Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc

Question

Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calculates the dollar amount of the tip as 3 times the tens digit of the amount of his bill. If the amount of Tom’s most recent cafeteria bill was 2-digit integer, was the tip calculated by Tom on this bill greater than 20 percent of the amount of the bill?

(1) The amount of the bill excluding tip was over $20
(2) The tip calculated by Tom was at least $4

(1) The amount of the bill excluding tip was over $20
(2) The tip calculated by Tom was at least $4

dabaobao · Answer

Similar to Q: https://gmatclub.com/forum/whenever-mar ... l#p2251680 Q: Actual Tip > 20% of Bill? Trick: Min/Max Method 1: Test Cases (Faster) 1) Consider to extremes in 20s Tip = 6 When bill is 21, 20% Tip = ~$4 => Yes When bill is 30, 20% Tip = ~$6 => Yes Sufficient 2) Consider to extremes in 20s Tip = 6 When bill is 21, 20% Tip = ~$4 => Yes When bill is 30, 20% Tip = ~$6 => Yes Sufficient ANSWER: D Solution 2: Slower List the Ranges: Bill Range: 11-19, 21-29, 31-39, ... Tip Range: 2 20% of the bill when: 1) bill > 20 2) tip > $3 Hence the Q is asking: Is bill > 20 or tip > 3? 1) bill > 20. Sufficient 2) Tip > 4. Sufficient Hence, answer = D.

ArupRS · Answer

chetan2u 
Not able to understand what the problem is asking. Could you please explain?

Regards,
Arup

chetan2u · Answer

Hi  ArupRS ,

Of course, the question is not written properly..
What it says is the bill is a 2-digit amount that is  $10\leq{bill}\leq{$99} . So, if the amount is a 2-digit number, we can write it as ab or 10a+b..
tip is 3a
So we are asked if tip 3a>20% of (10a+b)..... 3a>\frac{20}{100}(10a+b)...15a>10a+b......5a>b ...
Now max value of b can be 9, so if we know a is at least 2, 5a>b irrespective of the value of b.

Question becomes - Is 5a>b? . 
So, either we require to know the value of both a and b if a is 1, otherwise answer is always YES.

(1) The amount of the bill excluding tip was over $20
So, the tens digit or  a\geq{2} .
Suff

(2) The tip calculated by Tom was at least $4
so 3a>4..... a>\frac{4}{3} . Since a is an integer, a will be at least 2.
Again sufficient.

D

ArupRS · Answer

Nice explanation. Thank you so much .

Regards,
Arup Sarkar

MSIMBA · Answer

gAs given 1. tip is atleast 3 times than ten's digit 2. tip is 20 % of total bill?

1. min bill = 20, as per given items 
 3 * 2 = 6 min tip , 20 * 20 % = 4

Min tip > 20 % total bil

A sufficient

B. min tip is 4 
 if we take 19 ,than 1 * 3 = 3 , min bill < 4 
 take 20 ,than 2 * 3 = 6 min bill 6 (tip)
 & 2 0% of 20 = 4 , which is less than 6 (tip)

B sufficient

Both are sufficicent , D is answer

egmat · Answer

Understanding Tom's Tip Rule: 
If Tom's bill is a 2-digit number like $ 37 , the tens digit is  3 .
His tip = 3 × (tens digit) = 3 × 3 =  $9

What the question asks: 
Is this tip greater than  20%  of the bill?

Let's translate to algebra: 
Let the bill = $XY (where X = tens digit, Y = units digit)
- Bill amount =  10X + Y  dollars
- Tip =  3X  dollars
- 20% of bill = 0.20(10X + Y) =  2X + 0.2Y

The question becomes: Is 3X > 2X + 0.2Y? 
Simplifying: Is X > 0.2Y? →  Is 5X > Y?

Key Insight:   Since Y (units digit) can only be 0-9, if X ≥ 2, then 5X ≥ 10 > 9 ≥ Y. The answer will ALWAYS be YES!

Statement 1:  Bill > $20
This means X ≥ 2 (tens digit is at least 2).
If X ≥ 2 → 5X ≥ 10 → Since Y ≤ 9, we get 5X > Y.  Always YES. 
 SUFFICIENT

Statement 2:  Tip ≥ $4
Tip = 3X ≥ 4 → X ≥ 1.33 → X ≥ 2 (since X must be an integer)
Same logic: 5X ≥ 10 > Y.  Always YES. 
 SUFFICIENT

Answer: D

Each statement alone tells us the tens digit is at least 2, which guarantees the tip is always more than 20% of the bill.

Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc

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Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc

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