Percenatges

[Abdulla]

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 recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% 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.

The answer is B..

Any one has better approach than the OG.

[logitech]

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 recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% 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.

The answer is B..

Any one has better approach than the OG.

Let me try to beat OG

Bill is XY and the tip is 2X

Question is :

Is 2x/(10x+Y) > 15/100 ?

Or if we simplfy this expression: Is 10X>3Y

Remember Y can be between 0-9 so 3y Can be 27 MAX ( 3x9)

So if 10X>27 X needs to be greater than 2 :!:

Statement 1) 1<x<5 INSUF
Statement 2) tip = 8, so X = 4 which is greater than 2 SUF

Hence, B

Did I confuse you more than OG did ?

[Abdulla]

YES but .> it seems better but the problem is ME..

[JGaynor]

anyone else have an explanation for this problem?

[ymach3]

I tried picking up numbers...

Tip=2*(tenths digit of the Bill)

Bill Range is between 10 and 99 $

Possible tips = 2-18.

(i) says the bill is between 15-50.

Possible Tip values would be 2-10.

Consider a case where Bill -15 and Tip =2*1=2

Percentage=2/15 * 100=12 %(approx'ly)-----> NO-Not greater than 15%.

Another case when bill=40, which makes the tip amount=8

Percentage = 8/40 * 100=20 % --------> YES-Greater than 15%.


Hence, Insufficient.


Case (ii)

Tip=8 provides us sufficient information to say that the bill amount would fall in between 40 and 49.

consider bill ammount = 48, Percentage=8/48*100=33% (Apporox'ly) - YES ,greater than 15%.

Hence SUFFICIENT.

Forum browsers, Correct me if i am wrong.

[meghash3]

since the bill amt > 10 $, and tip is 8$, it is certainly less than 10 % , thsu B can answer the qeus alone, A does not

[outreach]

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 recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% 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.

The answer is B..

Any one has better approach than the OG.

TO ANSWER THE Q we either need the exact bill amt or tip value
1. no sufficient information
2. tip is 8
so the bill amt has to be between $40-$49

lets take the lowest number $40. a tip of $8 is 20% of the original bill amt of $40 - eq1
lets take the highest number $49. a tip of $8 is 16% of the original bill amt of $49 -eq2

both eq1 and eq2 implies that a tip of $8 is greater than 15% when the bill amt is between $40-$49

[kevincanspain]

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 recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% 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.

The answer is B..

Any one has better approach than the OG.

Logitech's algebraic solution is lovely and should be noted, as its approach can be applied to other questions.


Notice that Martin gives 20% of the tens digit and 0% of the units digit. Thus, percentage-wise, the lower the tens digit and the higher the units digit, the lower the tip. $19 produces a tip of just over 10% , whereas any bill that is multiple of $10 produces a tip of 20%.

(1) is thus insufficient
(2) the bill is in the 40-49 dollar range, so the stingiest tip would result from a $49 bill, but 8/49 > 8/50 = 16% SUFF

[singalong]

I understood till the expression Is 2x/(10x+Y) > 15/100 ?

Could someone explain me the next part please?

[dj_vinayak]

To me the two hints given contradict.

The bill cannot be both between 15 & 30 $ as given in A, and also be between 40 and 49& as inferred from b.