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If John is exactly 4 years older than Bill, how old is John?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Aug 12, 2019 5:06 am

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BTGmoderatorDC wrote:If John is exactly 4 years older than Bill, how old is John?

(1) Exactly 9 years ago John was 5 times as old as Bill was then.

(2) Bill is more than 9 years old.

OA A

Source: Official Guide
Say John is j years and Bill is b years old; thus, j = b + 4.

We have to get the value of j.

Let's take each statement one by one.

(1) Exactly 9 years ago John was 5 times as old as Bill was then.

j - 9 = 5(b - 9) => j = 5b - 36. From j = b + 4 and j = 5b - 36, we get j = 14. Sufficient.

(2) Bill is more than 9 years old.

b > 9. Can't get the value of j. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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by swerve » Mon Aug 12, 2019 7:39 am

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B

C

D

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From the first statement 1, we can create the equation:

\(
\begin{align*}
5(J+4)-9 &=J-9 \\
5J+20-45 &= J-9 \\
4J &= -9+25 \\
J &= 4.\end{align*}
\)
Sufficient \({\color{green}{\checkmark}}\)

From statement 2, we have

Given that \(B > 9\), we get, \(J - 4 > 9\) or \(J > 13\), but can't find a specific value for \(J\). Insufficient \({\color{red}\Large{\times}}\)
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