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# The set S is the set of all odd integers, and a and b are two elements

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Math Expert
Joined: 02 Sep 2009
Posts: 60605
The set S is the set of all odd integers, and a and b are two elements  [#permalink]

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10 Dec 2019, 05:43
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Difficulty:

45% (medium)

Question Stats:

55% (01:03) correct 45% (01:08) wrong based on 28 sessions

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The set S is the set of all odd integers, and a and b are two elements of set S. Which of the following must also be an element of set S?

I. $$ab$$

II. $$\frac{a}{b}$$

III. $$a^b$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

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Math Expert
Joined: 02 Aug 2009
Posts: 8341
Re: The set S is the set of all odd integers, and a and b are two elements  [#permalink]

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10 Dec 2019, 23:05
Bunuel wrote:
The set S is the set of all odd integers, and a and b are two elements of set S. Which of the following must also be an element of set S?

I. $$ab$$

II. $$\frac{a}{b}$$

III. $$a^b$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

A MUST be true question..

S consists of all odd integers.

a and b are also odd..

I. $$ab$$...ab will always be odd and will be part of the set S

II. $$\frac{a}{b}$$. If b is a factor of a, yes, otherwise no. for example a=9 and b=3 9/3=3 yes..
But say a=7 and b=3, 7/3 is a fraction and not odd integer..

III. $$a^b$$...The property of odd/even depends on the base, a, till the time b is positive integer. SO Yes a^b will be odd.

I and III

D
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Re: The set S is the set of all odd integers, and a and b are two elements   [#permalink] 10 Dec 2019, 23:05
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