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

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12 Feb 2011, 13:48

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70% (02:28) correct
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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

Re: whenever martin has a restaurant bill [#permalink]

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12 Feb 2011, 14:21

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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

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.

Re: whenever martin has a restaurant bill [#permalink]

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17 Oct 2013, 07:01

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.

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?

Re: whenever martin has a restaurant bill [#permalink]

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17 Oct 2013, 08:38

Expert's post

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.

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). _________________

(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.

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

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14 Feb 2016, 11:48

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