RBBmba@2014 wrote:For two positive integers A & B, what is the highest number that divides completely the product of integers from 1 to A and 1 to B such that B = A + 29.
(A) 1
(B) Product of all integers from 1 to A
(C) Product of all integers from 1 to B
(D) 29*A
(E) Can’t be determined
The product of the integers from 1 to A = A!.
Since B=A+29, the product of the integers from 1 to B = B! = (A+29)!.
Question stem, rephrased:
What is the greatest common factor of A! and (A+29)!?
Case 1: A=1
Here,
A! = 1! and (A+29)! = 30!.
The GCF of 1! and 30! =
1!.
Case 2: A=10
Here,
A! = 10! and (A+29)! = 39!.
The GCF of 10! and 39! =
10!.
Case 3: A=100
Here,
A! = 100! and (A+29)! = 129!.
The GCF of 100! and 129! =
100!.
In every case, the GCF = A!.
The correct answer is
B.
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