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Manager  Joined: 10 Nov 2010
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Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21 WE: Information Technology (Computer Software)
Whenever martin has a restaurant bill with an amount between  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:24) correct 33% (02:23) wrong based on 956 sessions

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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 _________________ The proof of understanding is the ability to explain it. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 59147 Re: Whenever martin has a restaurant bill with an amount between [#permalink] ### Show Tags 13 7 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

C is not correct.

You can solve this question algebraically but I think simple analysis would be better.

(1) The amount of the bill was between $15 and$50 --> 15<bill<50. Now if the bill was 20$then the tip would be 2*2=$4 (2 times tens digit) so more than 0.15*20=$3 (15% of the bill) but if the bill was 29$ then the tip would still be 2*2=$4 but in this case less than 0.15*29=~$4.5. Not sufficient.

(2) The tip calculated by the martin was $8 --> Tip=$8 means that: 40<=bill<50 (so that the tens digit of the bill to be 4). Now, even if the bill was exactly $50 (uppert limit), 15% of it would be 0.15*50=$7.5 and it's still less than $8. So the answer to the question is YES: the tip (8$) was greater than 15% of the bill. Sufficient.

Similar question: sally-s-bill-greater-than-25-of-the-amount-108351.html
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Manager  Joined: 05 Jul 2010
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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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1
yes, it has to be B. since the 15% of 50 is 7.5, and if the tip is 8, then the tip value between 40 to 50 will always be more than 7.5

where as for 1 the value can be less than 15% to more than 15%, depending if the amount is for example between 15 to 19, vs between 25 to 29
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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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Bunuel wrote:
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 C is not correct. You can solve this question algebraically but I think simple analysis would be better. (1) The amount of the bill was between$15 and $50 --> 15<bill<50. Now if the bill was 20$ then the tip would be 2*2=$4 (2 times tens digit) so more than 0.15*20=$3 (15% of the bill) but if the bill was 29$then the tip would still be 2*2=$4 but in this case less than 0.15*29=~$4.5. Not sufficient. (2) The tip calculated by the martin was$8 --> Tip=$8 means that: 40<=bill<50 (so that the tens digit of the bill to be 4). Now, even if the bill was exactly$50 (uppert limit), 15% of it would be 0.15*50=$7.5 and it's still less than$8. So the answer to the question is YES: the tip (8$) was greater than 15% of the bill. Sufficient. Answer: B. Similar question: sally-s-bill-greater-than-25-of-the-amount-108351.html Hi Bunuel, for this question. In the first statement, how do you know what amount for the bill to choose in order to increase your odds of having a yes/no answer. Do you tipically look for a lower/middle or upper range? Thanks Cheers J Math Expert V Joined: 02 Sep 2009 Posts: 59147 Re: Whenever martin has a restaurant bill with an amount between [#permalink] ### Show Tags jlgdr wrote: Bunuel wrote: 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

C is not correct.

You can solve this question algebraically but I think simple analysis would be better.

(1) The amount of the bill was between $15 and$50 --> 15<bill<50. Now if the bill was 20$then the tip would be 2*2=$4 (2 times tens digit) so more than 0.15*20=$3 (15% of the bill) but if the bill was 29$ then the tip would still be 2*2=$4 but in this case less than 0.15*29=~$4.5. Not sufficient.

(2) The tip calculated by the martin was $8 --> Tip=$8 means that: 40<=bill<50 (so that the tens digit of the bill to be 4). Now, even if the bill was exactly $50 (uppert limit), 15% of it would be 0.15*50=$7.5 and it's still less than $8. So the answer to the question is YES: the tip (8$) was greater than 15% of the bill. Sufficient.

Similar question: sally-s-bill-greater-than-25-of-the-amount-108351.html

Hi Bunuel, for this question. In the first statement, how do you know what amount for the bill to choose in order to increase your odds of having a yes/no answer. Do you tipically look for a lower/middle or upper range?

Thanks
Cheers
J Well, it depends on the question but to test extreme values might be a good thing to do.

For this question, as the tip is tied to the tens digit of the bill, then I chose two extreme amounts which have the same tens digit so generate the same tip (20 and 29).
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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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1
1
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 Exclamation

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

Hence, B
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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Given:

Let A = amount of the bill, in which 10 < A < 99
Let T = tip
Let t(A) = tens digit of the amount, -> T = 2*t(A)

Question:

T > 15%(A)?
2*t(A) > 15%(A)?
2*t(A) > $$\frac{3}{20}$$*A?
$$\frac{40}{3}$$ > $$\frac{A}{t(A)}$$?

(1) 15 < A < 30
If A = 20, t(A) = 2
$$\frac{40}{3}$$ > $$\frac{20}{2}$$? Yes
If A = 29, t(A) = 2
$$\frac{40}{3}$$ > $$\frac{29}{2}$$? No
Hence, insufficient.

(2) T = 8
8 = 2*t(A) --> 4=t*(A)
--> Possible values for T: 41, 42,...,49

If A = 49, t(A) = 4
$$\frac{40}{3}$$ > $$\frac{49}{4}$$? Yes
If A = 40, t(A) = 4
$$\frac{40}{3}$$ > $$\frac{40}{4}$$? Yes
Hence, sufficient.

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Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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Hi Bunuel,

Actually for GMAT DS problems, statements never contradict each other. However this question,
Statement 1 -> total paid amount is between 15 and 30
Statement 2 -> total paid amount is between 40 and 49 inclusive.

So each statement gives diff bill paid amount, contradicting each other. can this be so?
Math Expert V
Joined: 02 Sep 2009
Posts: 59147
Whenever martin has a restaurant bill with an amount between  [#permalink]

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hellosanthosh2k2 wrote:
Hi Bunuel,

Actually for GMAT DS problems, statements never contradict each other. However this question,
Statement 1 -> total paid amount is between 15 and 30
Statement 2 -> total paid amount is between 40 and 49 inclusive.

So each statement gives diff bill paid amount, contradicting each other. can this be so?

From (1): 15 < bill < 50.
From (2): 40 <= bill < 50.
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GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: Whenever martin has a restaurant bill with an amount between  [#permalink]

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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#p2251666 Solution: Trick: Min/Max 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

Is bill > 30 or tip > 4?

1) 15 < bill < 50. Not sufficient since b > 30.
2) Tip = 8. Sufficient since tip > 4

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