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21 Aug 2018, 03:36
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:28) correct
40%
(01:21)
wrong
based on 354
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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
If \(x\) and \(y\) are prime numbers, how many factors has \(x^2y^2\)?
1) \(xy=10\)
2) \(x+y\) is odd
21 Aug 2018, 05:13
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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.
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
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.
General Discussion
Chethan92
Joined: 18 Jul 2018
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Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
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WE:Engineering (Energy)
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21 Aug 2018, 03:42
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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
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
