Is the product of two numbers greater than 100?

(1) The sum of the two numbers is greater than 50.
(2) Each of the numbers is greater than 10.
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Statement 1: two number can be 50 & 1. the sum is 51 but the product is 50. similarly the two number can be 20 & 40. the sum is 60 and the product is 800. So we get a Yes & No. Hence insufficient

Statement 2: Logically if the two numbers are greater than 10 then their products will be greater than 10. Hence Sufficient

Mathematically, let the numbers be \(a\) & \(b\)
given that \(a>10\)----(1) &
\(b>10\)------(2)
as both \(a\) & \(b\) are positive, we can multiply the inequality without changing the sign. hence multiplying inequality 1 & 2 will give us

\(a*b>10*10\) or \(ab>100\) . Hence sufficient.

Option B

Thanks for pointing that out

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