GMATD11 wrote:
Whenever martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2times the tens digit of the amount of his bill.If the amount of the Martin's most recent restaurant bill was between $10 and $99, was the tip calculated by the 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 the martin was $8
1) as bill amount is between $15 and $50
tens digit can be any digit from 1,2,3,4
not sufficient
2) tip is 8
let y is the tens digit
2(y) = 8
y = 4
not sufficient
from 1 and 2
for any value of tens digit from 1 to 4 inclusive
and y=4
we can conclude that calculated tip ill be greater than the 15% of amount of bill
C
Similar to Q:
https://gmatclub.com/forum/whenever-tom ... l#p2251666Q: Actual Tip > 15% of Bill?
Trick: Min/Max
Method 1: Test Cases (Faster)
Similar to Bunuel's solution:
https://gmatclub.com/forum/whenever-mar ... ml#p8705981) Consider to extremes in 20s
Tip = 4
When bill is 21, 15% Tip = ~$3 => Yes
When bill is 30, 15% Tip = ~$4.5 => No
Not sufficient
2) Consider to extremes in 40s
Tip = 8
When bill is 40, 15% Tip = ~$6 => Yes
When bill is 50, 15% Tip = ~$7.5 => Yes
Sufficient
Method 2: Slower
List the Ranges:
Bill Range: 11-19, 21-29, 31-39, 41-49, ..., 91-99
Tip Range: 1.5<x<3, 3<x<4.5, 4.5<x<6, 6<x<7.5, ..., 13.5<x<15
Actual Tip: 2, 4, 6, ..., 18
Simplify the Q
Notice, tip > 15% of the bill when:
1) bill > 30
2) tip > $4
Hence the Q is asking:
Is bill > 30 or tip > 4?1) 15 < bill < 50. Not sufficient since b > 30.
2) Tip = 8. Sufficient since tip > 4
Hence, answer = B.