smushkas wrote:Hey guys,

I was wondering if anyone can give any hint how to deal with this kind of a problem? From the stem, we got 100%, but then comes extra 15%, this is really confusing and I got a bit lost. Any tricks/hints that we can figure out that the question is talking about 200%?


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


OA [spoiler]D[/spoiler]

Thanks in advance!

Use a Venn diagram it makes everything clearer.

From 1, solving for n = people who use both.

65% - n + 35% - n + n = 85%

From 2,

65% - 50% = 15% use both

so D

smushkas wrote:Hey guys,

I was wondering if anyone can give any hint how to deal with this kind of a problem? From the stem, we got 100%, but then comes extra 15%, this is really confusing and I got a bit lost. Any tricks/hints that we can figure out that the question is talking about 200%?


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


Thanks in advance!

The big problem is that you're making an assumption about something that was never explicitly stated - and we NEVER want to make assumptions in data sufficiency.

In one week, 65% of customers used the store coupon when purchasing the soap powder, and 35% used the manufacturer's coupon.

You read this as "65% of customers used store coupon and the OTHER 35% used manufacturer coupon." However, the word "other" doesn't actually appear. In other words, it's possible that some people used BOTH coupons. In fact, the question itself should have tipped you off, since we're asked,

Q: what percent of customers used both?

There's a quick and easy formula we can use when we have 2 overlapping groups:

Total # of Members = Group 1 + Group 2 + Neither - Both

So, from the original info, we know that:

100%x= 65%(x) + 35%(x) + neither - both

(1) tells us that 15% used neither. Once we fill in "neither" all that's left in our equation is "both" and a bunch of numbers, so we can solve: sufficient.

(2) tells us that 50% used the store but NOT the manufacturer's. Well, we started with 65%, if 50% used JUST the store, then 15% must have used both: sufficient.

Choose (d), each statement is sufficient on its own.

A long question and a long explanation. But thanks everyone.

I used the same approach as Stuart's solution but slightly different way of organizing the info.

Please see attached (a little fancy with my colors also )