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

Question

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

Source:   Nova GMAT  
Difficulty Level:   700

ashudhall · Answer

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
Answer should be B

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HKD1710 · Answer

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

Answer should be B.

14101992 · Answer

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.

chesstitans · Answer

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

14101992 · Answer

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

CrackverbalGMAT · Answer

From the question data, we know x is prime which is a very important piece of the puzzle. We have to find out if x = 7, essentially a Yes-No DS question.

From statement I alone, x=√n + 1. This only tells us that n has to be a perfect square; otherwise, √n and hence x will not be an integer and therefore violates the question data (primes are defined only for positive integers).

Since the information only tells us that n has to be a perfect square, it is insufficient to find out if x = 7.
For example, if n = 4, x = 5; but if n = 36, x = 7.
Statement I alone is insufficient to answer the question. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone,  x^2  – 11x + 28 = 0. The factors of 28 are -7 and -4, therefore, the roots of the given quadratic equation are 7 or 4. 
However, the question tells us very clearly that x is prime, therefore, 4 cannot be the value of x. The only value that satisfies is x = 7.
Statement II alone is sufficient to answer the question with a YES. Answer option C and E can be eliminated.

The correct answer option is B.

Hope that helps!
Aravind B T

CrackverbalGMAT · Answer

Hello chesstitans,

When you look at an equation like x = √n+1 and wonder “How can I solve an equation like this?”, I would say that you are not thinking of GMAT type of questions.

Even if GMAT wants you to solve this equation, there isn’t a way to do it algebraically since you have two unknowns in the equation. The only way in which such equations can be solved is by mapping the constraints to the equation.

Also, when you talk of higher exponents, till what extent are you thinking? Cube root, 4th root?? Anything higher than that, a standardized test will also know that it’s not realistically possible for most people to solve it in less than 3 minutes. So, we need to stop looking at GMAT as a test on Mathematics.

When you see equations on GMAT questions, do not always think “How can I solve them?”; also think “Should I solve them?” OR “Can they be solved?”

Clearly, in this question, you did not have to solve the equation because the question was not about finding THE value of x; instead, it was about finding if x was a particular value.

Hope that helps!
Aravind B T

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

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