Question: In the figure, line \(l_1,l_2,l_3\) are parallel to one another. Line- segments AC and DF cut the three lines. If AB = 3, BC = 4, and DE = 5, then which one of the following equals DF?

1. \(\frac{3}{30}\)
2. \(\frac{15}{7}\)
3. \(\frac{20}{3}\)
4. 6
5. \(\frac{35}{3}\)

Answer:

Solution with Explanation:
Approach Solution (1):

We will use the theorem that “Parallel lines divide two intercepts in equal ratio”.

Thus we can say that: \(\frac{AB}{BC}=\frac{DE}{EF}\)

Given values in the question are: AB = 3, BC = 4 and DE = 5

Thus, \(EF=\frac{4*5}{3}=\frac{20}{3}\)

Therefore, \(DF=\frac{20}{3}+5=\frac{35}{3}\)

Correct Option: E

Approach Solution (2):

As we know that parallel lines divide two intercepts in equal ratio. Hence, we will use this concept in this question.

\(\frac{AB}{BC}=\frac{DE}{EF}\)

Given values in the question are: AB = 3, BC = 4 and DE = 5

Put values in the above expression, we will get:

\(\frac{3}{4}=\frac{DE}{EF}\)
\(EF=\frac{20}{3}\)

Hence, DF=\(\frac{20}{3}+5\)

DF=\(\frac{20+15}{3}=\frac{35}{3}\)

Correct Option: E

“In the figure, lineare parallel to one another. Line- segments AC and DF cut the three lines. If AB = 3, BC = 4, and DE = 5, then which one of the following equals DF”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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