A Trussian's weight, in keils, can be calculated by taking the square

Question

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

Show Answer

Official Answer

C

(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

davedekoos · Accepted Answer

As shown above, backsolving can work for this problem. For similar problems where the numbers might not be as friendly to work with, we can also follow an algebraic approach.

Given:
Current weight is 3 less than what his weight will be when his age is doubled plus 17
Let  a  = current age
then current weight is  \sqrt{a}

\sqrt{a}+3=\sqrt{2a+17}

Square both sides

a+6\sqrt{a}+9=2a+17

Gather terms on one side

a-6\sqrt{a}+8=0

To make it look more familiar we can substitute  \sqrt{a}=x , now the equation looks like:

x^2-6x+8=0

Factor it

(x-2)(x-4)=0

x=2  or  x=4

Substituting  a  back in  (x=\sqrt{a})

\sqrt{a}=2  or  \sqrt{a}=4 
 a=4  or  a=16

Looking at the answer choices, only 16 is there.

Answer C

TehMoUsE · Answer

\sqrt{age} + 3 = \sqrt{2*age + 17} Start plugging in numbers, answer choice C would give an integer age. Lets try C \sqrt{16} + 3 = \sqrt{2*16 + 17} 4 + 3 = \sqrt{49} 7 = 7 Correct answer is C :-D

Bunuel · Answer

Check other  Age Problems HERE .

PareshGmat · Answer

Age ..................... Weight

x ............................  \sqrt{x}  ..................... Current age/weight

2x+17 ...................... \sqrt{2x+17}  ................ (Seventeen years after he is twice as old as he is now age/weight)

\sqrt{2x+17} - 3 = \sqrt{x}

Only 16 is a perfect square which fits in

Answer = C

douglasvg · Answer

I solved this one back solving, Found it was easier by this way.

Let x be the age in years

X = 2x + 17

For back solving I like to start from the middle one
C) (16 x 2) + 17 = 49 (which brings an integer of 7, can be correct, lets check the others)
D) 51 (it will increase by 2 always)
E) 53
B) 47
A) 45

C is the only answer which brings an integer, therefore its the right answer

BillyZ · Answer

Dear  Bunuel , Let us call the Trussian's current age a. Why my equation incorrect?  17-3\sqrt{a}=2a

KarishmaB · Answer

This is how you form your equation:

Weight = \sqrt{Age}

We need to find his current age so let's say it is y years.
Then, his current weight is  \sqrt{y}

"seventeen years after he is twice as old as now" is  (2y + 17) .
At that time his weight will be  \sqrt{(2y + 17)}

\sqrt{y} + 3 = \sqrt{(2y + 17)}

Try out the options now to see which value satisfies the equation.
y = 16 does.

Answer (C)

gmatophobia · Answer

Current weight = x
Current age = y

x =  \sqrt{y}

Given

\sqrt{2y + 17}  =  \sqrt{y}  + 3

Squaring on both sides

2y + 17 = y + 9 + 6 \sqrt{y}

Simplifying further,

y - 6 \sqrt{y}  + 8 = 0

\sqrt{y}  = 4 or  \sqrt{y}  = 2

Therefore y = 16 or 4

Option C

architkap · Answer

Maybe im missing something here but why is this rated 655-705? It took me approx 30 seconds to test options and find that only C would give integer value. We can also just look at the choices and see that C is the only one that has an integer answer as root. Is the trick here otherwise that it could be a decimal? Please enlighten me.

egmat · Answer

Hi architkap,

Your instinct is a good one, and honestly it's the  fastest  way to crack this specific question. But the rating doesn't come from the arithmetic. It comes from one step you did almost without noticing:  turning the sentence into an equation.

Look at how many people in this very thread stumbled on exactly that. BillyZ set it up as  17 − 3√a = 2a  and got stuck. stne wondered whether  √(2a+17)  could be split into  √(2a) + √17 . The trap is the phrase  "three keils less than he will weigh seventeen years after he is twice as old as he is now."  You have to unpack it as:

- "twice as old as he is now" -  2a 
- "seventeen years after" that -  2a + 17 
- weight then -  √(2a + 17) 
- "now weighs three keils less" -  √a = √(2a + 17) − 3

Getting that chain right, in order, is where most test-takers lose the point - not in plugging in  16 .

On your decimal question - you're exactly right to be suspicious.  "Only C gives an integer root" worked only because the answer choices were built to make one value land on a perfect square. That's a gift the writers handed you; it isn't guaranteed. If you solve it straight, the algebra gives:

-  2a + 17 = a + 6√a + 9  -  a − 6√a + 8 = 0 
- Let  x = √a :  x2 − 6x + 8 = 0  -  x = 2  or  x = 4  -  a = 4  or  a = 16

Notice it produces  two  valid roots. The "teenager" word is what kills  a = 4  and leaves  a = 16 . That extra filtering step is another reason it's rated where it is.

So: nothing wrong with your shortcut - but the difficulty lives in the translation and the two-root catch, both of which the answer choices let you sidestep here.

Answer: C

A Trussian's weight, in keils, can be calculated by taking the square

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GMAT Problem Solving (PS) Questions

A Trussian's weight, in keils, can be calculated by taking the square

Prep Toolkit

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