I'm not really sure how to go about statement 2?
Help is appreciated
Regards,
Maysaa
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Algebra and Primes?
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Statement 1: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.
Since x is odd, x² = (odd)(odd) = odd.
Thus, (x²+1)(x+5) = (odd + odd)(odd + odd) = (even)(even) = even.
SUFFICIENT.
Statement 2:
Since x² does not have a prime factor of 2, x itself does not have a prime factor of 2.
Implication:
x is ODD.
Since statement 2 implies the same information as statement 1, and statement 1 is sufficient, statement 2 is also SUFFICIENT.
The correct answer is D.
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Hi Maysaa,
This DS question is loaded with Number Property rules. If you understand (and can spot) those rules, then you'll be able to take advantage of many of the built-in patterns that will appear on Test Day (and save some time and effort).
Here, we're told that X is an INTEGER. The question asks if (X^2 + 1)(X+5) is even. This is a YES/NO question.
Even before we get to the two Facts, there's a pair of Number Properties built into the question.
IF X = ODD, then (X^2+1) = even and (X+5) = even, so the product will be (even)(even) = even.
IF X = EVEN then (X^2+1) = odd and (X+5) = odd, so the product will be (odd)(odd) = odd.
So, as complex as this question might look, it's really just asking "is X consistently even or consistently odd?"
In Fact 2, we're told that each prime factor of X^2 is greater than X. This means that X is NOT divisible by 2, 3, 5 or 7. Since we know that X is an integer, since it's NOT divisible by 2, it CANNOT be even. Thus, X MUST be odd. By extension, the answer to the question will ALWAYS be YES and Fact 2 is SUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
This DS question is loaded with Number Property rules. If you understand (and can spot) those rules, then you'll be able to take advantage of many of the built-in patterns that will appear on Test Day (and save some time and effort).
Here, we're told that X is an INTEGER. The question asks if (X^2 + 1)(X+5) is even. This is a YES/NO question.
Even before we get to the two Facts, there's a pair of Number Properties built into the question.
IF X = ODD, then (X^2+1) = even and (X+5) = even, so the product will be (even)(even) = even.
IF X = EVEN then (X^2+1) = odd and (X+5) = odd, so the product will be (odd)(odd) = odd.
So, as complex as this question might look, it's really just asking "is X consistently even or consistently odd?"
In Fact 2, we're told that each prime factor of X^2 is greater than X. This means that X is NOT divisible by 2, 3, 5 or 7. Since we know that X is an integer, since it's NOT divisible by 2, it CANNOT be even. Thus, X MUST be odd. By extension, the answer to the question will ALWAYS be YES and Fact 2 is SUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
Hey Rich,
Using statement 1, I did not "bother" with the first part (X^2 + 1) because I know that if X is odd, then (X+5) must be even , which would make the target question always us an even number and is sufficient to answer the question.
Is that a Risky strategy or not to be used??
Using statement 1, I did not "bother" with the first part (X^2 + 1) because I know that if X is odd, then (X+5) must be even , which would make the target question always us an even number and is sufficient to answer the question.
Is that a Risky strategy or not to be used??
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That seems like an excellent and very efficient strategy, definitely keep it up!Tmoni26 wrote:Hey Rich,
Using statement 1, I did not "bother" with the first part (X^2 + 1) because I know that if X is odd, then (X+5) must be even , which would make the target question always us an even number and is sufficient to answer the question.
Is that a Risky strategy or not to be used??
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Hi Tmoni26,
It looks like you're comfortable with the logic behind the Number Properties in this question. You'll find that that knowledge will come in handy on a variety of questions in the Quant section on Test Day, so you should stay on the lookout for those opportunities.
Since we know that X is an integer, and we're multiplying two parentheses that we KNOW are integers, if either of the two is EVEN, then the product will be EVEN. In real basic terms, it's not 'risky' if you know the rules and are paying attention to the details. Keep in mind that you'll still want to stay organized, take notes, etc. The silliest mistakes tend to happen when a Test Taker refuses to take notes (and to score at a high level, you really have to eliminate the silly mistakes from your work).
GMAT assassins aren't born, they're made,
Rich
It looks like you're comfortable with the logic behind the Number Properties in this question. You'll find that that knowledge will come in handy on a variety of questions in the Quant section on Test Day, so you should stay on the lookout for those opportunities.
Since we know that X is an integer, and we're multiplying two parentheses that we KNOW are integers, if either of the two is EVEN, then the product will be EVEN. In real basic terms, it's not 'risky' if you know the rules and are paying attention to the details. Keep in mind that you'll still want to stay organized, take notes, etc. The silliest mistakes tend to happen when a Test Taker refuses to take notes (and to score at a high level, you really have to eliminate the silly mistakes from your work).
GMAT assassins aren't born, they're made,
Rich
