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How old is he now?

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by neelgandham » Tue Jan 17, 2012 6:21 am
A Trussian's weight, in keils, can be calculated by taking the square root of his age in years. A Trussianteenager now weighs three keils less than he will seventeen years after he is twice as old as he is now. How old is he now?
(A) 14 (B) 15 (C) 16 (D) 17 (E) 18

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by shankar.ashwin » Tue Jan 17, 2012 6:41 am
Start with answer choices

Choice C:

If his current age = 16, weight = 4

17 + 2(16) = 49, weight = 7

Difference = 7-4 = 3 - Satisfies given condition. C IMO
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by Brent@GMATPrepNow » Tue Jan 17, 2012 6:48 am
neelgandham wrote:A Trussian's weight, in keils, can be calculated by taking the square root of his age in years. A Trussianteenager now weighs three keils less than he will seventeen years after he is twice as old as he is now. How old is he now?
(A) 14 (B) 15 (C) 16 (D) 17 (E) 18

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Ages
Let today's age = T
So, 17 years after he is twice as old as he is now = 2T + 17

Weights
Today's weight = root(T)
Future weight = root(2T + 17)

Big step
A Trussianteenager now weighs three keils less than he will seventeen years after he is twice as old as he is now.
This tells us that: root(T) + 3 = root(2T + 17)

Solve for T
Square both sides: T + 6root(T) + 9 = 2T + 17
Simplify: 6root(T) = T + 8


At this point, we can see that T must be a perfect square. So, we'll check the answer choices for perfect squares.

C --> If T = 16, we get 6root(16) = 16 + 8
Simplify to get 24 = 24

Answer = C

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by chieftang » Tue Jan 17, 2012 9:46 am
Pretty good question.

I ended up with a quadratic eqn T^2 - 20T + 64 = 0, factored to (T-16)(T-4)=0, and threw out the soln 4 without further thought since it wasn't an answer choice. Interestingly, though, that soln is the weight... But that left me with T=16 for the age. Answer C
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by ronnie1985 » Wed Jan 18, 2012 12:36 am
If the age of T is x then weight is √x.
The given conditions can be converted into the equation,
√(2x+17) - 3 = √x
Solving we get x = 16 or 4
Since T is teenager, he is 16 years of age.
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by GMATGuruNY » Wed Jan 18, 2012 11:08 am
neelgandham wrote:A Trussian's weight, in keils, can be calculated by taking the square root of his age in years. A Trussianteenager now weighs three keils less than he will seventeen years after he is twice as old as he is now. How old is he now?
(A) 14 (B) 15 (C) 16 (D) 17 (E) 18

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ALWAYS LOOK AT THE ANSWER CHOICES.

When a GMAT question involves a real-world situation, the implied values will be realistic.
The number of dogs sold will be an integer; the weight of a person will not be a radical.
How could a scale in the real world register a weight of 10√2 or 8√3?
Thus, since the current weight of the teenager is the square root of the correct answer, the only viable answer choice here is C.

The correct answer is C.

If we wanted to be very, very safe, we could quickly plug in answer choice C:
Current weight = √16 = 4.
17 years after he is twice as old = 17 + 2*16 = 49, implying a weight of 7.
Weight difference = 7-4 = 3.
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by hazelnut01 » Thu Mar 30, 2017 6:17 pm
neelgandham wrote:A Trussian's weight, in keils, can be calculated by taking the square root of his age in years. A Trussian teenager now weighs three keils less than he will seventeen years after he is twice as old as he is now. How old is he now?
(A) 14 (B) 15 (C) 16 (D) 17 (E) 18

Source: Manhattan Challenge Problems (2002, October 7 - Weighty Years)
Let us call the Trussian's current age a. Why my equation incorrect? 17−3√a=2a?
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by [email protected] » Fri Mar 31, 2017 9:23 am
Hi ziyuenlau,

This question can be solved rather easily by TESTing THE ANSWERS. If you're going to approach it algebraically though, then you have to be careful about whether your variables are referring to age OR weight.

According to the prompt, age is in YEARS and weight is in SQUARE-ROOT of YEARS.

For example:
X = age (in years)
√X = weight (in kiels)

The phrase "A Trussian teenager now WEIGHS three keils less than he will seventeen years after he is twice as old as he is now" focuses on the current WEIGHT relative to a future WEIGHT, so we're going to need a couple of square-root signs. It translates into:

√X = √(2X+17) - 3

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