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If x is an integer, is (x^2+1)(x+5) an even number?
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If x is an integer, is (x^2 + 1)(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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Originally posted by mybudgie on 04 Nov 2010, 18:37.
Last edited by Bunuel on 30 Jan 2016, 02:36, edited 2 times in total.
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If x is an integer, is (x^2+1)(x+5) an even number?
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04 Nov 2010, 19:11
If x is an integer, is (x^2+1)(x+5) an even number?The product of 2 integers to be even at least one of them must be even. So if \(x\) is an odd number then \((x^2+1)(x+5)=even*even=even\). (1) x is an odd number. Sufficient. (2) Each prime factor of x^2 is greater than 7 > first of all, prime factors of \(x^2\) are the same as the prime factors of \(x\): exponentiation does not "produce" new prime factors. So, each prime of \(x\) is greater than 7, which means that 2 is not a prime factor of \(x\), thus \(x\) is an odd number. Sufficient. Answer: D.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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19 Dec 2010, 23:45
I could not understand the reason for the explanation of teh second statement... Can you plsss please explain in a elaborative way...



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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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20 Dec 2010, 01:04
jullysabat wrote: I could not understand the reason for the explanation of teh second statement... Can you plsss please explain in a elaborative way... Exponentiation does not "produce" new prime factors means that the prime factors of a positive integer x and the prime factors of x^n (where n is a positive integer) are the same. For example if x=12=2^2*3 then it has two prime factors 2 and 3 and x^2=144=2^4*3^2 also has the same two prime factors 2 and 3. Now, (2) says: each prime factor of x^2 is greater than 7 > the prime factors of \(x^2\), or which is the same the prime factors of \(x\) can be 11, 13, 17, ... So 2<7 is not a prime factor of \(x\) which means that \(x\) must be odd, and as we concluded if \(x\) is an odd number then \((x^2+1)(x+5)=even*even=even\). Sufficient. Hope it's clear.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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23 Apr 2011, 16:19
agdimple333 wrote: if x is an integer, is (x^2 + 1) (x + 5) an even number?
(1) x is an odd number (2) each prime factor of x ^ 2 is greater than 7 Statement 1  if x is odd then x+5 is even and hence the expression is even, sufficient Statement 2  if each prime factor of x^2 is greater than 7, then all factors are odd and hence x^2 is odd and hence x^2+1 is even making the expression even, sufficient Answer D



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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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29 Jul 2011, 02:56
The answer should be (D). We need to state if we have enough information to conclude whether (x^2 +1) (x+5) is an even number. From statement (1), if x is odd, then x+5 will be even. Therefore (x^2 +1) (x+5) will be (odd +1)*(odd+5) = even * even = even From statement (2), we know that each prime factor of x^2 is greater than 7. This rules out 2 as being a factor of x^2. Since 2 is the only prime that is also even, this means that x^2 can therefore be expressed entirely as a product of primes, all of which are odd. Therefore x^2 is odd. Therefore (x^2 + 1) is even. Therefore (x^2 + 1) (x+5) is even. So (D).
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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29 Jul 2011, 04:01
siddhans wrote: If x is an integer, is (x^2 +1) (x+5) an even number? (1) x is an odd number (2) Each prime factor of x^2 is greater than 7 Question asks: Is \(x\) even? OR Is \(x\) odd? (1) \(x\) is odd. Sufficient. (2) All prime factors of \(x^2\) is greater than 7. Rule: If a number doesn't have at least one 2 as its prime factor, the number will be odd. Statement 2 is a convoluted way to say that there is NO 2 as a prime factor of \(x\) OR \(x\) is odd. Same as statement 1. Sufficient. Ans: "D"
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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Updated on: 23 May 2013, 04:53
If x is an integer, is (x^2+1)(x+5) an even number?
(1) x is an odd number
(2) Each prime factor of x^2 is greater than 7
Originally posted by pbull78 on 28 Jan 2012, 05:56.
Last edited by Bunuel on 23 May 2013, 04:53, edited 2 times in total.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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28 Jan 2012, 06:02
pbull78 wrote: If 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
although discussed but still need explanation of this not able to understand .......... 2) each prime factor of x2 is greater than 7
answer is D pbull78 you please format the question properly. Question should read: If x is an integer, is (x^2+1)(x+5) an even number?(1) x is an odd number > (x^2+1)(x+5)=(odd+odd)(odd+odd)=even*even=even. Sufficient. (2) Each prime factor of x^2 is greater than 7 > 2 is not a prime factor of x^2, so not a prime factor of x as well > x=odd > the same as above. Sufficient. Answer: D.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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28 Jan 2012, 06:20
i copied this question from source as it is
but still i am not able to understand this point
2) Each prime factor of x^2 is greater than 7 > 2 is not a prime factor of x^2, so not a prime factor of x as well > x=odd > the same as above. Can u expalin with example ?



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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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28 Jan 2012, 06:33
pbull78 wrote: i copied this question from source as it is
but still i am not able to understand this point
2) Each prime factor of x^2 is greater than 7 > 2 is not a prime factor of x^2, so not a prime factor of x as well > x=odd > the same as above. Can u expalin with example ? Each prime factor of x^2 is greater than 7 > as 2 is less than 7, then 2 is not a prime factor of x^2, which means that 2 is not a prime of x as well, because if it is a prime of x then x^2 would also have it. Or: Each prime factor of x^2 is greater than 7 > as 2 is less than 7, then 2 is not a prime factor of x^2, which means that x^2 is an odd number > x^2=odd > x^2=x*x=odd > x=odd. Or: Each prime factor of x^2 is greater than 7 > primes more than 7 are odd (in fact the only even prime is 2) > x is a product of some odd primes more than 7 > x^2 is an odd number > x=odd. Hope it's clear.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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29 Jan 2017, 18:33
If x is an odd number, x^2 must be odd => (x^2+1) must be even. By the same logic, (x+5) is even. As addition of two odd numbers results in an even number. Multiplication of two even numbers results in an even number. Thus (x^2+1)(x+5) is an even number. Satetment (1) is SUFFICIENT. And for (2), each prime factor of x^2 is greater than 7 implies that 2 is not a prime factor of x^2 and in turn 2 is not a prime factor of x. (As all the prime factors of x^2 are also prime factors of x) That means x is composed of 11, 13, 17, 19, 23 etc (Prime numbers greater than 7). Therefore x is an odd number => Equivalent to statement (1). Statement (2) is SUFFICIENT. The correct answer is D.
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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19 Jan 2018, 12:28
In statement 2. Can X not be 0? each prime number of X^2 is greater than 7. Understanding that 2 is the only prime number so if the prime factor of x^2 is above 7 then the only numbers we are left with are odd numbers. Since 0 a multiple of every number. Can x be 0? Maybe it's too dumb of a question but hey we are all here to learn. Thanks
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Re: If x is an integer, is (x^2+1)(x+5) an even number?
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19 Jan 2018, 12:34
Rocket7 wrote: In statement 2. Can X not be 0? each prime number of X^2 is greater than 7. Understanding that 2 is the only prime number so if the prime factor of x^2 is above 7 then the only numbers we are left with are odd numbers. Since 0 a multiple of every number. Can x be 0?
Maybe it's too dumb of a question but hey we are all here to learn. Thanks x cannot be 0 because 0 is divisible be primes which are less than 7 (2, 3, and 5).
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Re: If x is an integer, is (x^2 + 1)(x + 5) an even number? 1) x
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Re: If x is an integer, is (x^2 + 1)(x + 5) an even number? 1) x
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