If $x$ and $y$ are integers and $12x + 5y^2 = 0,$ which of the following must be true?

Question

If $x$ and $y$ are integers and $12x + 5y^2 = 0,$ which of the following must be true? (A) $x$ is a multiple of 10 (B) $x$ is a multiple of 15 (C) $x$ is a multiple of 25 (D) $x$ is not a multiple of 7 (E) $x$ is negative [spoiler]OA=B[/spoiler] Source: Veritas Prep

Jay@ManhattanReview · Answer

VJesus12 wrote: ↑Thu Jun 04, 2020 7:45 am If $x$ and $y$ are integers and $12x + 5y^2 = 0,$ which of the following must be true? (A) $x$ is a multiple of 10 (B) $x$ is a multiple of 15 (C) $x$ is a multiple of 25 (D) $x$ is not a multiple of 7 (E) $x$ is negative [spoiler]OA=B[/spoiler] Source: Veritas Prep Given that $12x + 5y^2 = 0,$ we have $x = \dfrac{-5y^2}{12}$ Since $x$ is an integer and 5 and 12 are co-prime to each other, $y^2$ must be a multiple of 12. Say $y^2 = 12p$, where $p$ is an integer Again, we have $y^2 = 12p$, thus, $y = 2√{3p}$. Since $y$ is an integer, $√{3p}$ must be an integer. Thus, $y^2=12*3p=36p$ Again, from $x = \dfrac{-5y^2}{12}=\dfrac{-5*36p}{12}= -15p$ => $x$ must be a multiple of 15. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes Oakland | GMAT Tutoring | GRE Prep Courses Albuquerque | El Paso Prep Classes SAT | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

deloitte247 · Answer

$$12x+5y^2=0$$ Express the equation in terms of x Note: x and y are integers of whole numbers $$\frac{12x}{12}=\frac{-5y^2}{12}$$ $$x=\frac{-5y^2}{12}$$ $$If\ \ y\ =\ 1$$ $$then\ x\ =\frac{-5\left(1ight)^2}{12}=\frac{-5}{12}=-0.42$$ $$x\ is\ not\ an\ integer\ so\ y
e1$$ $$If\ \ y\ =\ 2$$ $$then\ x\ =\frac{-5\left(2ight)^2}{12}=\frac{-20}{12}=-1.67$$ $$x\ is\ not\ an\ integer\ so\ y
e2$$ $$If\ \ y\ =\ 3$$ $$then\ x\ =\frac{-5\left(3ight)^2}{12}=\frac{-45}{12}=-3.75$$ $$x\ is\ not\ an\ integer\ so\ y
e3$$ $$If\ \ y\ =\ 4$$ $$then\ x\ =\frac{-5\left(4ight)^2}{12}=\frac{-80}{12}=-6.62$$ $$x\ is\ not\ an\ integer\ so\ y
e4$$ $$If\ \ y\ =\ 5$$ $$then\ x\ =\frac{-5\left(5ight)^2}{12}=\frac{-125}{12}=-10.42$$ $$x\ is\ not\ an\ integer\ so\ y
e5$$ $$If\ \ y\ =\ 6$$ $$then\ x=\frac{-5\left(6ight)^2}{12}=\frac{-180}{12}=-15$$ $$x\ is\ an\ integer\ so\ y=6\ or\ multiple\ of\ 6$$ $$and\ x=-15\ or\ multiple\ of\ 15$$ Answer =B

Scott@TargetTestPrep · Answer

VJesus12 wrote: ↑Thu Jun 04, 2020 7:45 am If $x$ and $y$ are integers and $12x + 5y^2 = 0,$ which of the following must be true? (A) $x$ is a multiple of 10 (B) $x$ is a multiple of 15 (C) $x$ is a multiple of 25 (D) $x$ is not a multiple of 7 (E) $x$ is negative [spoiler]OA=B[/spoiler] Solution: Let’s write: x = 5y^2/12 So, x is a multiple of 5. Further, notice that 12 has a factor of 3 and 5 is not divisible by 3; thus y^2 must be a multiple of 3. Finally, notice that every prime factor in the prime decomposition of y^2 appears an even number of times; thus y^2 has at least two factors of 3. After one of the factors of 3 cancels with the factor of 3 in the denominator, we still have at least one more factor of 3. Thus, y^2/12 has a factor of 3, which implies that x has a factor of 3. Since x has both a factor of 5 and a factor of 3, x must be a multiple of 15. Answer: B

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If \(x\) and \(y\) are integers and \(12x + 5y^2 = 0,\) which of the following must be true?

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Re: If \(x\) and \(y\) are integers and \(12x + 5y^2 = 0,\) which of the following must be true?

Re: If \(x\) and \(y\) are integers and \(12x + 5y^2 = 0,\) which of the following must be true?

GMAT/MBA Expert

Re: If \(x\) and \(y\) are integers and \(12x + 5y^2 = 0,\) which of the following must be true?

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