Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS –
Solution:
We need to determine whether the number of seconds required to travel d_1 feet at r_1 feet per second is greater than the number of seconds required to travel d_2 feet at r_2 feet per second. We can set this question up in the form of an inequality. Remember that:
time = distance/rate
Thus, we can now ask:
Is d_1/r_1 > d_2/r_2 ?
When we cross multiply we obtain:
Is (d_1)(r_2) > (d_2)(r_1) ?
Statement One Alone:
d_1 is 30 greater than d_2.
From statement one, we can create the following equation:
d_1 = 30 + d_2
Since d_1 = 30 + d_2, we can substitute 30 + d_2 in for d_1 in the inequality (d_1)(r_2) > (d_2)(r_1):
Is (30 + d_2)(r_2) > (d_2)(r_1) ?
We see that we still cannot answer the question. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
r_1 is 30 greater than r_2.
From statement two we can create the following equation:
r_1 = 30 + r_2
Since r_1 = 30 + r_2, we can substitute 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):
Is (d_1)(r_2) > (d_2)(30 + r_2) ?
We see that we still cannot answer the question. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two we have the following equations:
1) d_1 = 30 + d_2
2) r_1 = 30 + r_2
Since d_1 = 30 + d_2 and since r_1 = 30 + r_2, we can substitute 30 + d_2 for d_1 and 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):
Is (30 + d_2)(r_2) > (d_2)(30 + r_2) ?
Is (30)(r_2) + (d_2)(r_2) > (30)(d_2) + (d_2)(r_2) ?
Is (30)(r_2) > (30)(d_2) ?
Is r_2 > d_2 ?
Since we cannot determine whether r_2 is greater than d_2, statements one and two together are not sufficient to answer the question.
Answer: E
