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

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A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 03 Nov 2014, 08:12
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


Check other Age Problems HERE.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 03 Nov 2014, 13:18
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


\(\sqrt{age} + 3 = \sqrt{2*age + 17}\)

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
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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 03 Nov 2014, 20:44
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


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
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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 21 Dec 2015, 02:54
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

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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 30 Dec 2015, 07:57
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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
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A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 30 Mar 2017, 18:13
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


Dear Bunuel, Let us call the Trussian's current age a. Why my equation incorrect? \(17-3\sqrt{a}=2a\)
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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 31 Mar 2017, 03:58
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ziyuen wrote:
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


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


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)
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A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 16 Dec 2017, 06:23
VeritasPrepKarishma wrote:
ziyuen wrote:
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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

Kudos for a correct solution.


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


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)


Dear Karishma,

Is there any way to solve this equation algebraically ( A is the present age )
\(\sqrt{2A +17} -\sqrt{A}=3\)

I was thinking along the lines of \(\sqrt{2A +17}\) =\(\sqrt{2A}\) +\(\sqrt{17}\)obviously this is NOT true. Square root is not distributive over addition.

Is there any other way for simplification ?
Thank you.
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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 16 Dec 2017, 06:52
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Expert's post
stne wrote:
Dear Karishma,

Is there any way to solve this equation algebraically ( A is the present age )
\(\sqrt{2A +17} -\sqrt{A}=3\)

I was thinking along the lines of \(\sqrt{2A +17}\) =\(\sqrt{2A}\) +\(\sqrt{17}\)obviously this is NOT true. Square root is not distributive over addition.

Is there any other way for simplification ?
Thank you.


Algebraic way is given 3 posts above: https://gmatclub.com/forum/a-trussian-s ... l#p1624365
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Kudos [?]: 139367 [1], given: 12787

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Re: A Trussian's weight, in keils, can be calculated by taking the square [#permalink]

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New post 16 Dec 2017, 06:58
Bunuel wrote:
stne wrote:
Dear Karishma,

Is there any way to solve this equation algebraically ( A is the present age )
\(\sqrt{2A +17} -\sqrt{A}=3\)

I was thinking along the lines of \(\sqrt{2A +17}\) =\(\sqrt{2A}\) +\(\sqrt{17}\)obviously this is NOT true. Square root is not distributive over addition.

Is there any other way for simplification ?
Thank you.


Algebraic way is given 3 posts above: https://gmatclub.com/forum/a-trussian-s ... l#p1624365


Thank you Sir.
_________________

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Kudos [?]: 92 [0], given: 488

Re: A Trussian's weight, in keils, can be calculated by taking the square   [#permalink] 16 Dec 2017, 06:58
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