Query

[MI3]

Q: Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin' most recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill greater than 15 percent of the amount of the bill?
(1) The amount of the bill was between $15 and $30
(2) The tip calculated by Martin was $8

Answe I got was B, am I correct?

[sourabh33]

Before anything, the statements are contradictory therefore it may not have a valid solution. As per A the amount is between 15 and 30, versus as per B the amount has to be in 40's


Let Martin's Bill be represented as AB (A is 10's digit and B is unit's digit)
Now we can say that Bill Amount = 10A + B, and Tip = 2A

Paraphrasing the question, we can write
Is 2A > 0.15 (10A + B)
Is 2A > 1.5A + 0.15 B
Is 0.5A > 0.15B (Since amounts are positive, we can cross multiply without changing sign of inequality)
Is A/B > 3/10

Evaluating Statement 1
The Bill amount is between 15 and 30
{16,17,18,19,20,21,22,23,24,25,26,27,28,29}

Case 1 - When Amount is 16 Then A/B = 1/6 Therefore the tips is less than 15%
Case 2 - When Amount is 19 Then A/B = 1/9 Therefore the tips is less than 15%
Case 3 - When Amount is 21 Then A/B = 2/1 Therefore the tips is Greater than 15%

Therefore statement 1 is insufficient

Evaluating Statement 2

If the tip was 8, the amount could be {40,41.......49]}
Case 1 - When Amount is 41 Then A/B = 4/1 Therefore the tips is greater than 15%
Case 2 - When Amount is 49 Then A/B = 4/9 Therefore the tips is greater than 15%

Therefore Sufficient