Question

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

• A. 42
• B. 60
• C. 74
• D. 140
• E. None of the above.

Answer 1

The Correct Option is B

Let the numbers be Ha, Hb, Hc, Hd, He, Hf, Hg
where H is HCF.
Given that,
Ha + Hb + Hc + Hd + He + Hf + Hg = 1740 = 60 x 29
H(a + b + c + d + e + f + g) = 60 x 29
For H to be the largest, the sum of (a + b + c + d + e + f + g) must be minimum.
The minimum possible value of (a + b + c + d + e + f + g) is 28.
Thus, the maximum possible value of H must be 60.
Hence, option B is the correct answer.