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A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are in

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by Vincen » Tue Jun 02, 2020 7:48 am

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E

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Difficulty—

A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?

I. 3
II. 12
III. 24

A. None
B. I only
C. II only
D. I and II only
E. II and III only

[spoiler]OA=E[/spoiler]

Source: Princeton Revie
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Re: A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are i

by Jay@ManhattanReview » Wed Jun 03, 2020 1:30 am
Vincen wrote: ↑
Tue Jun 02, 2020 7:48 am
 A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?

I. 3
II. 12
III. 24

A. None
B. I only
C. II only
D. I and II only
E. II and III only

[spoiler]OA=E[/spoiler]

Source: Princeton Revie
Since 2 and 6 are in the set, 2*6 = 12 is in the set; similarly, 12*2 = 24 and 12*6 = 72 are in the set. However, we cannot say anything about the no. 3.

The correct answer: E

Hope this helps!

-Jay
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Re: A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are i

by Scott@TargetTestPrep » Sat Jun 06, 2020 5:43 am
Vincen wrote: ↑
Tue Jun 02, 2020 7:48 am
 A set of numbers is defined such that if \(x\) and \(y\) are in the set, \(xy\) is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?

I. 3
II. 12
III. 24

A. None
B. I only
C. II only
D. I and II only
E. II and III only

[spoiler]OA=E[/spoiler]

Solution:

Since 2 and 6 are in the set, 2 * 6 = 12 is also in the set. Since 12 is in the set, 2 * 12 = 24 is also in the set.

Answer: E

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