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How many two-digit numbers are divisible by both 5 and 6?

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How many two-digit numbers are divisible by both 5 and 6? [#permalink]

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New post 16 Oct 2017, 01:30
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (00:20) correct 21% (00:17) wrong based on 42 sessions

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Kudos [?]: 133105 [0], given: 12410

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How many two-digit numbers are divisible by both 5 and 6? [#permalink]

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New post 16 Oct 2017, 03:36
Bunuel wrote:
How many two-digit numbers are divisible by both 5 and 6?

(A) none
(B) one
(C) two
(D) three
(E) more than three

Two-digit numbers: 10 to 99

Divisible by 5 and 6 means:
For 5, must end in 5 or 0
For 6: must be divisible by 2 and 3

Use those prime factors: 5, 2, and 3
LCM = (5 * 2 * 3) = 30

30 is one multiple. Multiply by increasing integers

(30 * 1 = 30)
30 * 2 = 60
30 * 3 = 90

Next multiple of 30 is 120. Too large

There are three two-digit numbers divisible by 5 and 6: 30, 60, and 90

Answer
[Reveal] Spoiler:
D

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Re: How many two-digit numbers are divisible by both 5 and 6? [#permalink]

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New post 17 Oct 2017, 11:49
Bunuel wrote:
How many two-digit numbers are divisible by both 5 and 6?

(A) none
(B) one
(C) two
(D) three
(E) more than three


If a number is divisible by both 5 and 6, then it’s divisible by their LCM, which is 30. Thus, we need to find the number of two-digit numbers that are multiples of 30. We have:

30, 60, and 90

Answer: D
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Re: How many two-digit numbers are divisible by both 5 and 6? [#permalink]

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New post 22 Oct 2017, 15:07
D, three.
30, 60 and 90 all divisible by 5 and 6.
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I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

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Kudos [?]: 8 [0], given: 18

Re: How many two-digit numbers are divisible by both 5 and 6?   [#permalink] 22 Oct 2017, 15:07
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How many two-digit numbers are divisible by both 5 and 6?

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