Sometimes I can't solve a question because I have chosen the "wrong path", and since you only have 2 minutes per question I find it hard to "change the path" after a minute or so.

Most of these happen when I have to choose between drawing a table or using the Venn diagram (circles with intersections).

Take this DS question for example:

Customers can use a manufacturer's coupon and a store coupon to obtain a discount when buying soap powder in a certain store. In one week, 65% of customers used the store coupon when purchasing the soap powder, and 35% used the manufacturer's coupon. What percent of customers used both the manufacturer's coupon and the store coupon when purchasing the soap powder?

(1) 15% of customers used neither coupon when purchasing the soap powder

(2) 50% of customers used the store coupon but not the manufacturer's coupon when purchasing the soap powder Clich here to reveal the answer:

OA is (D), each statement by itself is sufficient

My first approach was to draw a Venn diagram such as this one:

SC = People that used the store coupon

MC = People that used the manufacturer's coupon

Using this approach I am able to determine

that statement 2 is sufficient since...

If the whole red circle is 65 then x = 65% - 50% = 15%

However,

I am unable to check statement 1 using a Venn diagram!

I can't find a graphic solution using the picture above.Instead I find myself using this table (which is the one the book also uses):

Then it is easy, because Z + 15% = 35%, so Z = 20%

Since X + Z = 35% then X = 15%

Another way I found useful was to use the following formula:

100%X = 65%X + 35%X - both%X + neither%X

Given that neither = 15% you can easily solve the equation above.

However, these are solutions I come with now that I have plenty of time.

In a real CAT I would have spent way too much time on this question, because I would have been stuck with the Venn diagram...

So my question would be... when do you know what's the best approach? (venn diagram vs table)

How would you draw the graphic solution of statement 1 using the Venn diagram above?
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