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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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Math Expert
Joined: 02 Sep 2009
Posts: 59561
If r is divisible by 10 and s is divisible by 9, rs must have at least  [#permalink]

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13 Aug 2018, 04:57
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Difficulty:

15% (low)

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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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.
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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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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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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

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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