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If f and g are integers, is fg + 2 prime?

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If f and g are integers, is fg + 2 prime?  [#permalink]

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New post Updated on: 11 Oct 2012, 23:40
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If f and g are integers, is fg + 2 prime?

(1) f is odd.
(2) g is even.

Originally posted by aditi1903 on 11 Oct 2012, 23:37.
Last edited by Bunuel on 11 Oct 2012, 23:40, edited 1 time in total.
Edited the question.
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Re: If f and g are integers, is fg + 2 prime?  [#permalink]

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New post 11 Oct 2012, 23:48
aditi1903 wrote:
If f and g are integers, is fg + 2 prime?

(1) f is odd.
(2) g is even.


Even when we take the statements together they are not sufficient to answer the question:

If f is any odd number and g=0, then fg+2=2=prime;
If f is any odd number and g=2, then fg+2 is some even number other than 2, thus not a prime.

Answer: E.
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Re: If f and g are integers, is fg + 2 prime?  [#permalink]

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New post 23 Jul 2018, 22:22
If we combine both the statement i.e f is odd and g is even in that case it is clear that fg+2 will be any even number other 2. Bunuel can you please help.
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Re: If f and g are integers, is fg + 2 prime?  [#permalink]

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New post 23 Jul 2018, 22:32
sghoshgt wrote:
If we combine both the statement i.e f is odd and g is even in that case it is clear that fg+2 will be any even number other 2. Bunuel can you please help.


The solution gives an example:
If f is any odd number and g=0, then fg+2 = 2 = prime;
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If f and g are integers, is fg + 2 prime?  [#permalink]

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New post 18 Dec 2018, 22:40
Given: ‘f’ and ‘g’ are integers.
To find: Is fg+2 prime?
Analysis of statement 1: f is odd.
Let’s draw a table:
Attachment:
table.PNG
table.PNG [ 12.63 KiB | Viewed 227 times ]

Hence statement 1 is not sufficient to answer. We can eliminate the options A and D.
Analysis of Statement 2: g is even
Let’s draw a table:
Attachment:
table 1.PNG
table 1.PNG [ 11.78 KiB | Viewed 226 times ]

Hence statement 2 is not sufficient to answer. We can eliminate the options B
Combining the 1 & 2 statements: we get:
Even after combining we cannot answer the question whether fg + 2 is prime or not.
The correct answer option is “E”.
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Re: If f and g are integers, is fg + 2 prime?  [#permalink]

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New post 19 Dec 2018, 05:34
sghoshgt wrote:
If we combine both the statement i.e f is odd and g is even in that case it is clear that fg+2 will be any even number other 2. Bunuel can you please help.


For Ex : f = 1, g =0 fg + 2 = 0 +2 = 2 , Prime

f = 1, g = 2 then fg + 2 = 2 + 2 = 4 , an even number other than 2 , Not a Prime

Not Sufficient

Choice E

Hope it is clear
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Re: If f and g are integers, is fg + 2 prime?   [#permalink] 19 Dec 2018, 05:34
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