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Is the prime number p equal to 37 ? (1) p = n2 + 1, where n

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Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 18 Aug 2010, 07:08
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C
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E

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Is the prime number p equal to 37 ?

(1) p = n^2 + 1, where n is an integer.

(2) p^2 is greater than 200.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-the-prime ... 74016.html

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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 18 Aug 2010, 15:05
zest4mba wrote:
Is the prime number p equal to 37 ?

(1) p = n2 + 1, where n is an integer.

(2) p2 is greater than 200.

it should be E

(1)

n=2 ==> 5 prime (No)
n=4 ==> n^2 +1 =17 prime (No)
n=6 ==> n^2 +1 =37 prime (yes)

2 p^2>200

17^2 >200

1 + 2 not suff

hence E

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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 18 Aug 2010, 20:33
I feel its E.

1) For n=1,2,3,4...6...infinity,w here n=6, p=37. But it p could have many values as there is no restriction on n.
2) Only info from here is that p > 15.

Combining 1 and 2, only info we get is p>15 so n>4 only, which is still insufficient.

OA please?

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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 20 Aug 2010, 02:27
I guess C

1) simplify the equation a bit to sqrt(P-1) = n and plug in a couple of primes

n being an interger is true for more than one prime

n=4 => P=5, for n=6 => P=37, etc.

Insuff..

2) every prime greater than 17 when squared is more than 200

Insuff..

Now two together, solve for equation sqrt(p-1)=n.... what prime number (greater than 17) when subtracted by 1 and brought to its square root, results in a interger....... 37

Sqrt(37-1)=6

You can run a couple more prime numbers to check, 41, 43, none result in n being an interger!!

Answer two together : C

OA Please??

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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 27 Aug 2010, 04:37
peader wrote:
I guess C

1) simplify the equation a bit to sqrt(P-1) = n and plug in a couple of primes

n being an interger is true for more than one prime

n=4 => P=5, for n=6 => P=37, etc.

Insuff..

2) every prime greater than 17 when squared is more than 200

Insuff..

Now two together, solve for equation sqrt(p-1)=n.... what prime number (greater than 17) when subtracted by 1 and brought to its square root, results in a interger....... 37

Sqrt(37-1)=6

You can run a couple more prime numbers to check, 41, 43, none result in n being an interger!!

Answer two together : C

OA Please??


The Answer should be E.
In your explanation st 1 and st 2 and insufficient which is correct. Now when solving together we have two cases and just not one case:


Sqrt(37-1)=6 where both conditions are fulfilled ( 37^2 >200 and 37 = 6^2+1)
and

Sqrt(17-1)=4 where both conditions are fulfilled ( 17^2 >200 and 17 = 4^2+1)

Hence not sufficient.
Ans- E
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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n [#permalink]

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New post 14 Aug 2017, 05:38
Is the prime number p equal to 37?

(1) p = n^2 + 1, where n is an integer. Prime p is 1 more than a perfect square. It could be 37, but it could also be other primes, for example, 5 or 17. Not sufficient.

(2) p^2 is greater than 200. 37^2 > 200, so p could be 37 but it could be any other prime greater than 13. Not sufficient.

(1)+(2) Still not sufficient. For example, p could be 37 or 17.

Answer: E.

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Re: Is the prime number p equal to 37 ? (1) p = n2 + 1, where n   [#permalink] 14 Aug 2017, 05:38
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