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# If x is a prime integer, does x = 7?

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If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 11:07
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Difficulty:

55% (hard)

Question Stats:

61% (01:44) correct 39% (02:08) wrong based on 22 sessions

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If x is a prime integer, does x = 7?

(1) $$x = \sqrt{n} + 1$$, where n is an integer.
(2) x^2 − 11x + 28 = 0

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Re: If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 11:15
A : X =sqrt {n} + 1 if n=16 then x would be 5, if n = 4 x would be 3 and if n =36 x would be 7. Hence insufficient
B : after solving equation we get x = 7,4 and since x is prime hence x =7. sufficient

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Re: If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 11:16
Bunuel wrote:
If x is a prime integer, does x = 7?

(1) $$x = \sqrt{n} + 1$$, where n is an integer.
(2) x^2 − 11x + 28 = 0

x is prime hence x can be 2,3,5,7,11.... is x=7?

stmt-1:

if n=16, then x=5

if n=16, then x=7

insufficient

stmt-2:
x^2 − 11x + 28 = 0 can be re-written as
(x-4) (x-7) = 0, for this to be true, x either has to be 4 or 7. but x is prime hence 4 is ruled out.
it means x = 7

suffiecient

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Re: If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 11:28
If x is a prime integer, does x = 7?

S1. x=root(n)+1, where n is an integer.

x=7 surely satisfies the condition that x is a prime number, when n=36.
x=2 also satisfies when n=1.
x=3 also satisfies when n=4.

Hence, insufficient!

S2. x^2 − 11x + 28 = 0 ---> (x-7) (x-4) = 0

So, x=7 or x=4. Given that x is a prime number. So, x=7.

Sufficient!

Hence, B will be the answer.
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Re: If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 11:48
ashudhall wrote:
A : X =sqrt {n} + 1 if n=16 then x would be 5, if n = 4 x would be 3 and if n =36 x would be 7. Hence insufficient
B : after solving equation we get x = 7,4 and since x is prime hence x =7. sufficient

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any way to problem the equation quickly, and what if the equation is expressed at higher exponent of x, how to solve such equation?
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If x is a prime integer, does x = 7?  [#permalink]

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15 May 2017, 12:04
chesstitans wrote:
ashudhall wrote:
A : X =sqrt {n} + 1 if n=16 then x would be 5, if n = 4 x would be 3 and if n =36 x would be 7. Hence insufficient
B : after solving equation we get x = 7,4 and since x is prime hence x =7. sufficient

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

any way to problem the equation quickly, and what if the equation is expressed at higher exponent of x, how to solve such equation?

If the equation is expressed at higher exponent of x, for example in this question, plug in the value of x=7 (asked in the question) and see whether the equation stands true. If it does, then your equation becomes (x-7) * rest of the equation which would further be simplified easily. If you take a difficult example, then am sure the probability of you seeing such a question on actual GMAT is very very less :D
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