# Question of the Day: Data Sufficiency #1

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question.

Bill went shopping for fruits and vegetables. He purchased a number of potatoes, onions, and lemons in a ratio of 1 : 3 : 5, respectively. How many potatoes did Bill buy?

(1) Bill bought a total of 27 potatoes, onions, and lemons

(2) Bill bought 9 onions

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

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

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

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are not sufficient.

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

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

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are not sufficient.

Question was not answered

Statement (1) If we know the total number of items bought, we can distribute them by dividing the number of objects (27) by the number of parts of the ratio (1 + 3 + 5 = 9). There is no need to solve the question any further. This statement alone is sufficient.

Alternatively, let be the number of potatoes bought by Bill. Then total items = , which is a single-variable equation that we could easily solve. This statement alone is sufficient.

The correct answer is either A or D.

Statement (2) If we know the quantity of one item purchased, we can find the values of the other items from the ratio. There is no need to solve the question. This statement alone is sufficient.

Alternatively, if Bill bought 9 onions and is the number of potatoes, then , i.e. . This statement alone is sufficient.

The correct answer is Choice (D).

47.7% of people answered this question correctly.