Question

From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30 ?
(1) If, during this period of time, the increase in the balance in the checking account had been 12 percent, then the balance in the account on May 30 would have been $504.
(2) During this period of time, the increase in the balance in the checking account was 8 percent.

• 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: (C)

Both statements together are sufficient, but neither statement alone is sufficient.

1. From statement 1, it is given that the amount on May 30 would have been $504iftheincreasehadbeen12$450. However, the balance on May 30 cannot be determined because the (actual) percent increase is not given. For example, if the increase had been 10%, then the balance on May 30 would have been (1.1) * ($450)=$495, which is different from $504. Thus, statement 1 is not sufficient.
2. From statement 2, it is given that the increase was 8%, the amount on May 30 could be $108(iftheamountonMay1was$100) and the amount on May 30 could be $216(iftheamountonMay1was$200).Thus, statement 2 is also insufficient.
3. Taking (1) and (2) together, it follows that the amount on May 30 was ($450)\ast (1.08)=$486.
   

• The correct answer is C; both statements together are sufficient.