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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] Whenever martin has a restaurant bill with an amount between   12 Feb 2011, 13:48
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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

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

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 with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   18 May 2014, 10:59
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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] Whenever martin has a restaurant bill with an amount between   12 Feb 2011, 15:14
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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] Whenever martin has a restaurant bill with an amount between   31 May 2013, 05:43
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   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.

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 with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   17 Oct 2013, 08:38
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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] Whenever martin has a restaurant bill with an amount between   05 Oct 2014, 00:37
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
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   14 Sep 2017, 21:31
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?
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Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   14 Sep 2017, 21:39
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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?


The statement do not contradict.
From (1): 15 < bill < 50.
From (2): 40 <= bill < 50.
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Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   Updated on: 31 Mar 2020, 04:53
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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

Show 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



Similar to Q: https://gmatclub.com/forum/whenever-tom ... l#p2251666


Q: Actual Tip > 15% of Bill?

Trick: Min/Max



Method 1: Test Cases (Faster)



Similar to Bunuel's solution: https://gmatclub.com/forum/whenever-mar ... ml#p870598


1) Consider to extremes in 20s
Tip = 4
When bill is 21, 15% Tip = ~$3 => Yes
When bill is 30, 15% Tip = ~$4.5 => No
Not sufficient

2) Consider to extremes in 40s
Tip = 8
When bill is 40, 15% Tip = ~$6 => Yes
When bill is 50, 15% Tip = ~$7.5 => Yes
Sufficient

Method 2: Slower



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

Hence the Q is asking:

Is bill > 30 or tip > 4?

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


Hence, answer = B.

Originally posted by dabaobao on 30 Mar 2019, 12:15.
Last edited by dabaobao on 31 Mar 2020, 04:53, edited 3 times in total.
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   30 Nov 2019, 03:59
I think there is something wrong with your solution. Compare 29 and 20. Both of them have tens less than 3 but one of them is correct and one is not. So we do not necessarily need a number with tens greater than 2 to satisfy the condition in the question.
gmatkum wrote:
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] Whenever martin has a restaurant bill with an amount between   30 Nov 2019, 04:06
Your answer is not correct because 20 is less than 30 and its tip is 4 but satisfies the condition in the question.
dabaobao 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

Show 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




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

Hence the Q is asking:

Is bill > 30 or tip > 4?

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


Hence, answer = B.
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   24 Dec 2019, 13:13
1) 15 to 50
152(1)= 2
2/15*100 =12.6%
50 2(5)=10
10/50*100=20% NS
2)
For 8 tip 2x= 8
X=4
Total amount from 40 to 49
8/40*100 =20%8/49*100 16%
So B
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   09 Mar 2020, 10:58
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Have tried a different approach. Please let me know if the thought process is sound.

Let tens digit of bill be 'a' and units digit be 'b'. Therefore, the bill is 'ab' (or 10a+b).
tip is 2 times the tens digit or in other other words - 2a

question: is 2a>15%(10a+b)
this can be broken down as:
is 2a>3/20(10a+b)
is 40a>30a+3b
is 10a>3b where 'a' is tens digit of the bill and 'b' is units digit

St 1: the amount of bill is between $15 and $30.
if the bill is $15, then 10*1 is not greater than 3*5
if the bill is $30, then 10*3 is greater than 3*0

St 1 is not sufficient

St 2: the tip is $8.
therefore, the tens digit is 4.
now irrespective of any amount between $40 to $49
10a will always be greater than 3b.

St 2 is sufficient. Answer is B
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   09 Feb 2021, 12:18
Similar Question: https://gmatclub.com/forum/whenever-hat ... 48458.html
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   02 Jul 2021, 03:13
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Since when are small birds allowed to eat in restaurants?
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Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   03 Jul 2021, 06:34
Here is my approach:

Given information: bill value X=bc=10b+c, 10<X<99 or 10<bc<99, tip t=2b
Question: t>15%X or t>15%*(10b+c) ?


Statement 1: 15<X<50 => 15<bc<50 => t must be in this range: 2.25<t<7.5
+ If X=16 => b=1 => t=2 which is not in the range.
+ If X=49 => b=4 => t=8 which is not in the range.
=> Insufficient.

Statement 2: tip t=8=2b => b=4 or X can be from 40 to 49.
+ If X=40 => 15% of X is 6 which is less than t=8
+ If X=50 (for the sake of calculation) => 15% of X is 7.5 which is less than t=8

2 answers are No, so B is Sufficient.
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Re: Whenever martin has a restaurant bill with an amount between [#permalink] Whenever martin has a restaurant bill with an amount between   30 Nov 2021, 07:48
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