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How many years did Dr. Jones live? (1) If Dr. Jones had

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How many years did Dr. Jones live? (1) If Dr. Jones had [#permalink]

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New post 14 Nov 2008, 09:45
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: Dr.Jones--26 [#permalink]

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New post 14 Nov 2008, 10:20
C

I'm not coming up with a great explanation on why.

When all else fails, I'll pick some numbers.

Lets say he was 40. If he became a doc at 30 (i.e., 10 years earlier) then he'd be a doc for 2/3 of his life, this implies that 30 would be 1/3 of his life ( 1 - 2/3) and so he'd live to 90. Any number we pick greater than 15 will work. 15 - 10 = 5, meaning he would have been a doc for 10 years which would be 10/15 or 2/3 of his life...it works. Then 18 - 10 = 8, so dies at 24 and difference is 16, or 16/24 or 2/3 of his life...also works. With the information we're given for (1), there are too many possibilities to narrow it down to a definitive answer.

(2) We're going to have the same problem for (2) alone as (1). If he would have waiting 10 years he would have been a doctor for only 1/3 of his life. So, this implies that whatever age + 10 years = 2/3 of his life that he was not a doc. Start with 30 (reasonable age to become a doctor). 26 + 10 = 36, which is 2/3 of his life as not a doc, so 18 would be 1/3, add that to 36 = 54 when he died. This also works for starting at 38. 38 + 10 = 48, which is 2/3 of his life not a doc, 1/3 as a doc. so 48 = 2/3 of x....x = 72. More than one plausible answer means insufficient in this type of a question.

Now check it with both rules from (1) & (2).

I started with 30 because it's a nice number to use when working with thirds.

30 - 10 = 20 and that'd be 1/3 of his life as not a doc under (1), so he'd died at 60 meaning 20 years as not a doc and 40 years as a doc. It fits. Now check (2). 30 + 10 = 40 becoming a doc and 1/3 of life then is as a doc and 2/3 is not, so 40 = 2/3 of x....x = 60. It works together....but if we can find another number that fits this too, we can't narrow it down and together they'd be insufficient. Try another number

26 + 10 = 36 (as we used with #2). If he was a doc for 1/3 of his life after this, then 36 is 1/3 of his life as not a doc. so he dies at 36 * 1.5 = 54. Now try it with rule from (1). 26 - 10 means he would have been a doc for 2/3 of his life and the 26 - 10 = 16 is the 1/3 of his life that he was not a doctor. 16 * 3 = 48, so it only works for 30 as the starting place, and he lived 60 years.

petercao wrote:
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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Re: Dr.Jones--26 [#permalink]

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New post 14 Nov 2008, 11:00
Awesome explanation jallen, but 16 * 3 = 48 :)

My jumping-off point is that both A and B alone are insufficient (should be obvious), so the answer is either C or E.

Now, this is an algebra problem:

d = the age when Dr. Jones became a doctor
a = Dr. Jones's current age

System of equations:

(d-10 / a) = 1/3
(d+10 / a) = 2/3

This can be solved for d (d=30) and, more importantly, for a (a=60).

So, the correct answer is C.
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Re: Dr.Jones--26 [#permalink]

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New post 14 Nov 2008, 11:03
I had C to begin with and when I did that math, i actually wrote out the "uh oh" that i said in my mind when i figured 16 * 3 = 54. lol Like I've said in teaching this stuff...on test day, 2 + 2 will become 5 in your mind. Write it out on the scratch paper. I fell victim to this as well.

rjacobs wrote:
Awesome explanation jallen, but 16 * 3 = 48 :)

My jumping-off point is that both A and B alone are insufficient (should be obvious), so the answer is either C or E.

Now, this is an algebra problem:

d = the age when Dr. Jones became a doctor
a = Dr. Jones's current age

System of equations:

(d-10 / a) = 1/3
(d+10 / a) = 2/3

This can be solved for d (d=30) and, more importantly, for a (a=60).

So, the correct answer is C.

_________________

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Re: Dr.Jones--26 [#permalink]

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New post 15 Nov 2008, 10:35
As jacobs said its a straight between C and E
But i found the algebra much simpler
combining the two we know 20=x/3 ==> x=60 (say the year he became doc sifted from 1968(stmt1) to 1978(actual year) to 1988(stmt 2) and age from stmt 1 from 2x/3 tostmt 2 x/3==> 1988-1968=20= 2x/3-x/3)
hence C
Re: Dr.Jones--26   [#permalink] 15 Nov 2008, 10:35
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