What's the fastest way to answer this question?
Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?
A) $52
B) $117
C) $130
D) $180
E) $234
D
Waxing floors and getting paid
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TOTAL HOURS worked = 15 + 20 + 30 = 65 HOURSAbeNeedsAnswers wrote:What's the fastest way to answer this question?
Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?
A) $52
B) $117
C) $130
D) $180
E) $234
D
TOTAL PAID = $780
RATE of pay = $780/65 hours = $12/hour
Makoto worked for 15 hours.
So, Makoto's payment = (15 hours)($12/hour) = $180
AnswerL D
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Hi AbeNeedsAnswers,
There are a variety of different ways to go about solving this problem. The question specifically uses the word "proportionally", so you could take advantage of the builtin ratios and solve it that way. In addition, the answer choices are 'spaced out' enough that we can use some estimation and avoid some of the specific calculations that you might use in other approaches.
The three people worked a total of 15+20+30 = 65 hours and Makoto worked 15 of those hours. Thus, he/she worked....
15/65 = 3/13 of the total hours
We're told that the workers are paid proportionally based on the number of hours worked. 3/12 = 1/4, so 3/13 is a little less than 1/4.
1/4 of $780 = $195
So we're looking for an answer that's a little less than $195. There's only one answer that fits....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
There are a variety of different ways to go about solving this problem. The question specifically uses the word "proportionally", so you could take advantage of the builtin ratios and solve it that way. In addition, the answer choices are 'spaced out' enough that we can use some estimation and avoid some of the specific calculations that you might use in other approaches.
The three people worked a total of 15+20+30 = 65 hours and Makoto worked 15 of those hours. Thus, he/she worked....
15/65 = 3/13 of the total hours
We're told that the workers are paid proportionally based on the number of hours worked. 3/12 = 1/4, so 3/13 is a little less than 1/4.
1/4 of $780 = $195
So we're looking for an answer that's a little less than $195. There's only one answer that fits....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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 Jay@ManhattanReview
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This is a typical question on Ratio and Proportion.AbeNeedsAnswers wrote:What's the fastest way to answer this question?
Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?
A) $52
B) $117
C) $130
D) $180
E) $234
D
Since each was paid in proportion to the number of hours he or she worked, $780 should be distributed in the ratio of 15 : 20 : 30, where 15 represents the share of Makoto.
On a ratio scale the total payment = 15 + 20 + 30 = 65
Thus, the share of Makoto = (15/65)*780 = $180.
The correct answer: D
Hope this helps!
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Have to remark how surprised I was that this (splendidly) titled thread actually contained GMAT content.
Anyway, my approach: Makoto worked 15 of the 65 hours worked in all, so she'd be paid 15/65, or 3/13, of the total. 3/13 * $780 is $180, and we're done!
Anyway, my approach: Makoto worked 15 of the 65 hours worked in all, so she'd be paid 15/65, or 3/13, of the total. 3/13 * $780 is $180, and we're done!

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Another idea: by the Lazy Testwriter Principle, which I invoke endlessly on this forum (guess who's been a testwriter!), the amount that Makoto was paid should be divisible by 15, since a Lazy Testwriter would make her hourly wage an integer. Only D is so divisible, making it very likely the answer.
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We are given that Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. Since Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, we can create the following proportion:AbeNeedsAnswers wrote:What's the fastest way to answer this question?
Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?
A) $52
B) $117
C) $130
D) $180
E) $234
Makoto payment : Nishi payment : Ozuro payment = 15x : 20x : 30x
We can create the following equation to determine x:
15x + 20x + 30x = 780
65x = 780
x = 12
Since x = 12, Makoto was paid 15 x 12 = 180 dollars.
Alternate Solution:
Since we know that Makoto's payment was equivalent to 15x, we know that his payment must be a multiple of 15. Since 180 is the only multiple of 15, the correct answer must be 180.
Answer: D
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 estebanmorillo
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I followed an approach similar to Jay's in solving this question. But I did find it a little bit lengthy to calculate: "(15/65)*780 = $180" Since, after simplifying as (3/13)*780, I had to multiply 780*3=2,340 and then divide 2,340/13.
Is there any fast approach to calculate this number?
Thanks!
Is there any fast approach to calculate this number?
Thanks!
Jay@ManhattanReview wrote:This is a typical question on Ratio and Proportion.AbeNeedsAnswers wrote:What's the fastest way to answer this question?
Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?
A) $52
B) $117
C) $130
D) $180
E) $234
D
Since each was paid in proportion to the number of hours he or she worked, $780 should be distributed in the ratio of 15 : 20 : 30, where 15 represents the share of Makoto.
On a ratio scale the total payment = 15 + 20 + 30 = 65
Thus, the share of Makoto = (15/65)*780 = $180.
The correct answer: D
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
Jay
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