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Let n be a 5-digit number, and let q and r be the quotient and the rem

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
Let n be a 5-digit number, and let q and r be the quotient and the rem  [#permalink]

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19 Mar 2019, 22:12
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Difficulty:

85% (hard)

Question Stats:

43% (02:54) correct 57% (02:36) wrong based on 44 sessions

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Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100. For how many values of n is q + r divisible by 11?

(A) 8180
(B) 8181
(C) 8182
(D) 9000
(E) 9090

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Joined: 02 Aug 2009
Posts: 8320
Re: Let n be a 5-digit number, and let q and r be the quotient and the rem  [#permalink]

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20 Mar 2019, 20:39
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3
Bunuel wrote:
Let n be a 5-digit number, and let q and r be the quotient and the remainder, respectively, when n is divided by 100. For how many values of n is q + r divisible by 11?

(A) 8180
(B) 8181
(C) 8182
(D) 9000
(E) 9090

There are 99999-10000+1=90000 possible values of n...

q+r divisible by 11 means the same as the number divisible by 11..
example - 11000 is divisible by 11... 11000=100*110+0 so q+r=110+0=110, divisible by 11
10000 is not divisible by 11, so is not q+r
Thus, we are looking for 5-digit numbers that are the multiples of 11
10010 is first multiple => 11*910, and 99990 is the last 5-digit multiple of 11=>11*9090
Total multiples = 9090-910+1=8180+1=8181

B
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Joined: 11 Mar 2019
Posts: 1
Re: Let n be a 5-digit number, and let q and r be the quotient and the rem  [#permalink]

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09 Apr 2019, 07:44
Is there another way of solving this question? EgmatQuantExpert
Re: Let n be a 5-digit number, and let q and r be the quotient and the rem   [#permalink] 09 Apr 2019, 07:44
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