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# Customers can use a manufacturer's coupon and a store coupon

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Intern
Joined: 27 Feb 2013
Posts: 6
Followers: 0

Kudos [?]: 3 [0], given: 2

Customers can use a manufacturer's coupon and a store coupon [#permalink]

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21 Mar 2013, 14:04
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:00) correct 34% (01:10) wrong based on 41 sessions

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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:
[Reveal] Spoiler:
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?
[Reveal] Spoiler: OA

Last edited by Reevak on 21 Mar 2013, 15:55, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 111

Kudos [?]: 272 [1] , given: 66

Re: How do you know how to approach a question? [#permalink]

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21 Mar 2013, 14:54
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Expert's post
Reevak wrote:

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?

Hi Reevak, the short answer is you should use a Venn Diagram when there is overlap between the two sets, and a matrix box when there is none. In this case, Venn diagram works best because you can clearly see the overlap between the two sets. As for statement 1, just put the 15% that use neither outside the two circles. This demonstrates that you now have 15% who use neither, 65% used the store coupon and 35% used the manufacturing coupon. This gives 115%, so at some point a certain percentage used both coupons, and that percentage has to get us back to 100%, so it must be 15%.

As for changing tracks, I often compare question solutions on the GMAT to the board game Cranium. In Cranium, you can use the fast way or the slow way to get to your destination. Obviously the fast way is always preferable, but you can't always use it, or don't know how to get there. The slow way, however, will get you there, it will just take a little longer. As long as you don't answer 37 questions the long way, you're probably okay. If you want to change tracks halfway through a question, you're basically starting over, which is fine if your original path wasn't going to get you where you wanted to go. If it'll take you 3 minutes to get there but you know you'll have the right answer, that's not a bad deal most of the time.

Hope this helps!
-Ron
_________________
Re: How do you know how to approach a question?   [#permalink] 21 Mar 2013, 14:54
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