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' $x$ ' is a positive integer and ' $y$ ' is a single-digit positive i
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22 Apr 2025, 03:18
22 Apr 2025, 03:18
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' $\(x\)$ ' is a positive integer and ' $\(y\)$ ' is a single-digit positive integer. The remainder, when $\(y - 4x\)$ is divided by 7 , is 2 .
Quantity A |
Quantity B |
The remainder when 10x + y is divided by 7 |
2 |
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Re: ' $x$ ' is a positive integer and ' $y$ ' is a single-digit positive i
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26 Apr 2025, 01:16
26 Apr 2025, 01:16
C
Re: ' $x$ ' is a positive integer and ' $y$ ' is a single-digit positive i
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26 Apr 2025, 04:15
26 Apr 2025, 04:15
Expert Reply
$\(y-4 x>0\)$, and the remainder is 2 when $\(y-4 x\)$ is divided by 7 .
$$
\(\begin{array}{lll}
\Rightarrow y-4 x=2 & \text { or } & y-4 x=9 \\
\Rightarrow y=2+4 x & \text { or } & y=9+4 x .
\end{array}\)
$$
If $\(x=1, y+=6\)$ or 13 .
As $x>0$ and $y$ is a single-digit positive integer, $y=6$.
Therefore, Column A: $\(10 x+y=16\)$ and the remainder when 16 divided by 7 is 2 , and Column B: 2 .
Hence, Column A = Column B.
Thus, the correct option is $C$.
$$
\(\begin{array}{lll}
\Rightarrow y-4 x=2 & \text { or } & y-4 x=9 \\
\Rightarrow y=2+4 x & \text { or } & y=9+4 x .
\end{array}\)
$$
If $\(x=1, y+=6\)$ or 13 .
As $x>0$ and $y$ is a single-digit positive integer, $y=6$.
Therefore, Column A: $\(10 x+y=16\)$ and the remainder when 16 divided by 7 is 2 , and Column B: 2 .
Hence, Column A = Column B.
Thus, the correct option is $C$.
