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shameekv1989
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21 Apr 2020, 17:47
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C
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If x and y are integers, what is the maximum value of x +2y?
(1) \(x^2 < 25\)
(2) \(\frac{x}{y} = \frac{4}{5}\)
(1) \(x^2 < 25\)
(2) \(\frac{x}{y} = \frac{4}{5}\)
ArunSharma12
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21 Apr 2020, 21:58
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shameekv1989
statement 1:
-5<x<5
not sufficient
statement 2:
x = 4a, y = 5a
x + 2y = 14a
not sufficient
combining both statements,
- 4a = -4, a =-1, x + 2y = -14
4a =0, a =0, x + 2y = 0
4a = 4, a =1, x + 2y = 14
Ans: C
21 Apr 2020, 23:31
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From the question data, x and y are integers. Therefore, x+2y will also be an integer.
To maximise the value of x+2y, we will have to maximise the values of x and y.
From statement I alone, \(x^2\) < 25. This tells us that -5<x<5. But, we do not have any information about y and hence statement I alone is insufficient to find the maximum value of x+2y.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone,\( \frac{x}{y} \)= \(\frac{4}{5}\). This means that x and y are in the ratio of 4:5.
Since a ratio does not represent the actual values, x and y can take any set of values which are in the ratio of 4:5. Therefore, it is not possible to find the maximum value of x+2y.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement II, we know that x should be a multiple of 4 and y should be a multiple of 5.
From statement I, we know that -5<x<5.
Therefore, the maximum value for x HAS to be 4. If x =4, y =5. This is sufficient to find the maximum value of x+2y.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
To maximise the value of x+2y, we will have to maximise the values of x and y.
From statement I alone, \(x^2\) < 25. This tells us that -5<x<5. But, we do not have any information about y and hence statement I alone is insufficient to find the maximum value of x+2y.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone,\( \frac{x}{y} \)= \(\frac{4}{5}\). This means that x and y are in the ratio of 4:5.
Since a ratio does not represent the actual values, x and y can take any set of values which are in the ratio of 4:5. Therefore, it is not possible to find the maximum value of x+2y.
Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement II, we know that x should be a multiple of 4 and y should be a multiple of 5.
From statement I, we know that -5<x<5.
Therefore, the maximum value for x HAS to be 4. If x =4, y =5. This is sufficient to find the maximum value of x+2y.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.
The correct answer option is C.
Hope that helps!
