost of the material is less than $4/kg. So, the average cost of the material is closer to the cost of A, than it is to the cost of B. Therefore, there must be more of material A in the mix than material B. This lets you definitively answer the question with a "yes." This statement is sufficient.

The correct answer is B.
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Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables and 1 Equation: Let the original condition in a DS question contain 2 variables and 1 Equation. Now, 2 variables and 1 Equation would generally require 1 more equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 more equation to match the numbers of variables and equations in the original condition, the logical answer is D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question. We have to find whether 'x > y'.

=> Given that cost: Material A($3 per kilogram) and Material B($5 per kilogram)
=> 10(Material K) = 3x + 5y

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y) + 1 Equation (10 = 3x + 5y).To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take look at each condition.

Condition(1) tells us that y > 4.

=> If y = 5 then x = 5. Is x > y - NO
=> If y = 4.5 then x = 5.5 , is x > y - YES

Since the answer is not a unique YES or NO, condition(1) is not sufficient by CMT 1.


Condition(2) tells us that The cost of the 10 kilograms of material K is less than $40.

=> 3x + 5y < 40

=> 3x + 5(10-x) < 40

=> 50 - 40 < 2x => 2x > 10 => x > 5

If x > y , then y will be less than x - is x > y - YES

Since the answer is a unique YES, condition (2) alone is sufficient by CMT 1.


Condition(2) alone is sufficient.

So, B is the correct answer.

Answer: B

Video solution from Quant Reasoning starts at 0:28

Solution:

Question Stem Analysis:

We need to determine whether x > y, given that 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B. Notice that x + y = 10.

Statement One Alone:

This is not sufficient. If y = 4.5, then x = 5.5, and hence x > y. However, if y = 5.5, then x = 4.5, and hence x is not greater than y.

Statement Two Alone:

The cost of the 10 kilograms of Material K, in terms of x and y, is 3x + 5y, and we can create the inequality:

3x + 5y < 40

3x + 3y + 2y < 40

3(x + y) + 2y < 40

Since x + y = 10, we have:

3(10) + 2y < 40

30 + 2y < 40

2y < 10

y < 5

Since y is less than 5, then x must be greater than 5 since x + y = 10. Thus, x > y. Statement two alone is sufficient.

Answer: B
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Answer: Option B

Video solution by GMATinsight



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Video solution starts at 1:36:05

Bunuel KarishmaB

Doubt – The question stem says that Material K consists of Material A and B. The solution assumes that Material K contains ‘ONLY’ Material A and B. Why is this correct? Shouldn’t the question explicitly mention ‘CONSISTS ONLY’?
Are there any other questions which play on this aspect?

"If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B"
implies that this is the composition of K. So we know that it does not consist of anything else.

When we say K consists of A and B, we mean that those are the two ingredients that make K.
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I had the same doubt. Bunuel could you please elaborate on this?

'Contains' means something may include a particular thing but there may be other things also present in it. 'Consists' means that a particular thing has only these many things present in it.

if A consists of B and C. It means only B and C are present in A.

If A contains B and C, It means B and C are present but there might be other components too.

I hope this is clear.



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