annusngh wrote:
How many numbers between 1 to 300 are divisible by 11 and 13 but not by both?
A. 45
B. 46
C. 48
D. 50
E. 52
Dear
annusngh,
I'm happy to respond.
We can solve this without listing.
Start with multiples of 11:
there are ten up to and including 110
there are twenty up to and including 220
that leaves us a gap of 80
we could fit 7 more multiples of 11, which would take up 7*11 = 77 of that gap, ending at 220 + 77 = 297
that's 27 multiples of 11 less than 300
Now, multiples of 13:
there are ten up to and including 130
there are twenty up to and including 260
that leaves us a gap of 40
we could fit three more multiples of 13, which would take up 3*13 = 39 of that gap, ending at 260 + 39 = 299
that's 23 multiples of 13 less than 300
Now, the
overlaps.
13*11 = 13*(10 + 1) = 130 + 13 = 143
Double that:
286
If we take any higher multiples of 143, clearly we'll be over 300. We have to subtract those two numbers from both lists.
number = (27 - 2) + (23 - 2) = 25 + 21 = 46
answer =
(B) Does all this make sense?
Mike
, Why we need to subtract the overlap instead of adding up the overlap since 143 and 286 are less than 300?
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