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Difficulty:
45%
(medium)
Question Stats:
68% (01:38) correct
32%
(01:55)
wrong
based on 947
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The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 8!?
A. 3(5!)
B. 4(5!)
C. 5(5!)
D. 6(5!)
E. 7(5!)
A. 3(5!)
B. 4(5!)
C. 5(5!)
D. 6(5!)
E. 7(5!)
02 Feb 2015, 04:59
Kudos
Bookmarks
Bunuel
VERITAS PREP OFFICIAL SOLUTION:
Remember that the Greatest Common Factor of two numbers represents the overlap of all prime factors of those two numbers. So what you're looking for in this case is a value that does not share any other prime factors with 8 * 7 * 6 * 5 * 4 * 3 * 2 other than 5 * 4 * 3 * 2.
Consequentially, the answer choice cannot include any prime factors of 8, 7, or 6 outside of the parentheses, where the common 5! already exists. A is incorrect because 3 is a factor of 6. B is incorrect because 4 is a factor of 8. D is incorrect because of the common 6 and E is incorrect because of the common 7. With choice C, however, there's no overlap in factors between 5 and the set 8, 7, 6, so that means that the Greatest Common Factor is, indeed, 5!.
27 Jan 2015, 11:44
Kudos
Bookmarks
It is given that GCD of two numbers is 5! => this is the maximum common factor in those two numbers.
First number is 8! = 8*7*6*5!
Lets review all the options for second number -
A. 3(5!) - here 3 is also common in addition to 5!. Hence 5! cant be the GCD of these two numbers
B. 4(5!) - Here 4 is common besides 5! and so this option is rejected
C. 5(5!) - only 5! is common in the two numbers and hence the Answer.
D. 6(5!) - 6 is common besides 5! and hence rejected on similar grounds
E. 7(5!) - 7 is common besides 5! and so this is aso rejected
Hence ans is C.
First number is 8! = 8*7*6*5!
Lets review all the options for second number -
A. 3(5!) - here 3 is also common in addition to 5!. Hence 5! cant be the GCD of these two numbers
B. 4(5!) - Here 4 is common besides 5! and so this option is rejected
C. 5(5!) - only 5! is common in the two numbers and hence the Answer.
D. 6(5!) - 6 is common besides 5! and hence rejected on similar grounds
E. 7(5!) - 7 is common besides 5! and so this is aso rejected
Hence ans is C.
