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al's age

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by grandh01 » Mon Aug 06, 2012 7:39 pm
Today Al is 3 times as old as Pat, In
13 years, Al will be one year less than
twice as old as Pat will be then. How
many years old is Al today?
(A) 12
(B) 33
(C) 36
(D) 42
(E) 49
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by Anurag@Gurome » Mon Aug 06, 2012 7:51 pm
grandh01 wrote:Today Al is 3 times as old as Pat, In
13 years, Al will be one year less than
twice as old as Pat will be then. How
many years old is Al today?
(A) 12
(B) 33
(C) 36
(D) 42
(E) 49
Let the current age of Al be A
Let the current age of Pat by P

A = 3P ... Equation (1)
After 13 years,
A + 13 = 2(P + 13) - 1 ... Equation (2)

Solving equations (1) and (2),
3P + 13 = 2(P + 13) - 1
3P + 13 = 2P + 26 - 1
P = 12
A = 3P implies A = 3 * 12 = 36

The correct answer is C.
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by armand_h » Tue Aug 07, 2012 2:03 am
A=3P, this implies that A is a multiple of 3, but all suggested solutions are multiple of 3, so this doesn't help.
A+13=2N-1, this implies that A is an even number, so the solution will be either 12, 36 or 42.
let's start with 12 this will give us the following age pairs: today (12,4), in 13 years (25,16), this is not the soluton
Now we try 36: today (36,12), in 13 years (49,25) this is the solution
Answer C
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by GMATGuruNY » Tue Aug 07, 2012 2:47 am
grandh01 wrote:Today Al is 3 times as old as Pat, In
13 years, Al will be one year less than
twice as old as Pat will be then. How
many years old is Al today?
(A) 12
(B) 33
(C) 36
(D) 42
(E) 49
We can plug in the answers, which represent Al's age.

Answer choice C: 36
Since Al's age is 3 times Pat's age, P = 12.
In 13 years, A = 36+13= 49 and P = 12+13 = 25.
Twice Pat's age = 2*25 = 50.
Success! Al's age is 1 less than twice Pat's age.

The correct answer is C.
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