Question: Cars P and Q started simultaneously from opposite ends of a straight 300-mile express way and traveled towards each other, without stopping, until they passed at location X. to the nearest mile, how many miles of the express way had car P traveled when the two cars passed each other?

1. Up to location X, the average speed of car Q was 15 miles per hour faster than that of car P
2. Up to location X, the average speed of car Q was \(1\frac{1}{3}\)times that of car P

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

The time taken for 2 cars to meet at point X = \(\frac{300}{p+q}\), where P and Q are respective speeds.
Thus, the distance traveled by car P =\(p*\frac{300}{p+q}\)
S1 states that q = p + 15, thus, substituting this above, we get \(p*\frac{300}{2p+15}\). Clearly depends upon value of p.
Insufficient

S2 states that q = \(p*\frac{4}{3}\), this yields = \(p*\frac{300}{p+q}=\frac{900}{7}\)

Sufficient

Correct Option: B

Approach Solution (2):

Time taken for P to meet Q at a common point is same for both P, and Q.

Time for P = \(\frac{Distance}{Speed}=\frac{x(assume)}{P(assume)}\)

Time for Q = \(\frac{300-x}{P+20}\) from A

Equate both as they are equal

So, \(\frac{x}{P}=\frac{300-x}{p+20}\) 

This cannot be solved easily.

From B time for Q = \(\frac{300-x}{1.33p}\)

Equate now, we will get:

\(\frac{x}{P}\)=\(\frac{300-x}{1.33p}\)

Hence we will solve this for x

Correct Option: B

Approach Solution (3):

From the question we are given the total distance. Now since both start simultaneously, time taken by both of them to reach X is same. When time is same, distance covered by them will be directly proportional to their speed.

From S2: We get the speed ratio and thus their distance ratio and we already know their sum i.e., 300

Hence, sufficient.

To make it clear:

\(\frac{s1}{s2}=\frac{d1}{d2} \)

\(s2=\frac{5}{3}s1\)

\(\frac{d1}{d2}=\frac{3}{4}\)

\(\frac{d1}{d2}=\frac{4}{3}\)

\(\frac{d2+d1}{d1}=\frac{7}{3}\)

\(\frac{300}{d1}=\frac{7}{3}\)

\(d1=\frac{900}{7}\)

Correct Option: B

“Cars P and Q started simultaneously from opposite ends of a straight 300-mile express way and traveled towards each other, without stopping, until they passed at location X. to the nearest mile, how many miles of the express way had car P traveled when the two cars passed each other?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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