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DS - Arithmetic

by rabbulnawaz » Thu May 12, 2011 10:17 am
A certain customer at a restaurant calculates his tip by adding a constant dollar amount to another sum that is directly proportional to the total bill for the meal. If his total bill for the meal was $24.00, what will the be the dollar amount of his tip?
(1) If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
(2) If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.

Can someone help me on this problem. I am not able to convert word->math on this question.
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by djiddish98 » Thu May 12, 2011 10:48 am
They try to trip you up with the language "another sum that is directly proportional to the total bill for the meal".

The way I interpret this is they mean a fixed %. It's a lot of words that are there just to confuse.

X = constant dollar
(y/100) = fixed percent

So your equation is X + (y/100)*bill = tip.

The introduction gives us the bill, $24.

So X + (y/100)*24 = tip <- our answer

Statement 1 tells us that X + (y/100)*28 = 4.80 - can only solve for x or y in terms of the other variable.

Statement 2 tells us that X + (y/100)*18 = 3.80 - can only solve for x or y in terms of the other variable.

When we take them together, we see that the tip is 1 dollar less when the bill is 10 dollars less. Therefore (y/100) = .1 or 10%.

You can subtract the two equations if you'd like. X's cancel. Factor out (y/100) so you get

(y/100)(28-18) = (4.80-3.80)

(y/100)(10) = 1

10y/100 = 1 -> 1y/10 = 1 -> y = 10

Now that we have Y we can solve for X. take either equation, plug in 10 and you see that X is $2.

for example X + (10/100)(18) -> x + 1.8 = 3.8

With this information, we can easily solve for $24 - you don't have to, but it's 2 + (10/100)(24) or $4.4
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by GMATGuruNY » Thu May 12, 2011 11:17 am
rabbulnawaz wrote:A certain customer at a restaurant calculates his tip by adding a constant dollar amount to another sum that is directly proportional to the total bill for the meal. If his total bill for the meal was $24.00, what will the be the dollar amount of his tip?
(1) If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
(2) If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.

Can someone help me on this problem. I am not able to convert word->math on this question.
Let y = tip.
Let m = fraction of the total bill that is included in the tip.
Let x = total bill.
Let b = constant that is added.

Thus, y = mx + b.

The expression above represents the equation of a line.

Question rephrased: Given the equation y=mx+b, what is the value of y when x=24?

Statement 1: If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
When x = 24+4 = 28, y = 4.80.
Gives us only one point on the line: (28,4.8)
Insufficient.

Statement 2: If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.
When x = 24-6 = 18, y = 3.8.
Gives us only one point on the line: (18,3.8).
Insufficient.

Statements 1 and 2 combined:
Given the two points (28,4.8) and (18,3.8), we can determine the equation of the line, enabling us to calculate the value of y when x=24.
Sufficient.

The correct answer is C.

Geeky side note:
The slope of the line is (4.8-3.8)/(28-18) = 1/10.
The slope indicates that for every $10 increase in the bill (the change in x), there will be a $1 increase in the tip (the change in y).
Last edited by GMATGuruNY on Thu May 12, 2011 1:13 pm, edited 1 time in total.
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by rabbulnawaz » Thu May 12, 2011 11:40 am
GMATGuruNY wrote:
rabbulnawaz wrote:A certain customer at a restaurant calculates his tip by adding a constant dollar amount to another sum that is directly proportional to the total bill for the meal. If his total bill for the meal was $24.00, what will the be the dollar amount of his tip?
(1) If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
(2) If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.

Can someone help me on this problem. I am not able to convert word->math on this question.
Let y = tip.
Let m = factor by which the total bill is multiplied.
Let x = total bill.
Let b = constant that is added.

Thus, y = mx + b.

The expression above represents the equation of a line.

Question rephrased: Given the equation y=mx+b, what is the value of y when x=24?

Statement 1: If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
When x = 24+4 = 28, y = 4.80.
Gives us only one point on the line: (28,4.8)
Insufficient.

Statement 2: If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.
When x = 24-6 = 18, y = 3.8.
Gives us only one point on the line: (18,3.8).
Insufficient.

Statements 1 and 2 combined:
Given the two points (28,4.8) and (18,3.8), we can determine the equation of the line, enabling us to calculate the value of y when x=24.
Sufficient.

The correct answer is C.

Geeky side note:
The slope of the line is (4.8-3.8)/(28-18) = 1/10.
The slope indicates that for every $10 increase in the bill (the change in x), there will be a $1 increase in the tip (the change in y).

Thanks. Now this question makes some sense. Now, I have broken this question this way:
C - Constant dollar amount added.
T - Tip
Sum directly proportional to the total bill means KP = B [ Where B - Bill; K- Proportional constant ]

then C + KP = T
Till this point I have understood. Now, as per statement-I, if the total bill is 28 then cant we write KP= 28 => C + 28 = 4.80 ?
I am substituting KP = 28 because, B=KP and total-bill now is 28.

Does this make sense.
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by GMATGuruNY » Thu May 12, 2011 11:58 am
rabbulnawaz wrote:
GMATGuruNY wrote:
rabbulnawaz wrote:A certain customer at a restaurant calculates his tip by adding a constant dollar amount to another sum that is directly proportional to the total bill for the meal. If his total bill for the meal was $24.00, what will the be the dollar amount of his tip?
(1) If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
(2) If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.

Can someone help me on this problem. I am not able to convert word->math on this question.
Let y = tip.
Let m = factor by which the total bill is multiplied.
Let x = total bill.
Let b = constant that is added.

Thus, y = mx + b.

The expression above represents the equation of a line.

Question rephrased: Given the equation y=mx+b, what is the value of y when x=24?

Statement 1: If the total bill for his meal had been four dollars greater, the customer would've calculated a tip of $4.80.
When x = 24+4 = 28, y = 4.80.
Gives us only one point on the line: (28,4.8)
Insufficient.

Statement 2: If the total bill for his meal had been six dollars less, the customer would've calculated a tip of $3.80.
When x = 24-6 = 18, y = 3.8.
Gives us only one point on the line: (18,3.8).
Insufficient.

Statements 1 and 2 combined:
Given the two points (28,4.8) and (18,3.8), we can determine the equation of the line, enabling us to calculate the value of y when x=24.
Sufficient.

The correct answer is C.

Geeky side note:
The slope of the line is (4.8-3.8)/(28-18) = 1/10.
The slope indicates that for every $10 increase in the bill (the change in x), there will be a $1 increase in the tip (the change in y).

Thanks. Now this question makes some sense. Now, I have broken this question this way:
C - Constant dollar amount added.
T - Tip
Sum directly proportional to the total bill means KP = B [ Where B - Bill; K- Proportional constant ]

then C + KP = T
Till this point I have understood. Now, as per statement-I, if the total bill is 28 then cant we write KP= 28 => C + 28 = 4.80 ?
I am substituting KP = 28 because, B=KP and total-bill now is 28.

Does this make sense.
The sum that is directly proportional to the total bill is the fraction of the total bill that is included in the tip.
Thus, you should represent this sum as KB, where K is the fraction of the total bill that is included in the tip.
Thus, your equation should be C + KB = T.
Since T=4.8 when B=28, the equation becomes C + K*28 = 4.8.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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