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What is the value of 2a/(a+1)+2b/(b+1)?

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by Max@Math Revolution » Sun Sep 08, 2019 10:38 pm

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[GMAT math practice question]

What is the value of 2a/(a+1)+2b/(b+1)?

1) a, b are integers
2) ab=1
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Sep 10, 2019 11:37 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since 2a/(a+1) + 2b(b+1) = (2a*(b+1) + 2b(a+1))/(a+1)(b+1) = (2ab + 2a + 2ab + 2b) / (ab+a+b+1) = (4ab + 2a + 2b) / (ab+a+b+1), the question asks the value of (4ab + 2a + 2b) / (ab+a+b+1).

Condition 1) is obviously not sufficient as it tells us nothing about the values of a and b.

Condition 2):
If ab = 1, then (4ab + 2a + 2b) / (ab+a+b+1) = (2a+2b+4) / (a+b+2) = 2(a+b+2)/(a+b+2) = 2. Condition 2) is sufficient.

Therefore, the answer is B.
Answer: B
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by deloitte247 » Thu Sep 12, 2019 4:51 am
$$We\ want\ to\ find\ the\ value\ of\ \frac{2a}{\left(a+1\right)}+\frac{2b}{\left(b+1\right)}$$
Statement 1: a, b are integers.
'a' and 'b' can be any positive integer, thus, this will result in varying answers.
If a=2 and b=3
$$=\frac{2\cdot2}{\left(2+1\right)}+\frac{2\cdot3}{\left(3+1\right)}=\frac{34}{12}=\frac{17}{6}$$
If a=4 and b=5
$$=\frac{2\cdot4}{\left(4+1\right)}+\frac{2\cdot5}{\left(5+1\right)}=\frac{98}{30}=\frac{49}{15}$$
Therefore, statement 1 is NOT SUFFICIENT.

Statement 2: ab=1
The product of two numbers that can equal to 1 is 1 and 1.
So, a=1 and b=1;
$$Therefore=\frac{2\cdot1}{\left(1+1\right)}+\frac{2\cdot1}{\left(1+1\right)}=1+1=2$$
Hence, statement 2 is sufficient.

Only statement 2 is sufficient, therefore, option B is the correct answer.

Thanks
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