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Set X consists of the positive multiples of 5, and set Y consists of

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Set X consists of the positive multiples of 5, and set Y consists of  [#permalink]

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New post 13 Jul 2018, 00:53
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A
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C
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E

Difficulty:

  95% (hard)

Question Stats:

32% (02:43) correct 68% (02:42) wrong based on 54 sessions

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Set X consists of the positive multiples of 5, and set Y consists of the odd prime numbers less than 20. If set Z consists of every distinct integer less than 100 that is the product of one element from set X and one element from set Y, then set Z consists of how many elements?

A. 12
B. 14
C. 15
D. 16
E. 18

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Re: Set X consists of the positive multiples of 5, and set Y consists of  [#permalink]

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New post 13 Jul 2018, 03:33
1
x: {5;10;15;20;25;30;35...}
y: {3;5;7;11;13;17;19}

To find z, let's take the first value of x, 5. It can be multiplied by all 7 values of y as the result will be less than 100.
When x = 10, we can multiply it only by the first 3 values of y, otherwise it will be greater than 100.
When x = 15, only by the first 2.
When x = 20, only by the first one.
When x = 25, only by the first one.
When x = 30, only by the first one.
For x greater than 30, we cannot multiply it by any value of y or it will exceed 100.

There is a total of 7+3+2+1+1+1 = 15 possible values, but be careful with the duplicate value of 75 (15*5 and 25*3) as the set must consist of distinct integers. Therefore the value is 14.

Answer B.
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Re: Set X consists of the positive multiples of 5, and set Y consists of &nbs [#permalink] 13 Jul 2018, 03:33
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