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

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Math Expert
Joined: 02 Sep 2009
Posts: 51263
How old is Robert now? (1) The product of his age now and his age  [#permalink]

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22 Feb 2018, 19:47
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:07) correct 23% (01:11) wrong based on 41 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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Posts: 1412
Location: India
Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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22 Feb 2018, 22:51
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.

BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 830
Location: India
GMAT 1: 710 Q49 V36
Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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22 Feb 2018, 23:24
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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Joined: 11 Sep 2015
Posts: 3243
Re: How old is Robert now? (1) The product of his age now and his age  [#permalink]

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23 Feb 2018, 09:10
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

Cheers,
Brent
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Joined: 26 Sep 2016
Posts: 62
How old is Robert now? (1) The product of his age now and his age  [#permalink]

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23 Feb 2018, 15:11
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

How old is Robert now? (1) The product of his age now and his age &nbs [#permalink] 23 Feb 2018, 15:11
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