Data Sufficiency

Hi,

Questions of this kind can be easily solved by making use of the mixture diagram given below.



The mixture diagram always gives you a ratio in which two quantities are mixed. The only thing that you need to keep in mind is that the values you need to use as the higher value, lower value and mean value have to be associated with the word 'per' (percents, average, per km, per kg etc.). The mixture diagram can also be used to explain the weighted average concept.

Now in the question we have two brands of nuts, Brand W containing 24% cashews by weight and Brand X containing 9% of cashews by weight. w pounds of Brand W nuts need to be mixed with x pounds of Brand X nuts to produce y pounds of a mixture containing 15% cashews by weight. The quantities associated with the word per are the percentages of cashew by weight. So representing these values in the mixture diagram



This means that for every 2 parts of Brand W we need to have 3 parts of Brand X if we need the overall percentage of cashews by weight to be 15%.

Statement 1 : w = 30

Since we know w : x = 2 : 3 and w = 30, we can easily find out the value of x. Sufficient

Statement 2 : y = 75

Since we know the ratio 2 : 3 and the total i.e. w + x = y = 75, we can easily solve for the individual values of w and x. Sufficient.

Answer : D

CrackVerbal Academics Team

24/100(w) + 9/100(x) = 15/100(y) and y=w+x
24w+9x = 15(w+x)
9w=6x
3w=2x

(1) w=30
3w=2x
3*30 = 2x
x = 45
SUFFICIENT

(2) y=75
3w=2x
y=w+x
75=2x/3 + x
x=45
SUFFICIENT

SO D