M7MBA wrote: ↑

Sun Jun 14, 2020 8:30 am

If \(7(a - 1) = 17(b - 1),\) and \(a\) and \(b\) are both positive integers the product of which is greater than 1, then what is the least possible sum of \(a\) and \(b?\)

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Observing \(7(a - 1) = 17(b - 1),\) we find that 7 and 17 are co-prime to each other; thus, we have \((a - 1) = 17=> a = 18\) and \(7=(b - 1)=b=8\)

So, the least possible sum of \(a\) and \(b\) = 18 + 8 = 26

Correct answer: E

Hope this helps!

-Jay
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M7MBA wrote: ↑

Sun Jun 14, 2020 8:30 am

If \(7(a - 1) = 17(b - 1),\) and \(a\) and \(b\) are both positive integers the product of which is greater than 1, then what is the least possible sum of \(a\) and \(b?\)

A. 2
B. 7
C. 17
D. 24
E. 26

[spoiler]OA=E[/spoiler]

Solution:

Since a and b are positive integers and ab > 1, then a and b are both greater than 1.
Since 7 and 17 do not have any common factors other than 1, we see that a - 1 must be divisible by 17 and b -1 must be divisible by 7. So a and b are both greater than 1, we need a - 1 = 17 and b - 1 = 7 in order to have the least possible sum of a and b. In that case, a = 18 and b = 8, and their sum is 26.

Answer: E