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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] New post 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

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Re: whenever martin has a restaurant bill [#permalink] New post 12 Feb 2011, 13:21
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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.

Answer: B.

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] New post 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] New post 31 May 2013, 04:43
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Re: whenever martin has a restaurant bill [#permalink] New post 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 :)
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Re: whenever martin has a restaurant bill [#permalink] New post 17 Oct 2013, 07:38
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.

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 :)


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] New post 18 May 2014, 09:59
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] New post 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.

Answer: B
Re: Whenever martin has a restaurant bill with an amount between   [#permalink] 04 Oct 2014, 23:37
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