Data Sufficiency

Whenever Martin has a restaurant bill with an amount between $10 - $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 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 $50
2. The tip calculated by Martin was $8

I have no idea how to break down the stem, and therefore am unable to answer if sufficient or not. Thank you for your help.

I guess the answer is B

My explanation :

Given : 1) Bill between $10 - $99
2) Tip is 2 times the tens digit of the amount of his bill

Asked : was the tip calculated by Martin on this bill greater than 15 percent of the amount of the bill?

CASE 1 The amount of the bill was between $15 and $50
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So the tip he received is either 1*2 or 2*2 or 3*2 or 4*2

Now 2,4,6,8

Some of them are greather than 15% of the bill some of them are less than 15% of the bill...So insufficient

Example : Let bill be 15$, Tips is 2$ < 15% of 15 (2.25$)
Let bill be 40$, Tips is 8$> 15% of 40 (6$)

CASE 2 The tip calculated by Martin was $8
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It says bill amount is between 40 and 49.
15% of 40 is 6 and 15% of 49 is less than 8. Hence Suff

so it would be C then

yalanand wrote:I guess the answer is B

My explanation :

Given : 1) Bill between $10 - $99
2) Tip is 2 times the tens digit of the amount of his bill

Asked : was the tip calculated by Martin on this bill greater than 15 percent of the amount of the bill?

CASE 1 The amount of the bill was between $15 and $50
---------------------------------------------------------------------

So the tip he received is either 1*2 or 2*2 or 3*2 or 4*2

Now 2,4,6,8

Some of them are greather than 15% of the bill some of them are less than 15% of the bill...So insufficient

Example : Let bill be 15$, Tips is 2$ < 15% of 15 (2.25$)
Let bill be 40$, Tips is 8$> 15% of 40 (6$)

CASE 2 The tip calculated by Martin was $8
---------------------------------------------------------------------

It says bill amount is between 40 and 49.
15% of 40 is 6 and 15% of 49 is less than 8. Hence Suff

No the answer would be B

1. The amount of the bill was between $15 and $50
2. The tip calculated by Martin was $8

In case of choice 2, $8 is possible only between bill amounts of $40-$49,
and 8/40 =20%, which is greater than 15%

Or

and 8/49= 16/3% , which is greater than 15% again

therefore B is sufficient

There was a great explanation in one of manhattan's books about this question. Here it goes:

t=tens digit
u=units digit
10t+u=bill
2t=amount of the tip

The stem question goes like this:

2t > 0.15(10t+u)
2t > 1.5t + 0.15u which is 10t/3>u
if you manage to rephrase the question to here you won't have any trouble in finding what you are looking for under a minute.

1. 1 <= t <=4

2. 2t=8; t=4

You can easily substitute in the final stem and get your answer.

it's B.

Sorry, I forgot to put the answer when I posted, which is B.

Thank you for the explanations!

I understand why hypik21 thought the answer was C, since an $8 tip is possible in both statements. How do we overcome this?

480ocean wrote:I understand why hypik21 thought the answer was C, since an $8 tip is possible in both statements. How do we overcome this?

I overlooked the statement where it says the tip is twice the TENS digit. Only 4 fits the criteria and any tip more than 7.5 qualiies since .15 times 49.99 is less than 7.5

Ok, I'm an idiot. I didn't pay enough attention to realize this is a Yes/No question - which I should have caught again in yalanand's answer.

Study over-load, and my brain is playing tricks on me.