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
