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
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If John is exactly 4 years older than Bill, how old is John?
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BTGmoderatorDC
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Jay@ManhattanReview
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Say John is j years and Bill is b years old; thus, j = b + 4.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
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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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 \({\color{red}\Large{\times}}\)
\(
\begin{align*}
5(J+4)-9 &=J-9 \\
5J+20-45 &= J-9 \\
4J &= -9+25 \\
J &= 4.\end{align*}
\)
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 \({\color{red}\Large{\times}}\)
