Solution

Given:• While making a non-stop trip, a bus averaged m mph for the first 5 hours and n mph, for the remaining 4 hours.

To find:• The average speed of the bus, in mph, for the whole trip.

Approach and Working: We know, average speed of a journey is equal to the ratio of total distance covered and total time taken to cover that distance.

In this case,

• Total distance covered = 5 x m + 4 x n = 5m + 4n

• Total journey time = 5 + 4 = 9 hours

• Hence, average speed should be \(\frac{5m+4n}{9}\)

So, we can answer the question, if we can find the value of (5m+4n)

Analysing Statement 1As per the information given in statement 1, 7.5m + 6n = 465

Dividing both sides of the equation by 1.5, we get,

• \(\frac{1}{1.5} (7.5m + 6n) =\frac{1}{1.5} * 465\)

Or, 5m + 4n = 310

As we can find the value of 5m + 4n, we can get our answer.

Hence, statement 1 is sufficient.

Analysing Statement 2As per the information given in statement 2, 2m + 3n = 180

From this equation, we cannot separately calculate m and n. Also, we cannot obtain the value of 5m + 4n.

Hence, statement 2 is not sufficient.

Therefore, the correct answer is option A.

_________________

Register for free sessions

Number Properties | Algebra |Quant Workshop

Success Stories

Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant

Articles and Question to reach Q51 | Question of the week

Must Read Articles

Number Properties – Even Odd | LCM GCD

Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2

Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability

Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry

Algebra- Wavy line

Practice Questions

Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com