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If r is divisible by 10 and s is divisible by 9, rs must have at least

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If r is divisible by 10 and s is divisible by 9, rs must have at least  [#permalink]

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New post 13 Aug 2018, 04:57
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A
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C
D
E

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Question Stats:

79% (01:09) correct 21% (01:11) wrong based on 60 sessions

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If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

(A) Two
(B) Four
(C) Twelve
(D) Fourteen
(E) Sixteen
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Re: If r is divisible by 10 and s is divisible by 9, rs must have at least  [#permalink]

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New post 13 Aug 2018, 05:52
1
Let's consider R =10 and S = 9. Then, RS=90.
Prime Factorizing 90 Gives \(2^1\)\(3^2\)\(5^1\).
Number of factors is given by the formula \(2^p\)\(3^q\)\(5^r\) = (p+1)(q+1)(r+1)
P=1, Q=2, R=1. Then number of factors = 2*3*2 =12 factors.
C is the answer.
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Re: If r is divisible by 10 and s is divisible by 9, rs must have at least  [#permalink]

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New post 13 Aug 2018, 06:40
Bunuel wrote:
If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

(A) Two
(B) Four
(C) Twelve
(D) Fourteen
(E) Sixteen

Min value of \(R = 10\) & Min value of \(S = 9\)

So, Min value of \(RS = 90\)

Now, \(90 = 2*3^2*5\)

So, The number of Factors of \(RS = (1+1)(2+1)(1+1) = 12\), Answer must be (C) \(12\)
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Re: If r is divisible by 10 and s is divisible by 9, rs must have at least  [#permalink]

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New post 13 Aug 2018, 10:45
Bunuel wrote:
If r is divisible by 10 and s is divisible by 9, rs must have at least how many factors?

(A) Two
(B) Four
(C) Twelve
(D) Fourteen
(E) Sixteen



r is divisible by 10

s is divisible by

rs could be 90 or its multiples.

let's factorize 90 = 5*2*3*3 = 3^2 * 5 * 2

Total number of factors: (2+1) (1+1) ( 1+1) = 12

The best answer is C.
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Re: If r is divisible by 10 and s is divisible by 9, rs must have at least   [#permalink] 13 Aug 2018, 10:45
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