Question

Is the number of seconds required to travel $d_1$ feet at $r_1$ feet per second greater than the number of seconds required to travel $d_2$ feet at $r_2$ feet per second?
(1) $d_1$ is 30 greater than $d_2$
(2) $r_1$ is 30 greater than $r_2$

• 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.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

Determine if is greater than .

1. Although it is given that d1 = d2 + 30, without information about r1 and r2 it is impossible to determine if is greater than . For example, if d1 = 60, d2 = 30, r1 = 90, and r2 = 60, then d1 = d2 + 30, but and , so is greater than . On the other hand, if d1 = 90, d2 = 60, r1 = 60, and r2 = 30, then d1 = d2 + 30, but and , so is not greater than ; NOT sufficient.
2. Although it is given that r1 = r2 + 30, without information about d1 and d2 it is impossible to determine if is greater than . Taking similar examples from the above statement 1 we can conclude that statement 2 is NOT SUFFICIENT.

• Taking (1) and (2) together is of no more help than either (1) or (2) taken separately because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.
• The correct answer is E; both statements together are still not sufficient.