Age

[bia]

How many years did Dr.Jones live?

1) If Dr.Jones had become a doctor 10 years earlier than he did, he would have been a doctor for exactly 2/3 of his life.
2) if Dr.Jones had become a doctor 10 years later than he did, he would have been a doctor for exactly 1/3 of his life

[II]

Ok ... so lets express this algebraically, and assign variables to the unknowns.

The question asks Dr Jones' age. How many years did he live ? So let the number of years he lived = x.

Now lets looks at statement 1:
Lets assign variable y to be the number of years Dr Jones was a Dr.

"If Dr.Jones had become a doctor 10 years earlier than he did"
We can express this as y + 10
"2/3 of his life"
We can express this as (2/3)x
So we can write the equation: y + 10 = (2/3)x.

We can see that we have 2 unknowns and only 1 equation. Hence this is INSUFFICIENT to solve for x.

Now lets look at statement 2, and use the same variables:
"If Dr.Jones had become a doctor 10 years later than he did"
We can express this is y - 10
"1/3 of his life"
We can express this as (1/3)x.
So we can write out the equation: y - 10 = (1/3)x

Again, we have 2 unknowns and only one equation. INSUFF.

With both statement together (1) and (2):
We now have 2 unknowns and 2 equations, can solve for x, hence the answer is C
from statement 1: y + 10 = (2/3)x
from statement 2: y - 10 = (1/3)x

Statement 2 can be simplified by getting y alone on the left hand side:
y = (1/3)x + 10.
We can then substitute this in the equation from statement 1:
((1/3)x + 10) + 10 = (2/3)x
(1/3)x + 20 = (2/3)x
20 = (1/3)x
60 = x

So the Dr lived for 60 years.

Note: We could easily have seen, using the "2 unknowns need to equations to solve" rule, that A,B, and D can be eliminated as answer choices. So we are left with C and E.

Can you please confirm that C is the right answer.

Thanks.
II

[bia]

It's correct. Thanks

[bia]

I thought "If Dr.Jones had become a doctor 10 years earlier than he did" means y - 10

Did I have a reading skill problem?

[luvaduva]

y isn't the year he became a doctor, but rather the number of years he was a doctor.

If he became a doctor 10 years earlier, then the number of years as a doctor increases by 10 => y + 10

[Stuart@KaplanGMAT]

I thought "If Dr.Jones had become a doctor 10 years earlier than he did" means y - 10

Did I have a reading skill problem?

The beauty of DS is that translation errors such as the one you made are irrelevant.

The # of equations/# of unknowns rule is THE most powerful tool for DS. If you recognize that each statement gives you one distinct linear equation and that you have 2 unknowns, you know that you can solve for anything related to the system.

The best DS experts don't even bother translating equations, they just make sure that the equations are, in fact, distinct and linear and then count the # of equations and # of unknowns.

Note, there are lots of exceptions to the rule and that knowing the exceptions is very important if you hope to score high on the GMAT.