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If p, q, and r are non-negative integers such that the remainder when
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Bunuel
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If p, q, and r are non-negative integers such that the remainder when [#permalink] New post  24 May 2018, 05:42
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If p, q, and r are non-negative integers such that the remainder when \(10^p – q\) is divided by 3 is equal to r, what is the value of R?


(1) p = 7

(2) q = 4
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If p, q, and r are non-negative integers such that the remainder when [#permalink] New post  24 May 2018, 10:32
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Bunuel wrote:
If p, q, and r are non-negative integers such that the remainder when \(10^p – q\) is divided by 3 is equal to r, what is the value of R?


(1) p = 7

(2) q = 4


There are only three remainders possible when a number is divided by \(3\) and they are \(0\), \(1\) & \(2\). Also \(10^p\) will always leave a remainder of \(1\) when divided by \(3\), irrespective of the value of \(p\). Hence to know the value of \(r\), we only need to know the value of \(q\)

Statement 1: Nothing mentioned about \(q\). Insufficient

Statement 2: Directly provides the value of \(q\). Sufficient

for the sake of calculation: \(\frac{10^p – q}{3}=\frac{10^p}{3} – \frac{q}{3}\)

\(\frac{10^p}{3}\) will leave a remainder of \(1\) and \(\frac{4}{3}\) will also leave a remainder of \(1\). Hence \(r=1-1=0\)

Option B
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