Whenever martin has a restaurant bill with an amount between : GMAT Data Sufficiency (DS)
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# Whenever martin has a restaurant bill with an amount between

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

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12 Feb 2011, 12:48
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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 [Reveal] Spoiler: 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 [Reveal] Spoiler: OA _________________ The proof of understanding is the ability to explain it. Math Expert Joined: 02 Sep 2009 Posts: 36618 Followers: 7099 Kudos [?]: 93539 [8] , given: 10578 Re: whenever martin has a restaurant bill [#permalink] ### Show Tags 12 Feb 2011, 13:21 8 This post received KUDOS Expert's post 5 This post was BOOKMARKED 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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Re: whenever martin has a restaurant bill [#permalink]

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12 Feb 2011, 14:14
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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31 May 2013, 04:43
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Re: whenever martin has a restaurant bill [#permalink]

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17 Oct 2013, 06:01
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. 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 Joined: 02 Sep 2009 Posts: 36618 Followers: 7099 Kudos [?]: 93539 [0], given: 10578 Re: whenever martin has a restaurant bill [#permalink] ### Show Tags 17 Oct 2013, 07:38 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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18 May 2014, 09:59
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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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04 Oct 2014, 23:37
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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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14 Feb 2016, 10:48
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Re: Whenever martin has a restaurant bill with an amount between   [#permalink] 14 Feb 2016, 10:48
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