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If ab = c where a, b, and c are positive integers and a and b are prim

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If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 18 Nov 2019, 02:04
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If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.

(2) a is odd.
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Re: If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 18 Nov 2019, 02:45
Bunuel wrote:
If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.

(2) a is odd.



ab=c
#1
c is even
a or b is 2
insuffieint
#2
a is odd
b can be even or odd insufficient
from 1 &2
a= odd and b = even
IMO C
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If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 18 Nov 2019, 03:32
Bunuel wrote:
If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.

(2) a is odd.


Answer C

Explanation: As given, A*B=C
Only 2 is the even prime number, else all rest prime number is odd.
We need the value of B.

1. Given C is even. So it will be only possible when either A or B is Even (as only one can be even prime number, As we want the result as odd number, i.e. C should be odd)
So, Either A or B can be odd or even. so insufficient.

2. Now Given A is odd. So, resultant C (No details given) It can be odd or even
A(odd) * B(odd or Even)= C (odd or Even)
So insufficient

1&2, A(odd) * B(has to be even, as resultant is even)= C (Even)
therefore, both statements 1 & 2 are required. So Answer is C

Please provide kudos, if you find my answer explanation good enough :thumbup: :thumbup: (really need of kudos) :(
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Re: If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 18 Nov 2019, 08:51
Bunuel wrote:
If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.

(2) a is odd.


Asked: If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.
a or b or both could be even prime number (2)
NOT SUFFICIENT

(2) a is odd.
b could be any prime number
NOT SUFFICIENT

(1) + (2)
(1) c is even.
(2) a is odd.
If c is even, and a is odd, b must be even prime number = 2
SUFFICIENT

IMO C
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If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 19 Nov 2019, 12:28
2 scenarios

2x11 = 22
2x3 =6
Hence C.

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Re: If ab = c where a, b, and c are positive integers and a and b are prim  [#permalink]

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New post 19 Nov 2019, 12:44
If ab = c where a, b, and c are positive integers and a and b are prime numbers, what is the value of b?

(1) c is even.

(2) a is odd.

Answer is C
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Re: If ab = c where a, b, and c are positive integers and a and b are prim   [#permalink] 19 Nov 2019, 12:44
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