Dear neeti1813,
I'm happy to help. Good practice with fractions. For basic rules of fractions, see:
http://magoosh.com/gmat/2012/fractions-on-the-gmat/

First, we will re-write the prompt question by adding 1/5 to both sides, and finding a common denominator so that we can add the fractions.
Is \(q > \frac{6}{7} + \frac{1}{5}\)?
Is \(q > \frac{30}{35} + \frac{7}{35}\)?
Is \(q > \frac{37}{35}\)?

This number is 2/35 larger than 1. Notice that 1/10 of 35 is 3.5, so 2 is less than 1/10 of 35, so this number, 37/35, is between 1 and 1.1. That gives us a ballpark sense of its size.

Statement #1: 1/6 of 9 is less than the value of q.
In other words,
\(q > \frac{9}{6}\)
\(q > \frac{3}{2}\)
Well, if q is bigger than 3/2 = 1.5, then it definitely is bigger than 37/35. This allows us to give a definitive "yes" to the prompt question. This statement, alone and by itself, is sufficient.

Statement #2: Two times the value of q is greater than 7/4
In other words,
\(2q > \frac{7}{4}\)
\(q > \frac{7}{8}\)
Well, hmmm. This does not help us, because this would allow q = 1, which is less than 37/35, or q = 100, which is greater than 37/35. Consistent with the information in this statement, we could pick a value of q that give us either a "yes" or "no" answer to the prompt. No definitive answer is possible, based on this statement. In other words, alone and by itself, this statement is insufficient.

Answer = (A)

Does all this make sense?
Mike
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yes definitely ...... thanks mike

Great explanation Mike.

I did it a bit differently which I think would be a bit faster than simplifying the fraction to get a decimal. Please let me know what you think.

Let's simplify the equation first. The question asks if \(q - \frac{1}{5} > \frac{6}{7}\)?

=> \(q > \frac{6}{7} + \frac{1}{5}\)

=> \(q > \frac{30}{35} + \frac{7}{35}\)

=> \(q > \frac{37}{35}\)

1) 1/6 of 9 is less than the value of q
So,
\(q > \frac{9}{6}\)

\(q > \frac{3}{2}\)

\(q > \frac{{3 * 17.5}}{{2 * 17.5}}\)

\(q > \frac{Something more than 51}{35}\)

So, \(q > \frac{37}{35}\) is true. ----> Sufficient

2) Two times the value of q is greater than 7/4
Which means,
\(2q > \frac{7}{4}\)

\(q > \frac{7}{8}\)

Now, we can try to equate the two fractions, but it'll be much faster to realize that \(\frac{7}{8} < 1\) and \(\frac{37}{35} > 1\).

So, \(q > \frac{37}{35}\) might or might not be true. ----> Insufficient

Hence the answer is A.
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