Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase 2 of the above products?

My Answer

B1=60% B2=50% B3=35%

B1+B2+B3 = 100% B1 = 10%

Now how can I find the answer from this... I can't understand the answer they provide to this question.

Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase 2 of the above products?

My Answer

B1=60% B2=50% B3=35%

B1+B2+B3 = 100% B1 = 10%

Now how can I find the answer from this... I can't understand the answer they provide to this question.

Thanks in advance for the help

100 = m + c + a - (mc + ca + am) - 2 (mca) 100 = 60 + 50 + 35 - (mc + ca + am) - 2 (10) (mc + ca + am) = 145 - 100 - 20 (mc + ca + am) = 25 _________________

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Great explanation, THX!!!

But, If you're not so algebraic, like me =) You can also see this conceptually why this is true. Because just by looking at the derived equation, one might wonder, why? Or for me, why "-2B?" Why not just -B?

I enlightened myself by making an actual Vann diagram. With 3 post-its, I made three circles and overlapped them. Then it became so clear why the equation tells you to do -2B instead of -B or -3B

anyone like me, who just can't ACCEPT the equation as is, unless you actually SEE it, it might help.