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

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Director
Joined: 24 Oct 2016
Posts: 533
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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Updated on: 30 Mar 2019, 12:02
2
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:57) correct 51% (02:36) wrong based on 68 sessions

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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.
Director
Joined: 24 Oct 2016
Posts: 533
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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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. _________________ If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything. Manager Joined: 23 Jan 2018 Posts: 221 Location: India WE: Information Technology (Computer Software) Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc [#permalink] ### Show Tags 15 Jun 2019, 05:43 chetan2u Not able to understand what the problem is asking. Could you please explain? Regards, Arup Math Expert Joined: 02 Aug 2009 Posts: 7981 Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc [#permalink] ### Show Tags 15 Jun 2019, 09:26 1 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 _________________ Manager Joined: 23 Jan 2018 Posts: 221 Location: India WE: Information Technology (Computer Software) Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc [#permalink] ### Show Tags 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
Manager
Joined: 04 Jun 2017
Posts: 109
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20
GPA: 3.82
Re: Whenever Tom pays an amount of 2-digit integer in a cafeteria, he calc  [#permalink]

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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
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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