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data sufficiency

by [email protected] » Thu Aug 30, 2012 9:34 am
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 bill was between $10 and $99, was the tip calculates by 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 martin was $8.
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by neelgandham » Thu Aug 30, 2012 9:53 am
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 bill was between $10 and $99, was the tip calculates by martin on this bill greater than 15 percent of the amount of the bill?

Since the amount on the bill is a two digit number, it can be represented in the form 10A + B. Then the amount of the tip = 2A.
Is 2A/(10A+B) > 15/100 ?
i.e. 200A > 150A + 15B ?
i.e. 50A > 15B ?
i.e 10A>3B ?

We can now rephrase the question to - If the amount on the bill is 10A + B and the tip is 2A, Is 10A > 3B ?
1 the amount of the bill was between $15 and $50.
If 10A + B = 16, then A = 1 and B = 6. 10*1 < 3*6 (10A < 3B)
If 10A + B = 31, then A = 2 and B = 1. 10*3 > 3*1 (10A > 3B)
Since we don't have a definite answer, statement I is insufficient to answer the question.
2 the tip calculated by martin was $8.
Tip = 2A = 8. So the value of A is 4
10A = 40 is always greater than 3B(3B = 0 if B = 0 and 3B = 27 if B = 9).
So, statement II is sufficient to answer the question

Answer B
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by vk_vinayak » Thu Aug 30, 2012 9:57 am
[email protected] 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 bill was between $10 and $99, was the tip calculates by 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 martin was $8.
Is tip > 15% of the bill

1. If amount is 15, Tip=2, 15% of the bill is 2.25. => Is tip > 15% of the bill? NO
If amount is 50, tip=10, 15% of the bill is 7.5. => Is tip > 15% of the bill? Yes. INSUF

2. If amount is 40, tip=8, 15% of the bill is 6. => Is tip > 15% of the bill? YES
If amount is 49, tip=8 15% of the bill is<7.5 => Is tip > 15% of the bill? YES. SUF

Ans is B.
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by adthedaddy » Thu Aug 30, 2012 10:17 am
Nice approach Vinayak :-)
"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs
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