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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  [#permalink]

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New post Updated on: 30 Mar 2019, 12:02
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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

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Originally posted by dabaobao on 30 Mar 2019, 11:50.
Last edited by dabaobao on 30 Mar 2019, 12:02, edited 1 time in total.
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Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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New post 30 Mar 2019, 12:00
dabaobao wrote:
Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calculates the dollar amount of the tip as 3imes 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



Similar to Q: https://gmatclub.com/forum/whenever-mar ... l#p2251680

Solution:



Trick: Min/Max



List the Ranges:
Bill Range: 11-19, 21-29, 31-39, ...
Tip Range: 2<x<4, 4<x<6, ...
Actual Tip: 3, 6, 9, ...

Simplify the Q



Notice, tip > 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.

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Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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New post 15 Jun 2019, 05:43
chetan2u
Not able to understand what the problem is asking. Could you please explain?

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Arup
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Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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New post 15 Jun 2019, 09:26
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dabaobao wrote:
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



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.

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Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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New post 15 Jun 2019, 10:47
chetan2u wrote:
dabaobao wrote:
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



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


Nice explanation. Thank you so much .

Regards,
Arup Sarkar
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Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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New post 15 Jun 2019, 20:25
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
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Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc   [#permalink] 15 Jun 2019, 20:25
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