dabaobao wrote:
Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calculates the dollar amount of the tip as 3 times the tens digit of the amount of his bill. If the amount of Tom’s most recent cafeteria bill was 2-digit integer, was the tip calculated by Tom on this bill greater than 20 percent of the amount of the bill?
(1) The amount of the bill excluding tip was over $20
(2) The tip calculated by Tom was at least $4
Hi
ArupRS,
Of course, the question is not written properly..
What it says is the bill is a 2-digit amount that is \($10\leq{bill}\leq{$99}\). So, if the amount is a 2-digit number, we can write it as ab or 10a+b..
tip is 3a
So we are asked if tip 3a>20% of (10a+b).....\(3a>\frac{20}{100}(10a+b)...15a>10a+b......5a>b\)...
Now max value of b can be 9, so if we know a is at least 2, 5a>b irrespective of the value of b.
Question becomes - Is 5a>b? .
So, either we require to know the value of both a and b if a is 1, otherwise answer is always YES.
(1) The amount of the bill excluding tip was over $20
So, the tens digit or \(a\geq{2}\).
Suff
(2) The tip calculated by Tom was at least $4
so 3a>4.....\(a>\frac{4}{3}\). Since a is an integer, a will be at least 2.
Again sufficient.
D
Nice explanation. Thank you so much .