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

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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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