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Juan Set 1 Paper 1 · Q3

Paper 1Algebra

Let aa, bb, cc, dd be positive integers, and let

M=6a⋅5b,N=10c⋅9dM=6^a\cdot5^b,\qquad N=10^c\cdot9^d

be positive integers such that

gcd⁡(M,N)=23⋅32⋅5,lcm⁡(M,N)=25⋅33⋅55.\gcd(M,N)=2^3\cdot3^2\cdot5,\qquad \lcm(M,N)=2^5\cdot3^3\cdot5^5.

What is a+b+c+da+b+c+d?

A8
B9
C10
D11
E12

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