If Father's age is 1 less than twice the son's age

[BTGmoderatorDC]

If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son

How will i know the correct statement in this?

OA A

[DavidG@VeritasPrep]

If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son

How will i know the correct statement in this?

OA A

Son's Age: S
Father's Age: 2S - 1

Statement 1: If the digits of the father's age are the reverse of the digits of the son's age, then we can call the father's age: 10m + n and the son's age 10n +m. Notice that the difference of their ages would be 10m + n - (10n +m) = 9m - 9n = 9(m -n) = This value must be a multiple of 9, as it's 9 * some integer. (This is a decent rule to file away: the difference of two two-digit numbers whose tens and units digits are reversed will always be a multiple of 9.)

If we know that the difference of their ages must be a multiple of 9, then we can say that (2s - 1) - s = 9*T, where T is some integer.
Or s - 1 = 9*T, and s = 9T + 1. Now we can find values for s by setting T equal to simple positive integers. Notice, also that both the father's and son's age must be a two-digit number, and the father must be older than the son.

T = 0 ---> s =9*0 + 1 = 1 ---> Nope; s must be a two-digit number
T = 1 ---> s = 9*1 + 1 = 10---> Nope; the father can't be 01.
T = 2 ---> s = 9*2 + 1 = 19 ---> Nope. Father would be 91 and 91 is not one less than 2*19.
T = 3 ---> s = 9*3 + 1 = 28 ---> Nope. Father would be 82 and 82 is not one less than 2*28.
T = 4 ---> s = 9*4 + 1 = 37 ---> YES. Father would be 73 and 73 IS one less than 2*37.
T = 5 ---> s = 9*5 + 1 = 46 ---> Nope. Father would be 64 and 64 is not one less than 2*46.
T = 6 ---> s = 9*6 + 1 = 55 ---> Nope. Father would also be 55, and the father has to be older than the son. At this point we can stop, as, from here on out, the son will end up being older than father.

The only value that works is when s = 37. Because we can find a unique value statement 1 alone is sufficient.

Statement 2: obviously not sufficient. All we know is that 2S - 1 - S >= 25; this could yield many values.

The answer is A

[DavidG@VeritasPrep]

If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son

How will i know the correct statement in this?

OA A

Side note: Ideally, you'd like to be able to prove whether a statement is sufficient. If you can't, and you have a scenario similar to the one we see here, in which statement 2 is clearly not sufficient on its own, and statement 1 so complex that you feel you need to guess, supposing that the complex statement alone is sufficient is a reasonable way to proceed.