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What is the remainder when a positive integer ‘P’ is divided by 33?

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What is the remainder when a positive integer ‘P’ is divided by 33?  [#permalink]

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04 Jan 2019, 09:35
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What is the remainder when a positive integer ‘P’ is divided by 33?

(1) When P is divided by 11, the remainder is 5.
(2) When P is divided by 99, the remainder is 5.
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Re: What is the remainder when a positive integer ‘P’ is divided by 33?  [#permalink]

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04 Jan 2019, 10:58
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STAT1
When P is divided by 11, the remainder is 5
Now P can be taken as P = 11k + 5 (Dividend = Divisor * Quotient + Remainder)

Now when 11k+5 (which is P) is divided by 33 then we can get multiple remainders depending on the value of k
Example
k = 0 then P = 5 and P/33 remainder is 5
k = 1 then P = 16 and P/33 remainder is 16
k = 2 then P = 27 and P/33 remainder is 27
Since we get multiple values for remainders so NOT SUFFICIENT

STAT2
When P is divided by 99, the remainder is 5
As in STAT1, P = 99t + 5
Now, when 99t + 5 (which is P) is dividend by 33 then we get a remainder of 5 ( 0 remainder from 99t and 5 remainder from 5 => total remainder of 5)
Since, we get only one value of remainder in this case so it is SUFFICIENT

Hope it helps!
akurathi12 wrote:
What is the remainder when a positive integer ‘P’ is divided by 33?

(1) When P is divided by 11, the remainder is 5.
(2) When P is divided by 99, the remainder is 5.

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Re: What is the remainder when a positive integer ‘P’ is divided by 33?  [#permalink]

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04 Jan 2019, 11:15
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akurathi12 wrote:
What is the remainder when a positive integer ‘P’ is divided by 33?

(1) When P is divided by 11, the remainder is 5.
(2) When P is divided by 99, the remainder is 5.

$$P \ge 1\,\,{\mathop{\rm int}} \,\,\left( * \right)$$

$$P = 33M + R$$

$$M\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} \,\,\,,\,\,\,0 \le R\,\,{\mathop{\rm int}} \,\, \le 32$$

$$? = R$$

$$\left( 1 \right)\,\,P = 11K + 5\,\,\,,\,\,\,K\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} \,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,K = 0\,\,\,\, \Rightarrow \,\,\,R = 5\,\, \hfill \cr \,{\rm{Take}}\,\,K = 1\,\,\,\, \Rightarrow \,\,\,R = 16\, \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( 2 \right)\,\,P = 99L + 5\,\,\,,\,\,\,L\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,\,\,P = 33\left( {3L} \right) + 5\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,M = 3L \hfill \cr \,? = R = 5\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}} \hfill \cr} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: What is the remainder when a positive integer ‘P’ is divided by 33? &nbs [#permalink] 04 Jan 2019, 11:15
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