A bicycle rider rides four stages of a race in 2 hours and 45 minutes. The four stages are named with four different colors: blue, yellow, red, and white. What is the rider’s average speed for the whole race?

(1) The red and blue stages combined are 55 miles long.
(2) The blue and yellow stages combined are 42 miles long.

Kudos for a correct solution.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

IMO : E

\(Avg Speed = \frac{Total Distance Traveled}{Total Time Taken}\)
Total Time is given = 2hr 45 min.

St 1: The red and blue stages combined are 55 miles long.

Only two stages distances are given.
Hence not suff

St 2: The blue and yellow stages combined are 42 miles long.

Only two stages distances are given.
Hence not suff

Combined:

Only three stages distances are given.
Hence not suff
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos ¯\_(ツ)_/¯

PRINCETON REVIEW OFFICIAL SOLUTION:

Before looking closely at the statements, we should consider the question and determine what we’re looking for. The question asks for an average speed, so this is a question about rates and we should write down the rate formula: Rate = Distance / Time. The time is given to us, so the only thing we need to know in order to find the rate is the distance. That’s the missing piece of this puzzle. This means that when we turn to the statements we’re no longer thinking about rate, we’re thinking about distance. If the statement allows us to find the total distance of the race then it is sufficient. If not, it’s insufficient.

Statement 1 tells us the combined distance of two of the stages, but that isn’t enough to know the distance of the whole race. Thus Statement 1 is insufficient.

Statement 2 also tells us the combined distance of only two stages, and is therefore insufficient for the same reason as Statement 1.

When we combine the statements we have to be a bit careful. It may seem that now we have all four stages, but in fact the blue stage was mentioned twice, and nowhere do we have any information about the white stage.

There is no way to know the total distance of the race, and the answer is (E).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources