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Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
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Russ19 wrote:
If \(p\) is a positive integer less than\( 70\), and \(71^2 − 142p + p^2\) is divisible by \(49\), what is the remainder when \(p\) is divided by \(7\)?

A) 0
B) 1
C) 2
D) 4
E) 6


Solution:
  • According to the question, \(p\) is a positive integer less than \(70\)
  • And \(71^2 − 142p + p^2=49k\) where k is an integer
    \(⇒(71-p)^2=49k\)
    \(⇒71-p=7\sqrt{k}\)
    \(⇒p=71-7\sqrt{k}\)
  • Remainder when \(p\) is divided by \(7=(\frac{71-7\sqrt{k}}{7})_r=(\frac{71}{7})_r-(\frac{7\sqrt{k}}{7})_r=1-0=1\)

Hence the right answer is Option B
GMAT Club Bot
Re: If p is a positive integer less than 70, and 71^2 142p + p^2 is divi [#permalink]
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