If John has exactly 10 coins each of which was minted in 1910 or 1920 or 1930, how many of his coins were minted in

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If John has exactly 10 coins each of which was minted in 1910 or 1920 or 1930, how many of his coins were minted in 1920 ?

(1) Exactly 6 of his coins were minted in 1910 or 1920.
(2) Exactly 7 of his coins were minted in 1920 or 1930.



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BTGmoderatorDC wrote:
Wed Oct 20, 2021 6:12 pm
If John has exactly 10 coins each of which was minted in 1910 or 1920 or 1930, how many of his coins were minted in 1920 ?

(1) Exactly 6 of his coins were minted in 1910 or 1920.
(2) Exactly 7 of his coins were minted in 1920 or 1930.



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Statement 1.
Exactly \(6\) of his coins were minted in \(1910\) or \(1920.\)
But how many in \(1920?\)
All \(6, 5,4,3, \cdots\) Or nothing. Not Sufficient \(\Large{\color{red}\chi}\)

Statement 2.
Exactly \(7\) of his coins were minted in \(1920\) or \(1930.\)
But how many in \(1920?\)
All \(7,6,5, \cdots\) Or nothing at all. Not Sufficient \(\Large{\color{red}\chi}\)

Combining 1 and 2:
Let \(1910\) be \(A\)
\(1920\) be \(B\) and \(1930\) be \(C\)
\begin{align}
\begin{cases}
A+B=6 &\quad (1) \\
B+C=7 &\quad (2) \\
A+B+C=10 &\quad (3)
\end{cases}
\end{align}

Equating \((1) \& (3)\), we get
\(C=4\)

And from equation \((2) \& (3)\), we get
\(A=3\)

Therefore, \(B=3\)
So, \(3\) coins were minted in \(1920\) C

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swerve wrote:
Thu Oct 21, 2021 2:34 pm
BTGmoderatorDC wrote:
Wed Oct 20, 2021 6:12 pm
If John has exactly 10 coins each of which was minted in 1910 or 1920 or 1930, how many of his coins were minted in 1920 ?

(1) Exactly 6 of his coins were minted in 1910 or 1920.
(2) Exactly 7 of his coins were minted in 1920 or 1930.



OA C

Source: GMAT Prep
Statement 1.
Exactly \(6\) of his coins were minted in \(1910\) or \(1920.\)
But how many in \(1920?\)
All \(6, 5,4,3, \cdots\) Or nothing. Not Sufficient \(\Large{\color{red}\chi}\)

Statement 2.
Exactly \(7\) of his coins were minted in \(1920\) or \(1930.\)
But how many in \(1920?\)
All \(7,6,5, \cdots\) Or nothing at all. Not Sufficient \(\Large{\color{red}\chi}\)

Combining 1 and 2:
Let \(1910\) be \(A\)
\(1920\) be \(B\) and \(1930\) be \(C\)
\begin{align}
\begin{cases}
A+B=6 &\quad (1) \\
B+C=7 &\quad (2) \\
A+B+C=10 &\quad (3)
\end{cases}
\end{align}

Equating \((1) \& (3)\), we get
\(C=4\)

And from equation \((2) \& (3)\), we get
\(A=3\)

Therefore, \(B=3\)
So, \(3\) coins were minted in \(1920\) C
Or you could have saved yourself some time and just linked to identical solution on this page: https://gmatclub.com/forum/if-john-has- ... l#p2526921
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