Question

If Pat saved $600ofhisearningslastmonth,howmuchdidPatearnlastmonth?\left(1\right)Patspent$\frac{1}{2}$ofhisearningslastmonthforlivingexpensesandsaved$\frac{1}{3}$ of the remainder.
(2) Of his earnings last month, Pat paid twice as much in taxes as he saved.

• 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.

Answer 1

Answer: (A)

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Arithmetic Operations with rational numbers

Let $E$ be Pat's earnings last month. Find a unique value for $E$.

(1) Pat spent $\frac{1}{2}E$ for living expenses and so $E-\frac{1}{2}E=\frac{1}{2}E$ remained. Pat saved $\frac{1}{3}$ what remained, so Pat saved $\frac{1}{3}\left(\frac{1}{2}E\right)=\frac{1}{6}E$. But Pat saved $600,so$600 =\frac{1}{6}E$ and this gives a unique value for E; SUFFICIENT.

(2) Pat saved $600lastmonthandpaid2($600) in taxes, but there is no way to determine Pat's earnings last month; NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.