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If P is a positive integer, P= ?

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If P is a positive integer, P= ? [#permalink]

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If P is a positive integer, P= ?

1. When a positive number N is divided by P, the remainder is 12.
2. \(\frac{N}{P} = 29.15\)

Source : Experts Global
[Reveal] Spoiler: OA

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If P is a positive integer, P= ? [#permalink]

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pushpitkc wrote:
If P is a positive integer, P= ?

1. When a positive number N is divided by P, the remainder is 12.
2. \(\frac{N}{P} = 29.15\)

Source : Experts Global


It should be C

1- Clearly insufficient. There are infinite values of N/P that can result in a remainder of 12.
2- Clearly insufficient. Multiple pairs of N/P that can divide to 29.15 for example 2915/100 or 29150/1000.

Combined 1+2 - This appears to be sufficient. Remainder 12 is the 0.15 part of 29.15. We can equate the divisor.

\(0.15x = 12\) --> \(x = \frac{12}{0.15} = 80\)

\(N = 80*29 + 12\)
\(N = 2332\)

\(N/P = 2332/80\)
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Re: If P is a positive integer, P= ? [#permalink]

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New post 21 Sep 2017, 14:53
pushpitkc wrote:
If P is a positive integer, P= ?

1. When a positive number N is divided by P, the remainder is 12.
2. \(\frac{N}{P} = 29.15\)

Source : Experts Global


Statement One Alone:

When a positive number N is divided by P, the remainder is 12.

We can create the following equation:

N/P = Q + 12/P (where Q is a positive integer)

We see that we cannot determine P. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

N/P = 29.15

We can expand the statement to read:

N/P = 29 + 15/100 (where P = 100)

N/P = 29 + 3/20 (where P = 20)

Since we have two values for P, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we see that :

N/P = 29 + 3/20

and

N/P = Q + 12/P

Thus:

3/20 = 12/P

3P = 20 x 12

P = 20 x 4 = 80

(Note: We could have used 12/100 instead of 3/20 to set up the proportion; the result for P would be the same.)

Answer: C
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Re: If P is a positive integer, P= ?   [#permalink] 21 Sep 2017, 14:53
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