The easy way:

w:m= 5:6 total= 11, so only women 5:11,

and left-handed people to right-handed people are 7 to 9. total 16, so only left-handed 7:16.

Now the main calculation, Just divide them, man

Bigger (\(\frac{5}{11}\)) > Smaller (\(\frac{7}{16}\)).
SO A IS ANSWER.

The ratio of women to men is 5 to 6
So, out of every 11 people, 5 are women and 6 are men.
So, 5/11 of the people are women (and 6/11 of the people are men)
If T = the TOTAL number of people, then \(\frac{5}{11}T=\) the number of women in the group


The ratio of left-handed people to right-handed people is 7 to 9
So, out of every 16 people, 7 are left-handed and 9 are right-handed.
In other words, 7/16 of the people are are left-handed (and 9/16 of the people are are right-handed)
If T = the TOTAL number of people, then \(\frac{7}{16}T=\) the number of left-handed people in the group

We get:
Quantity A: \(\frac{5}{11}T\)
Quantity B: \(\frac{7}{16}T\)

Since we know T is POSITIVE, we can safely divide both quantities by T to get:
Quantity A: \(\frac{5}{11}\)
Quantity B: \(\frac{7}{16}\)

At this point, it's probably easiest to convert each fraction to a decimal to get:
Quantity A: ≈ 0.45
Quantity B: ≈ 0.44

Answer: A

Cheers,
Brent

(A). Write two different Part : Part : Whole relationships. In each relationship, the two parts sum to the whole.
Women : Men : Total = 5 : 6 : 11, so Women : Total = 5 : 11.
Left-handed : Right-handed : Total = 7 : 9 : 16, so Left-handed : Total = 7 : 16.
In other words, women account for 5/11= 45.45% of the group, left-handed people for 7/16 = 43.75% of the group.
Since the total number of people is the same (it’s the same group, whether divided by gender or handedness), the percents can be compared directly. There must be more women than left-handed people in the group. Quantity A is greater.

Source: MGRE answer key

It could be solved by another way like this...
#Total number has to be divided by both 11 & 16. Now multiply this 11*16=176.
women=(176/11)*5=80
On the other hand Left-Handed people =(176/16)*7=77
Thus Answer Quantity A