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How many positive 3-digit numbers are multiples of 20, but not of 55?

 May 26, 2019
 #1
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(100, 120, 140, 160, 180, 200, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860, 900, 920, 940, 960, 980)=41 Numbers.

 

220, 440, 660, 880  are multiples of both 20 and 55, which are excluded from the above count.

 May 26, 2019
edited by Guest  May 26, 2019
 #2
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Thanks Guest.   laugh

 

How many positive 3-digit numbers are multiples of 20, but not of 55?

 

100 to 999

45 are multiples of 20

 

To be a multiple of 20 and of 55 then the factors must be     2*2*5*11*X = 220X

1000/220=4.5..

So X can be 1,2,3, or 4

Hence there are four 3 digit numbers that are multiples of both 55 and 20

 

So the answer is 45-4 = 41 

 

Guest like guest already told you    wink

 May 27, 2019

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