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TheUltimateWinner
Joined: 23 Feb 2015
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Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,465
04 May 2019, 10:27
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B
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:
63% (01:35) correct
37%
(01:47)
wrong
based on 73
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If x is a positive integer, does 5x have have an odd number of factors?
1) x is divisible by 5
2) x is a perfect square
1) x is divisible by 5
2) x is a perfect square
04 May 2019, 18:43
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IMO B.
An odd number of factors can only be achieved when a number is a perfect square, because a number's factors always come in pairs except for cases of a perfect square. For a non-perfect square, 50 for example, its factors would come in pairs like 1 and 50, 2 and 25, etc., thus making its number of factors always even. However, for a perfect square like 100, its factors would come in pairs except for 10, which is multiplied by itself, making the number of factors always odd. Therefore 5x must either be definitively a perfect square, or definitively not a perfect square.
I ONLY = INSUFFICIENT.
If x is divisible by 5, can we tell of 5x is a perfect square? If x=5, then 5x=25... a perfect square. If x=10, then 5x=50... not a perfect square. We cannot tell if 5x is a perfect square, and thus cannot tell if its number of factors is odd or even.
II ONLY = SUFFICIENT
This translates to "is there any perfect square (x) that, when multiplied by 5, will yield another perfect square?" Definitively, multiplying any perfect square by 5 will never yield another perfect square.
1*5=5, no
4*5=20, no
9*5=45, no
16*5=80, no
etc.
An odd number of factors can only be achieved when a number is a perfect square, because a number's factors always come in pairs except for cases of a perfect square. For a non-perfect square, 50 for example, its factors would come in pairs like 1 and 50, 2 and 25, etc., thus making its number of factors always even. However, for a perfect square like 100, its factors would come in pairs except for 10, which is multiplied by itself, making the number of factors always odd. Therefore 5x must either be definitively a perfect square, or definitively not a perfect square.
I ONLY = INSUFFICIENT.
If x is divisible by 5, can we tell of 5x is a perfect square? If x=5, then 5x=25... a perfect square. If x=10, then 5x=50... not a perfect square. We cannot tell if 5x is a perfect square, and thus cannot tell if its number of factors is odd or even.
II ONLY = SUFFICIENT
This translates to "is there any perfect square (x) that, when multiplied by 5, will yield another perfect square?" Definitively, multiplying any perfect square by 5 will never yield another perfect square.
1*5=5, no
4*5=20, no
9*5=45, no
16*5=80, no
etc.
18 Jan 2022, 07:57
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