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# How old is Robert now? (1) The product of his age now and his age

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Joined: 02 Sep 2009
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How old is Robert now? (1) The product of his age now and his age  [#permalink]

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22 Feb 2018, 20:47
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Difficulty:

15% (low)

Question Stats:

79% (01:15) correct 21% (01:24) wrong based on 82 sessions

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How old is Robert now?

(1) The product of his age now and his age five years from now is 24.

(2) Six years from now he will be three times as old as he is now.

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Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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22 Feb 2018, 23:51
Bunuel wrote:
How old is Robert now?

(1) The product of his age now and his age five years from now is 24.

(2) Six years from now he will be three times as old as he is now.

Let us assume the age of Robert now as 'x' years.

Statement 1
Age now = x, age after five years = x+5. Given:
x*(x+5) = 24. Only positive value of 'x' that satisfies this is '3'. (3*8 = 24).
This means Robert's age now is '3 years. Sufficient.

Statement 2
Age now = x, age after six years = x+6. Given:
x+6 = 3*x or 2x = 6 or x=3.
This means Robert's age now is '3' years. Sufficient.

Hence D answer
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Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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23 Feb 2018, 00:24
Bunuel wrote:
How old is Robert now?

(1) The product of his age now and his age five years from now is 24.

(2) Six years from now he will be three times as old as he is now.

1)

x(x+5) = 24
x^2 + 5x + 24 = 0
x= -8 or 3
age is positive thus age=3

sufficient

2)

x+6 = 3x

x= 3

sufficient

(D) imo
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Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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23 Feb 2018, 10:10
Top Contributor
Bunuel wrote:
How old is Robert now?

(1) The product of his age now and his age five years from now is 24.

(2) Six years from now he will be three times as old as he is now.

Let N = Robert's age NOW

Target question: What is the value of N?

Statement 1: The product of his age now and his age five years from now is 24.
If N = Robert's age NOW...
then N+5 = Robert's age in 5 years

We can write: N(N + 5) = 24
Expand: N² + 5N = 24
Rewrite as: N² + 5N - 24 = 0
Factor: (N + 8)(N - 3) = 0

So, EITHER N = -8 OR N = 3
Since Robert's age cannot be NEGATIVE, we can conclude with certainty that N = 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Six years from now he will be three times as old as he is now.
If N = Robert's age NOW...
then N+6 = Robert's age in 6 years

We can write: N + 6 = 3N
Solve: N = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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How old is Robert now? (1) The product of his age now and his age  [#permalink]

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23 Feb 2018, 16:11
St 1) The product of his age now and his age five years from now is 24.
If Robert is today r years old , five years from now he will be r+5 . We can set an equation r(r+5)=24
$$r^2+5r-24=0$$ we can solve for r (we will omit the negative root) sufficient

(2) Six years from now he will be three times as old as he is now. If Robert is today r years old , six years from now he will be r+6. We can set the equation r+6=3r and solve for r sufficient

Answer D
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Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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29 Jul 2019, 04:57
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Re: How old is Robert now? (1) The product of his age now and his age   [#permalink] 29 Jul 2019, 04:57
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# How old is Robert now? (1) The product of his age now and his age

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