Data Sufficiency

Veritas Prep

A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves. Did the store receive at least 250 gloves in the shipment?

1) 44% of the left-handed gloves in the shipment were black.
2) The shipment included 84 black, right-handed gloves.

OA C

Statement 1
44% of the left handed gloves in the shipment were black, so there is no information about the right handed gloves hence, the statement 1 is INSUFFICIENT.

Statement 2
The shipment includes 84 blacks, right handed glove, no information on the left handed once, hence solution 2 is INSUFFICIENT.

Combining both statements together
Given that Black : Brown = 6x :5x respectively.
Number of black gloves will be a multiple of 6 and number of brown gloves will be a multiple of 5.

From statement 1, 44% of the left handed gloves were black.
Number of left handed gloves will be a multiple of 25.
From statement 2, we have 84 blacks, right handed gloves
Total number of black gloves for both right handed and left handed gloves
$$=\left(\frac{11}{25}\right)Y+84=6x$$
Since both 84 and 6x are multiples of 6,then 11Y/25 must also be a multiple of 6, hence Y will be a multiple of both 6 and 25 or a multiple of 150.
Least value of Y = 150
$$84+\frac{\left(11\cdot150\right)}{25}=6x$$
$$84+\frac{\left(1650\right)}{25}=6x$$
$$84+66=6x$$
$$150=6x$$
$$x=\frac{150}{6}=25;\left(\min imum\ value\ of\ x\right)$$
$$Total=6x+5x=11x$$
$$Total=6\left(25\right)+5\left(25\right)=11\left(25\right)$$
$$Total=150+125=275$$
$$275=275$$
$$275>250$$
Hence statement 1 and 2 combined are SUFFICIENT.
$$answer\ is\ Option\ C\ $$