Percenatges

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Fri Nov 14, 2008 4:42 pm

Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin's recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% of the amount of the bill?

1) The amount of the bill was between $15 and $50.
2) The tip calculated by Martin was $8.

The answer is B..

Any one has better approach than the OG.

Abdulla

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 14, 2008 4:42 pm

logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Percenatges

by logitech » Fri Nov 14, 2008 5:08 pm

Abdulla wrote:Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin's recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% of the amount of the bill?

1) The amount of the bill was between $15 and $50.
2) The tip calculated by Martin was $8.

The answer is B..

Any one has better approach than the OG.

Let me try to beat OG

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 :!:

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

Hence, B

Did I confuse you more than OG did ?

LGTCH
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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Fri Nov 14, 2008 5:53 pm

YES

but .> it seems better but the problem is ME..

Abdulla

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JGaynor: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Mar 27, 2010 9:00 am

by JGaynor » Fri Apr 09, 2010 4:35 pm

anyone else have an explanation for this problem?

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ymach3: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon Jul 13, 2009 4:25 pm; Thanked: 1 times

by ymach3 » Fri Apr 09, 2010 11:41 pm

I tried picking up numbers...

Tip=2*(tenths digit of the Bill)

Bill Range is between 10 and 99 $

Possible tips = 2-18.

(i) says the bill is between 15-50.

Possible Tip values would be 2-10.

Consider a case where Bill -15 and Tip =2*1=2

Percentage=2/15 * 100=12 %(approx'ly)-----> NO-Not greater than 15%.

Another case when bill=40, which makes the tip amount=8

Percentage = 8/40 * 100=20 % --------> YES-Greater than 15%.

Hence, Insufficient.

Case (ii)

Tip=8 provides us sufficient information to say that the bill amount would fall in between 40 and 49.

consider bill ammount = 48, Percentage=8/48*100=33% (Apporox'ly) - YES ,greater than 15%.

Hence SUFFICIENT.

Forum browsers, Correct me if i am wrong.

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meghash3: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Mar 24, 2010 4:51 am; Thanked: 1 times

by meghash3 » Sat Apr 10, 2010 2:56 am

since the bill amt > 10 $, and tip is 8$, it is certainly less than 10 % , thsu B can answer the qeus alone, A does not

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Sat Apr 10, 2010 6:50 am

Abdulla wrote:Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin's recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% of the amount of the bill?

1) The amount of the bill was between $15 and $50.
2) The tip calculated by Martin was $8.

The answer is B..

Any one has better approach than the OG.

TO ANSWER THE Q we either need the exact bill amt or tip value
1. no sufficient information
2. tip is 8
so the bill amt has to be between $40-$49

lets take the lowest number $40. a tip of $8 is 20% of the original bill amt of $40 - eq1
lets take the highest number $49. a tip of $8 is 16% of the original bill amt of $49 -eq2

both eq1 and eq2 implies that a tip of $8 is greater than 15% when the bill amt is between $40-$49

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Sat Apr 10, 2010 2:56 pm

Abdulla wrote:Whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. If the amount of Martin's recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill grater than 15% of the amount of the bill?

1) The amount of the bill was between $15 and $50.
2) The tip calculated by Martin was $8.

The answer is B..

Any one has better approach than the OG.

Logitech's algebraic solution is lovely and should be noted, as its approach can be applied to other questions.

Notice that Martin gives 20% of the tens digit and 0% of the units digit. Thus, percentage-wise, the lower the tens digit and the higher the units digit, the lower the tip. $19 produces a tip of just over 10% , whereas any bill that is multiple of $10 produces a tip of 20%.

(1) is thus insufficient
(2) the bill is in the 40-49 dollar range, so the stingiest tip would result from a $49 bill, but 8/49 > 8/50 = 16% SUFF

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

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singalong: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Wed Feb 09, 2011 6:42 amFollowed by: 1 member; Thanked: 1 times

by singalong » Wed Aug 17, 2011 7:27 am

I understood till the expression Is 2x/(10x+Y) > 15/100 ?

Could someone explain me the next part please?

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dj_vinayak: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon Jan 25, 2010 9:46 am; Thanked: 1 times; GMAT Score:720

by dj_vinayak » Fri Jul 27, 2012 8:36 am

To me the two hints given contradict.

The bill cannot be both between 15 & 30 $ as given in A, and also be between 40 and 49& as inferred from b.

Stay Hungry Stay Foolish

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