Solution

Given:• A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order

• A bus started from P and moved to M at an average speed of 30 mph

• After crossing M, it increased its speed to 50 mph, towards N

• From N, it further increased its speed to 60 mph till it reached Q

To find:• The average speed of the bus throughout the whole journey

Approach and Working: The given scenario can be depicted using the following table:

Let us assume that the distance between P and M is x, between M and N is y, and between N and Q is z.

Therefore, the average speed of the whole journey = (x + y + z) / (x/30 + y/50 + z/60)

Analysing Statement 1• As per the information given in Statement 1, the ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3

o Let us assume the time taken for the individual parts of the journey to be 2t, t, and 3t

• As we know the distances are x, y, and z respectively, we can say:

o \(\frac{x}{30}\) = 2t or, x = 60t

o \(\frac{y}{50}\) = t or, y = 50t

o \(\frac{z}{60}\) = 3t or, z = 180t

• We can represent the present scenario as follows:

• Therefore, the average speed = total distance travelled/ total time taken

o Or, average speed = (x + y + z)/(2t + t + 3t) = (60t + 50t + 180t)/6t = \(\frac{290t}{6t} = \frac{145}{3}\) mph

• Hence, Statement 1 is sufficient to answer

Analysing Statement 2• As per the information given in Statement 2, out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN

o Given that distance NQ is more than 3 times the distance MN, we cannot get any exact value of MN

• Hence, Statement 2 is not sufficient to answer

Hence, the correct answer is Option A.

Answer: 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 | Statistics-1 | Statistics-2

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 | Inequalities

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