Walkabout wrote:
Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?
(1) d1 is 30 greater than d2
(2) r1 is 30 greater than r2.
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.
The answer is E.
_________________
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews