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mlane25269
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I am getting 132 since 5/132 is greater than 3/80.
132 x 3 = 396 and 5 x 80 = 400.
GMATprep PS question
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Source: Beat The GMAT — Problem Solving |
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AleksandrM
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szapiszapo
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I believe it's 133
the minimum ratio of 3/80 means that you can have 3 assistants for 80 students max, i.e. 1 assistant for 80/3 students max.
For 5 assistants, you can therefore have at maximum 5*80/3 = 133,33 students, hence 133 seems the appropriate answer
the minimum ratio of 3/80 means that you can have 3 assistants for 80 students max, i.e. 1 assistant for 80/3 students max.
For 5 assistants, you can therefore have at maximum 5*80/3 = 133,33 students, hence 133 seems the appropriate answer
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AleksandrM
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You end up with equal ratios with 133 in the denominator. If the ratio has to be greater than 3/80, then 5 has to be divided by a smaller number, 132.
The answer is 133:
Setting up a proportion works well for this question.
3/80 = 5/x
3X = 400
X = 133.333...
Since there cannot be .33.... of a student in a class, the maximum number of students with 5 TA's is 133.
Setting up a proportion works well for this question.
3/80 = 5/x
3X = 400
X = 133.333...
Since there cannot be .33.... of a student in a class, the maximum number of students with 5 TA's is 133.
Correct, (3/80) has to be less than (5/X)
And 133 maximizes the number of students while keeping the relationship between the two ratios true. Compare the value of the two fractions by cross-multiplying:
(3/80)(5/133) gives the value of the first fraction as 399 and the value of the second fraction as 400. Thus, (5/133) > (3/80). Also notice that when comparing the fractions they're only one number apart, illustrating that if the number of students in the class is 134 the relationship between the ratios would not hold true and if the number of students in the class is 132 there is still room for more students to be in the class while keeping the relationship between the ratios true.
(3/80)(5/132) gives the value of the first fraction as 396 and the value of the second fraction as 400. 396 is less than 399, thus, 132 does not maximize the number of students.
Also, I came across this problem recently while taking a gmatprep test. The OA is 133.
And 133 maximizes the number of students while keeping the relationship between the two ratios true. Compare the value of the two fractions by cross-multiplying:
(3/80)(5/133) gives the value of the first fraction as 399 and the value of the second fraction as 400. Thus, (5/133) > (3/80). Also notice that when comparing the fractions they're only one number apart, illustrating that if the number of students in the class is 134 the relationship between the ratios would not hold true and if the number of students in the class is 132 there is still room for more students to be in the class while keeping the relationship between the ratios true.
(3/80)(5/132) gives the value of the first fraction as 396 and the value of the second fraction as 400. 396 is less than 399, thus, 132 does not maximize the number of students.
Also, I came across this problem recently while taking a gmatprep test. The OA is 133.
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mlane25269
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beeparoo
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WHAT! You solved it the same as I did but what would make you think that the answer is 132? It's clear to me that the max number of students can be 133, while still satisfying the condition that S remain less than 133.33.sibbineni wrote:S<133.33
So the answer should be 132 as it is asked maximum
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AleksandrM
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beeparoo,
The question is asking you to have a ratio that is GREATER than 3/80. If you set up the information as 5/x > 3/80, the 133 you get in the denominator makes > not true, because the two are actually equal. HOWEVER, you then know that the maximum number of students that you can have and still hold the > as true, will be 132 students, as it makes the entire ratio 5/132 greater than 3/80.
Remember for a ratio to go up in value either the denominator has to DECREASE or the numerator has to INCREASE.
This question can be rephrased as: what is the biggest possible denominator for x that will hold true for 5/x > 3/80.
The question is asking you to have a ratio that is GREATER than 3/80. If you set up the information as 5/x > 3/80, the 133 you get in the denominator makes > not true, because the two are actually equal. HOWEVER, you then know that the maximum number of students that you can have and still hold the > as true, will be 132 students, as it makes the entire ratio 5/132 greater than 3/80.
Remember for a ratio to go up in value either the denominator has to DECREASE or the numerator has to INCREASE.
This question can be rephrased as: what is the biggest possible denominator for x that will hold true for 5/x > 3/80.
5/133 does not equal 3/80
Use the bow-tie method to compare the value of the two fractions
5/133(3/80) => the value of 5/133 is 400 and the value of 3/80 is 399.
The question states that the ratio must be greater than 3/80. Thus, 133 is the largest possible number you can plug in that will hold true to the relationship.
Compare the value of 5/132 to that of 3/80...
5/132(3/80) => the value of 5/132 is 400 and the value of 3/80 is 396.
Thus, 132 still holds true for the relationship, but it does not maximize the number of students while still keeping the relationship true.
Answer is 133
Use the bow-tie method to compare the value of the two fractions
5/133(3/80) => the value of 5/133 is 400 and the value of 3/80 is 399.
The question states that the ratio must be greater than 3/80. Thus, 133 is the largest possible number you can plug in that will hold true to the relationship.
Compare the value of 5/132 to that of 3/80...
5/132(3/80) => the value of 5/132 is 400 and the value of 3/80 is 396.
Thus, 132 still holds true for the relationship, but it does not maximize the number of students while still keeping the relationship true.
Answer is 133
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AleksandrM
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Okay, I am getting a bit tired of this. Does anyone have the actual answer provided in GMATPrep???
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Ian Stewart
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The answer is certainly 133. From the posts above, I have the impression that you think, with 133 students, that the ratio of teachers to students would be exactly equal to 3/80. It's not. Try calculating the two ratios (5/133, 3/80) on a calculator if you need to confirm.
