chieftang wrote:Today, Bill is 1/4 the age of his father. 12 years ago, Bill was 1/12 the age of his father. How old will Bill's father be one decade from today?

A. 58
B. 66
C. 72
D. 76
E. 82

Happy New Years, BTG!!

GMATGuruNY wrote:=

chieftang wrote: Answer choice E:
Bill's age = (1/4)72 = 18.
12 years ago, Bill's age = 18-12 = 6, which 1/12 of 72.
Success!

Mitch, there's a bit of a gotcha in this one that is subject to interpretation: 1/12 of 72 is 1/12 of the father's age today, but 12 years ago both Bill and his father were 12 years younger! So, Bill's father would have been 60 years old 12 years ago if the answer were E. That's not how you've interpreted it and your value plug-ins clearly bear out the correct interpretation.

But, if we were to set this one up algebraically, then how would we know from the outset to interpret "12 years ago, Bill was 1/12 the age of his father" as "12 years ago, Bill's age was 1/12 of his father's current age" rather than "12 years ago, Bill was 1/12 the age of his father (12 years ago)" ? It feels like you have to solve it both ways and then see which one works out. Incidentally, answer choices for each interpretation are given (both interpretations yield integers for the father's age)! And it's only after solving for the father's age and then plugging it in to determine Bill's age that you can see one interpretation gives a fraction for Bill's age and the other interpretation gives an integer for both Bill and his father!!

Thanks.

chieftang wrote:Today, Bill is 1/4 the age of his father. 12 years ago, Bill was 1/12 the age of his father. How old will Bill's father be one decade from today?

A. 58
B. 66
C. 72
D. 76
E. 82

Happy New Years, BTG!!

chieftang wrote:

GMATGuruNY wrote:=

chieftang wrote: Answer choice E:
Bill's age = (1/4)72 = 18.
12 years ago, Bill's age = 18-12 = 6, which 1/12 of 72.
Success!

Mitch, there's a bit of a gotcha in this one that is subject to interpretation: 1/12 of 72 is 1/12 of the father's age today, but 12 years ago both Bill and his father were 12 years younger! So, Bill's father would have been 60 years old 12 years ago if the answer were E. That's not how you've interpreted it and your value plug-ins clearly bear out the correct interpretation.

But, if we were to set this one up algebraically, then how would we know from the outset to interpret "12 years ago, Bill was 1/12 the age of his father" as "12 years ago, Bill's age was 1/12 of his father's current age" rather than "12 years ago, Bill was 1/12 the age of his father (12 years ago)" ? It feels like you have to solve it both ways and then see which one works out. Incidentally, answer choices for each interpretation are given (both interpretations yield integers for the father's age)! And it's only after solving for the father's age and then plugging it in to determine Bill's age that you can see one interpretation gives a fraction for Bill's age and the other interpretation gives an integer for both Bill and his father!!

Thanks.

Note the phrases in red:
Today, Bill is 1/4 the age of his father. 12 years ago, Bill was 1/12 the age of his father.
Generally, the same phrasing should refer to the same value -- in this case, the father's current age -- unless we are explicitly told otherwise.

If the second sentence wished to refer to the age of the father 12 years ago, I would expect wording along the following lines:
Twelve years ago, Bill was 1/12 as old as his father WAS THEN.

That being said, I agree that the intent of the problem is subject to interpretation.

user123321 wrote:

chieftang wrote:Today, Bill is 1/4 the age of his father. 12 years ago, Bill was 1/12 the age of his father. How old will Bill's father be one decade from today?

A. 58
B. 66
C. 72
D. 76
E. 82

Happy New Years, BTG!!

There is ambiguity in this question for sure. As we need to interpret 12 years ago bill was 1/12 the age of his father as, B-12 = (F-12)/12
But unfortunately the current answer seems not present among the choices.
But if we take B-12 = F/12 then we are getting answer as 82.
is it from a standard source?

user123321

GMATGuruNY wrote:=

chieftang wrote:Today, Bill is 1/4 the age of his father. 12 years ago, Bill was 1/12 the age of his father. How old will Bill's father be one decade from today?

A. 58
B. 66
C. 72
D. 76
E. 82

Happy New Years, BTG!!

We can plug in the answers, which represent the age of Bill's father 10 years from today.

Since Bill today is 1/4 the age of his father, when 10 is subtracted from the correct answer, the result should be a multiple of 4.
The only viable answer choices are A (58-10 = 48) and E (82-10 = 72).
Eliminate B, C and D.

chieftang wrote:Thanks again for the feedback. Hopefully this type of ambiguity doesn't pop up often.

By the way, answer choice B was initially viable too and shouldn't have been eliminated immediately... B (66-10 = 56). 56 is a multiple of 4, and would make Bill 14 years old today. But it doesn't work out since it isn't divisible by 12.