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.
DS - Arithmetic
This topic has expert replies
- rabbulnawaz
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Fri Aug 20, 2010 2:52 pm
-
- Senior | Next Rank: 100 Posts
- Posts: 57
- Joined: Fri Jan 14, 2011 10:01 am
- Thanked: 10 times
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
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
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let y = tip.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 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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
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.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
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.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- rabbulnawaz
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Fri Aug 20, 2010 2:52 pm
GMATGuruNY wrote:Let y = tip.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 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.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The sum that is directly proportional to the total bill is the fraction of the total bill that is included in the tip.rabbulnawaz wrote:GMATGuruNY wrote:Let y = tip.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 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.
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
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.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
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.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3