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