and 1/2 sold tuna melt sandwich then 1/2 sold veggie melt so 150 sandwich sold tuna and 150 sandwich sold veggie. By this statement we can find the Veggie melt/Female i.e. 150/200.

It seems that you have misunderstood the question here. It's not asking for the ratio of veggie melts to females. It's asking for the fraction of veggie melts that were bought by females. Meaning - out of those 150 veggie melts, what proportion was bought by females?

The easiest way to approach this problem is by setting up an Overlapping Sets table:



Use the statement information to fill in the table. Our goal is to find the number of veggie melts bought by females out of total veggie melts.

(1) 1/2 of all sandwiches sold yesterday were tuna melts, and 1/3 of all customers yesterday were male.



Not enough information.

(2) Yesterday, twice as many tuna melts were bought by females as there were veggie melts bought by males.



Again, not enough information.

Statements 1 and 2 together:



We can create and solve an equation for the value of veggie melts bought by females, so we have sufficient information.

The answer is C.

For more on overlapping sets, see:
https://www.beatthegmat.com/rainbow-trou ... tml#555603
https://www.beatthegmat.com/survery-resu ... tml#576105
https://www.beatthegmat.com/ds-question- ... tml#677080

I'd like to point out that ceilid's "overlapping sets table" (aka Double Matrix Method) can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of customers, and the two characteristics are:
- male or female
- had tuna melt or had veggie melt

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent