Ratio of black to brown = 6x : 5x
Total no. of black gloves = multiple of 6
Total no. of brown gloves = multiple of 5
Target question => Did the store receive at least 250 gloves?
Statement 1: 44% of the left-handed gloves in the shipment were black.
Let the total no. of left-handed gloves = y
$$\frac{44}{100}\cdot y=\frac{11}{25}y$$
y is a multiple of 25 and black left-handed glove is a multiple of 11. However, the color or number of right-handed glove is unknown. Hence, statement 1 is NOT SUFFICIENT.
Statement 2: The shipment included 84 black, right-handed gloves.
There is no information about left-handed gloves. Therefore, statement 2 is NOT SUFFICIENT.
Combining both statements together:
Total no of black gloves = 6x
$$6x=\frac{11}{25}y+84$$
From the question stem, black gloves is a multiple of 6 since 84 is also a multiple of 6. Then, 11y/25 must be a multiple of 6 and y must be a multiple of 25 and 6.
Minimum value of y = 25*6 = 150
$$6x=84+\frac{1650}{25}$$
$$6x=84+66$$
$$6x=150$$
$$x=\frac{150}{6}=25$$
The minimum value of x = 25
Total is at least = 6 (25) + 5 (25) = 150 + 125 = 275, which is greater than 250. Therefore, both statements combined together are SUFFICIENT. Hence, option C is the correct answer.
