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20 Feb 2025, 23:44
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:14) correct
0% (00:00) wrong based on 2 sessions
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Time
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Not Attempted Yet
If \(\frac{52}{x}\) is a positive integer, how many integer values are possible for x?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
22 Feb 2025, 10:45
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OE
If 52/x is a positive integer, then x is a positive factor of 52 (i.e., x divides evenly into 52). This question can most easily be solved by listing positive factor pairs for 52, as listing in pairs will help prevent omissions. Each pair multiplies to 52.
The factors of 52 are:
1 & 52
2 & 26
4 & 13
Check to make sure this list is complete. Looking down the left column, 1 and 2 made the list, then 3 didn’t divide evenly into 52, then 4 did. Since 4 pairs with 13, check the other integers between 4 and 13. Since 5, 6, 7, 8, 9, 10, 11, and 12 don’t divide evenly into 52, this list is complete. There are 6 factors, so the answer is (B).
If 52/x is a positive integer, then x is a positive factor of 52 (i.e., x divides evenly into 52). This question can most easily be solved by listing positive factor pairs for 52, as listing in pairs will help prevent omissions. Each pair multiplies to 52.
The factors of 52 are:
1 & 52
2 & 26
4 & 13
Check to make sure this list is complete. Looking down the left column, 1 and 2 made the list, then 3 didn’t divide evenly into 52, then 4 did. Since 4 pairs with 13, check the other integers between 4 and 13. Since 5, 6, 7, 8, 9, 10, 11, and 12 don’t divide evenly into 52, this list is complete. There are 6 factors, so the answer is (B).
