Vincen wrote: ↑

Thu Jan 14, 2021 12:28 pm

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 \(\$40.\)

Answer: B

Source: Official Guide

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