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's bill was between $10 and $99, was the tip calculates by martin on this bill greater than 15 percent of the amount of the bill?
Since the amount on the bill is a two digit number, it can be represented in the form 10A + B. Then the amount of the tip = 2A.
Is 2A/(10A+B) > 15/100 ?
i.e. 200A > 150A + 15B ?
i.e. 50A > 15B ?
i.e 10A>3B ?
We can now rephrase the question to -
If the amount on the bill is 10A + B and the tip is 2A, Is 10A > 3B ?
1 the amount of the bill was between $15 and $50.
If 10A + B = 16, then A = 1 and B = 6. 10*1 < 3*6 (10A < 3B)
If 10A + B = 31, then A = 2 and B = 1. 10*3 > 3*1 (10A > 3B)
Since we don't have a definite answer, statement I is insufficient to answer the question.
2 the tip calculated by martin was $8.
Tip = 2A = 8. So the value of A is 4
10A = 40 is always greater than 3B(3B = 0 if B = 0 and 3B = 27 if B = 9).
So, statement II is sufficient to answer the question
Answer
B
