shashwats wrote:Q:Each of the products produced yesterday was checked by x or y. 0.5% of the products checked by x are defective and 0.8% of the products checked by y are defective. If the total defective rate of all the products checked by x and y is 0.75%, what fraction of the products was checked by y?
Defective rate of X: 0.5%.
Defective rate of Y: 0.8%.
Defective rate of the MIXTURE of X and Y: 0.75%.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with X and Y's percentages (0.5% and 0.8%) on the ends and the mixture's percentage (0.75%) in the middle.
X 0.5%------------0.75%-----------0.8% Y
Step 2: Calculate the distances between the percentages.
X 0.5%----
.25-----0.75%----
.05-----0.8% Y
Step 3: Determine the ratio of X to Y in the mixture.
The required rate of X to Y is the RECIPROCAL of the distances in red.
X:Y = .05 : .25 = 5:25 = 1:5.
Since X:Y = 1:5, of every 6 products, 1 was checked by X and 5 were checked by Y.
Thus:
Y/total = 5/6.
For two similar problems, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html
Last edited by GMATGuruNY on Wed May 15, 2013 8:51 am, edited 1 time in total.
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