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

Question

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

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

Chethan92 · Answer

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

KSBGC · Answer

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.

GMATGuruNY · Answer

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)...

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.

D

MathRevolution · Answer

=>

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 · Answer

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.

saurabh9gupta · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards