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If p and r are prime numbers, which of the following must also be pr
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28 Jul 2021, 10:45
28 Jul 2021, 10:45
Expert Reply
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Question Stats:
85% (00:56) correct
14% (00:32) wrong based on 14 sessions
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If p and r are prime numbers, which of the following must also be prime?
(A) \(pr\)
(B) \(p + r\)
(C) \(pr + 1\)
(D) \(p^2 + r^2\)
(E) None of the above
(A) \(pr\)
(B) \(p + r\)
(C) \(pr + 1\)
(D) \(p^2 + r^2\)
(E) None of the above
If p and r are prime numbers, which of the following must also be pr
[#permalink]
28 Jul 2021, 18:28
28 Jul 2021, 18:28
1
Solution:
We can solve this question by solving each option choice. Note the we have even and odd prime numbers. And even + odd= odd & odd+odd= even and similarly for multiplication odd x odd= odd & even x odd= odd
(A) pr---> taking p=2 & r=3 we get 6 which is not a prime number. Also note, when do numbers are multiplied the value will not be prime if nothing but the it will have p and q as its prime factor apart from the number and 1.- OUT
(B) p+r---> when we take p-2 & r=3 we get a prime number 5. However, if we take both odd prime number we get an even number and we know no other even number other than 2 is not a prime number- OUT
(C) pr+1----> odd x odd= odd+1=even. Thus , this is also not a prime number. OUT
(D)\( p^2+r^2\)----> odd^2 + odd^2 = odd+odd= even. Not a prime number- OUT
(E) None of the above---> The only option choice we are left with- Correct
IMO E
Hope this helps!
We can solve this question by solving each option choice. Note the we have even and odd prime numbers. And even + odd= odd & odd+odd= even and similarly for multiplication odd x odd= odd & even x odd= odd
(A) pr---> taking p=2 & r=3 we get 6 which is not a prime number. Also note, when do numbers are multiplied the value will not be prime if nothing but the it will have p and q as its prime factor apart from the number and 1.- OUT
(B) p+r---> when we take p-2 & r=3 we get a prime number 5. However, if we take both odd prime number we get an even number and we know no other even number other than 2 is not a prime number- OUT
(C) pr+1----> odd x odd= odd+1=even. Thus , this is also not a prime number. OUT
(D)\( p^2+r^2\)----> odd^2 + odd^2 = odd+odd= even. Not a prime number- OUT
(E) None of the above---> The only option choice we are left with- Correct
IMO E
Hope this helps!
gmatclubot
If p and r are prime numbers, which of the following must also be pr [#permalink]
28 Jul 2021, 18:28
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