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# Is r*s a prime number?

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Is r*s a prime number?  [#permalink]

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23 Nov 2019, 21:45
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Difficulty:

25% (medium)

Question Stats:

84% (00:44) correct 16% (00:50) wrong based on 44 sessions

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Is r*s a prime number?

(1) s is a prime number.
(2) r is a positive integer.

Chetan’s question

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Re: Is r*s a prime number?  [#permalink]

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23 Nov 2019, 21:57
Statement-1
S is prime no. No information about S.
Take s=2, 2*1= 2 prime
2.*1/2= 1 not prime.

Statement- 2
R is positive integer
Take r=1, 1*2 prime
1*4 not prime.

Statement 1+2
S prime, and r positive integer,
s= 2, r= 1 will lead 1*2=2 prime
s= 2, r=2 will lead 2*2 = 4 not prime.

E is answer.
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Re: Is r*s a prime number?  [#permalink]

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24 Nov 2019, 05:02
chetan2u wrote:
Is r*s a prime number?

(1) s is a prime number.
(2) r is a positive integer.

Chetan’s question

#1
if s is prime, value of r is not know , as it can be -ve or fraction or 0
insufficient
#2
r is + integer , but value of s not know insufficient
from 1 &2
we cannot conclusively say that r*s would be a prime no. as r may or may not be 1
IMO E
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Re: Is r*s a prime number?  [#permalink]

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24 Nov 2019, 10:22
chetan2u wrote:
Is r*s a prime number?

(1) s is a prime number.
(2) r is a positive integer.

Chetan’s question

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 2 variables (r and s) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If s = 2 and r = 1, then rs=2 is a prime number and the answer is 'yes'.
If s = 2 and r = 2, then rs=4 is not a prime number and the answer is 'no'.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Is r*s a prime number?  [#permalink]

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24 Nov 2019, 19:47
chetan2u wrote:
Is r*s a prime number?

(1) s is a prime number.
(2) r is a positive integer.

Chetan’s question

#1. Let s be 2, if r=1 (r*s) is prime but for r=2, (r*s) is not-prime. Insufficient.
#2. Let r be 1, if s if 2 (r*s) is prime but for r=12, (r*s) is not-prime. Insufficient.

#1 + #2

Let s be 2/3/5, take any prime number
For r=1 (r being Integer >0), r=1 (r*s) is prime but for r=2, (r*s) is not-prime. Insufficient. E
Re: Is r*s a prime number?   [#permalink] 24 Nov 2019, 19:47
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# Is r*s a prime number?

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