My most recent blog posts have concerned tricky Data Sufficiency questions about systems of equations. Specifically, they’ve been about what can go wrong when you misremember a rule and assume that it’s possible to solve for two variables if and only if you’re given two equations, and generally that it’s possible to solve for n variables if and only if you’re given n equations.
Today’s post is a short test to see whether you can avoid the traps I’ve recently written about. So that your eyes aren’t drawn to the answer key, we’ll publish it as a separate post. The best way to use the answer key is to read your answers to someone else, and have them tell you what you got wrong. Then retry those questions you got wrong, without first learning what the right answer is. In case you want a hint, after each question below we’ve included a link to the relevant recent post. Don’t use the hint on your first attempt at a question, and don’t use it at all if you don’t need it.
Over my next four blog posts I’ll also publish explanations, just a couple of questions at a time.
1. What is the value of x?

(1) 5x + 3y = 15
(2) y = 5 – (5/3)x
(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
(hint)
2. If y = 2(x + 1) what is the value of x + y?

(1) x + (6/y) = 3
(2) y = x + 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
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
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
5. What is the value of m+n?

(1) mn = 8
(2) 2m = n
(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
6. If xy = 12, what is the value of x – y?

(1) x > y
(2) x + y = 7
(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
7. If p + q = 2r + 3, what is the value of p?

(1) p – r = 6
(2) r = (q/2) + 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
8. What is the value of x?

(1) x – (4/y) = 2
(2) x + 2y = 8
(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
Ready for the answers? Here’s the key.
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