Today, we present the explanations to questions #34 from our Tricky Data Sufficiency Questions challenge post. You can find the explanations to questions #12 here. Let’s get started.
Question #3
3. If 2x = 2y – 3z, what is the value of z?

(1) y = x + 2
(2) x = y – 2
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient
Whenever the question stem presents you with an equation with multiple variables and asks you to solve for one of them, you should immediately rewrite the equation to find a more useful question. Specifically, you should isolate the variable you’re asked to solve for and then focus on the expression equal to that variable.
Here’s what that would look like for this problem:
2x = 2y – 3z
Add 3z and subtract 2x from each side of the equation to isolate the z term.
3z = 2y – 2x
Factor the two from the righthand side of the equation.
3z = 2(y – x)
Divide each side of the equation by 3.z
Because this is Data Sufficiency, ask, “What do I need to know to know the value of ?” The answer to that question is simply “y x.”
Turn to Statement (1) and try to isolate y – x.
y = x + 2
Subtract y from each side of the equation.
y – x = 2
Statement (1) is sufficient. Eliminate B, C, and E.
Turn to Statement (2) and try to isolate y – x.
x = y – 2
Subtract x from and add 2 to each side of the equation.
y – x = 2
Statement (2) is sufficient. Eliminate A. The correct answer is D.
Question #4
4. On each lab that René completed he received either 100 points or 85 points. On how many labs did he score 100 points?

(1) René’s scores for his completed labs totaled 1140 points.
(2) René completed a total of twelve labs.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient
This problem yields a system of linear equations.
Let the number of labs on which René earned a score of 100 points=x.
The total score for these labs=100x.
Let the number of labs on which René earned a score of 85 points=y.
The total score for these labs=85y.
The total score for all labs=100x+85y.
The question asks us to solve for x.
Statement (1) can be rewritten as 100x+85y=1140.
Statement (2) can be rewritten as x+y=12.
When a DS story problem yields a system of distinct linear equations but implicitly requires that solutions be integers, the smart thing to do is to test values. Generally the numbers involved won’t be very large, so the arithmetic won’t be too daunting.
Statement (1): First, stipulate an integer value for y, then calculate 85y, then subtract that product from 1140. If the difference left isn’t a multiple of 100, don’t consider it further:
Since only one integer value for y yields an integer value for x, and since both x and y must be integers, Statement (1) is sufficient. Eliminate B, C, and E.
Statement (2): Any pair of integers that sum to 12 is a possible pair of values for x and y, so Statement (2) is not sufficient. Eliminate D. The correct answer is A.
Remember to check back on Wednesday for the explanations to questions #5 and #6. In the meantime, you can check your answers here.
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