If x is an integer, is(x^2+)(x+5) an even number?
1) x is an odd number
2) Each prime factor of x^2 is greater than 7.
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(x^2+)(x+5) an even number
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Statement 1: x is oddIf X is an integer, is (x2 + 1)(x + 5) an even number?
(1) x is an odd number.
(2) Each prime factor of x² is greater than 7.
If x=1, then (x²+1)(x+5) = (1² + 1)(1 + 5) = 2*6 = 12.
If x=3, then (x²+1)(x+5) = (3² + 1)(3 + 5) = 10*8 = 80.
If x=5, then (x²+1)(x+5) = (5² + 1)(5 + 5) = 26*10 = 260.
The cases above illustrate that -- if x is odd -- then (x²+1)(x+5) = even.
SUFFICIENT.
Statement 2: Each prime factor of x² is greater than 7.
Since each prime factor of x² is greater than 7, each prime factor of X ITSELF must be greater than 7.
Options for x:
11, 13, 17, 19, 23...
Notice that only ODD VALUES FOR X will satisfy statement 2.
As we saw in statement 1, if x is odd, then (x²+1)(x+5) = even.
SUFFICIENT.
The correct answer is D.
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Statement 2: Each prime factor of x² is greater than 7.
Since each prime factor of x² is greater than 7, each prime factor of X ITSELF must be greater than 7.
Options for x:
11, 13, 17, 19, 23...
Notice that only ODD VALUES FOR X will satisfy statement 2.
As we saw in statement 1, if x is odd, then (x²+1)(x+5) = even.
SUFFICIENT.
Hi GMATGuruNY ,
Many thanks for your reply.
Just a quick question. In statement 2 its given that x^2 is greater that 7. So will x^2 be 11,13,17...?
Please advise.
Many thanks in advance.
SJ
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As noted in my post above:jain2016 wrote:Statement 2: Each prime factor of x² is greater than 7.
Since each prime factor of x² is greater than 7, each prime factor of X ITSELF must be greater than 7.
Options for x:
11, 13, 17, 19, 23...
Notice that only ODD VALUES FOR X will satisfy statement 2.
As we saw in statement 1, if x is odd, then (x²+1)(x+5) = even.
SUFFICIENT.
Hi GMATGuruNY ,
Many thanks for your reply.
Just a quick question. In statement 2 its given that x^2 is greater that 7. So will x^2 be 11,13,17...?
Please advise.
Many thanks in advance.
SJ
Since each prime factor of x² is greater than 7, each prime factor of X ITSELF must be greater than 7.
Thus, the least possible values for x are as follows:
11, 13, 17, 19, 23...
Thus, the least possible values for x² are as follows:
11², 13², 17², 23²...
For every value in the blue list, the prime-factorization is composed solely of prime numbers greater than 7.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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