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# If x and y are prime numbers, how many factors has x^2y^2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are prime numbers, how many factors has x^2y^2?  [#permalink]

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21 Aug 2018, 02:36
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:12) correct 44% (00:56) wrong based on 106 sessions

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[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are prime numbers, how many factors has $$x^2y^2$$?

1) $$xy=10$$
2) $$x+y$$ is odd

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College Re: If x and y are prime numbers, how many factors has x^2y^2? [#permalink] ### Show Tags 21 Aug 2018, 04:13 2 1 To count the factors of a positive integer: 1. Prime-factorize the integer 2. Write the prime-factorization in the form (a^p)(b^q)(c^r)... 3. The number of factors = (p+1)(q+1)(r+1)... MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x$$ and $$y$$ are prime numbers, how many factors has $$x^2y^2$$? 1) $$xy=10$$ 2) $$x+y$$ is odd Only two cases are possible: Case 1: x≠y Here, to determine the number of factors for $$x^2y^2$$, we add 1 to each exponent and multiply: (2+1)(2+1) = 9 factors Case 2: x=y, with the result that $$x^2y^2 = x^4$$ Here, to determine the number of factors for $$x^4$$, we add 1 to the exponent: 4+1 = 5 factors Implication: To determine the number of factors, we need to know whether x=y. Statement 1: Only one pair of prime numbers has a product of 10: 2 and 5. Thus, x≠y. SUFFICIENT. Statement 2: Since x+y = odd, either x or y is ODD, while the other value is EVEN. Thus, x≠y. SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. ##### General Discussion Senior Manager Joined: 18 Jul 2018 Posts: 498 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If x and y are prime numbers, how many factors has x^2y^2? [#permalink] ### Show Tags 21 Aug 2018, 02:42 From statement 1: xy = 10. Only poasible combination of x and y is (2,5) or (5,2). This is sufficient. From statement 2: x+y = odd. Here also only possible combination is either x or y should be even. X or Y = 2.Hence sufficient. D is the answer Posted from my mobile device _________________ When you want something, the whole universe conspires in helping you achieve it. Director Joined: 31 Oct 2013 Posts: 876 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) If x and y are prime numbers, how many factors has x^2y^2? [#permalink] ### Show Tags 21 Aug 2018, 04:06 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x$$ and $$y$$ are prime numbers, how many factors has $$x^2y^2$$? 1) $$xy=10$$ 2) $$x+y$$ is odd Note: x and y are prime numbers. We are looking for the number of factors of $$x^2y^2$$. Total number of factors = (2+1) (2+1) = 3*3 = 9. is this question okay ? or i am wrong. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are prime numbers, how many factors has x^2y^2? [#permalink] ### Show Tags 23 Aug 2018, 01:10 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. If $$x$$ and $$y$$ are different prime numbers, then $$xy$$ has $$(2+1)(2+1) = 9$$ factors. If $$x$$ and $$y$$ are the same prime number, then $$xy$$ has $$4+1 = 5$$ factors. Condition 1) Since $$x$$ and $$y$$ are prime numbers and $$xy = 10$$, either $$x = 2$$ and $$y = 5,$$ or $$x = 5$$ and $$y = 2.$$ So, $$x$$ and $$y$$ are different prime numbers. Thus, condition 1) is sufficient. Condition 2) Since $$x$$ and $$y$$ are prime numbers and $$x + y$$ is odd, one of them is even and the other one is odd. So, $$x$$ and $$y$$ are different prime numbers. Thus, condition 2) is sufficient. Therefore, D is the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are prime numbers, how many factors has x^2y^2?  [#permalink]

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30 Aug 2018, 22:19
selim wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are prime numbers, how many factors has $$x^2y^2$$?

1) $$xy=10$$
2) $$x+y$$ is odd

Note: x and y are prime numbers.

We are looking for the number of factors of $$x^2y^2$$.

Total number of factors = (2+1) (2+1) = 3*3 = 9.

is this question okay ? or i am wrong.

That is right.
The point of this question is that x and y are different prime number or not.
From each of conditions, we can conclude x and y are different prime numbers, and the number of factors is (2+1)(2+1) = 3.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Joined: 10 Jan 2013
Posts: 157
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
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Re: If x and y are prime numbers, how many factors has x^2y^2?  [#permalink]

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30 Aug 2018, 22:39
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are prime numbers, how many factors has $$x^2y^2$$?

1) $$xy=10$$
2) $$x+y$$ is odd

Good Question!

x and y are primes - could be 2 and any other prime number or any other prime pair (apart from 2)

1. xy =10 ; possibility - 2 and 5 (sufficient)

2. x + y = odd -- here again the possiblilty is 2 and any other number ( sufficient)

D
Re: If x and y are prime numbers, how many factors has x^2y^2? &nbs [#permalink] 30 Aug 2018, 22:39
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# If x and y are prime numbers, how many factors has x^2y^2?

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