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

by BTGmoderatorDC » Wed Oct 20, 2021 6:12 pm

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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.

OA C

Source: GMAT Prep

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Re: 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

by swerve » Thu Oct 21, 2021 2:34 pm

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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.

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}
\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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Re: 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

by [email protected] » Wed Oct 27, 2021 9:04 am

00:00

A

B

C

D

E

Global Stats

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}
\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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