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Re: A marketing firm determined that, of 200 households surveyed [#permalink]
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16 Nov 2017, 02:36
Bunuel wrote: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? (A) 15 (B) 20 (C) 30 (D) 40 (E) 45 Diagnostic Test Question: 6 Page: 21 Difficulty: 650 15 x>Both then 3x for only B 60+x+3x = 120 x = 15
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A marketing firm determined that, of 200 households surveyed [#permalink]
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05 Mar 2018, 11:13
I tried this question using: Total = Group 1 + Group 2  Both + Neither. 200 = 60 + 3Both  Both + 80 200 = 140 + 2Both 60 = 2Both Both = 30. Can someone give me some pointer on why my answer is wrong but when I used the same approach for question 14 on OG 2017, page 14. I was able to have it correct. Thank you.



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Re: A marketing firm determined that, of 200 households surveyed [#permalink]
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22 Mar 2018, 12:51
Bunuel wrote: SOLUTIONA marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?(A) 15 (B) 20 (C) 30 (D) 40 (E) 45 Given: "For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) > \(x=15\). Answer: A. Attachment: A marketing firm determined.JPG Hello Bunuel i reviewed the whole thread before to ask a question but i still dont understand IF: neither is 80 A soap = 60 both = x only 3 used B only so 200 = 60+3 x+80 i used the formula  > total = group1 +group 2 both +neither so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ...



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A marketing firm determined that, of 200 households surveyed [#permalink]
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22 Mar 2018, 18:36
dave13 wrote: Bunuel wrote: SOLUTIONA marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?(A) 15 (B) 20 (C) 30 (D) 40 (E) 45 Given: "For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) > \(x=15\). Answer: A. Attachment: A marketing firm determined.JPG Hello Bunuel i reviewed the whole thread before to ask a question but i still dont understand IF: neither is 80 A soap = 60 both = x only 3 used B only so 200 = 60+3 x+80 i used the formula  > total = group1 +group 2 both +neither so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ... hi I am not Bunuel the great, but I will try to help you understand the concept Yes, I agree with you, the formula you have applied to the problem is okay, but to get this formula help you, you have to put the values with great care okay, let me explain to you, where you went wrong Total = group1 + grpup2  both + neither here, in this formula, group1 or grpup2 doesn't exclude the possibilities where people can use both brands. You can see this arrangement as inclusive OR. When you select gorup1 (brand A) chances are still there that, some customers using brand B are also counted. When you select brand B, as before, chances are still there that, some customers using Brand A, are counted. thus, to avoid the double counting, "both" is subtracted once. As I mentioned earlier, since it is inclusive OR, "both" is counted once. So, when you say "A + B", it means A, and B, or both. now if you want to use this formula, you have do so as under 200 = (60 + x) + (3x + x)  x + 80 =) x = 15 so, as you can see, the formula doesn't intend to mean, group1 = only A and group2 = only B, but rather, it means group1 = only A + those who are using A and B both OR you can simply solve the problem as follows 120 = 60 + 3x + x =) x =15 since, 80 uses neither, total is 120, 60 uses only A, 3x uses only B, and x uses both hope this helps and is clear! thanks and cheers!



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A marketing firm determined that, of 200 households surveyed [#permalink]
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23 Mar 2018, 03:17
gmatcracker2018 wrote: dave13 wrote: Bunuel wrote: SOLUTIONA marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?(A) 15 (B) 20 (C) 30 (D) 40 (E) 45 Given: "For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) > \(x=15\). Answer: A. Attachment: A marketing firm determined.JPG Hello Bunuel i reviewed the whole thread before to ask a question but i still dont understand IF: neither is 80 A soap = 60 both = x only 3 used B only so 200 = 60+3 x+80 i used the formula  > total = group1 +group 2 both +neither so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ... hi I am not Bunuel the great, but I will try to help you understand the concept Yes, I agree with you, the formula you have applied to the problem is okay, but to get this formula help you, you have to put the values with great care okay, let me explain to you, where you went wrong Total = group1 + grpup2  both + neither here, in this formula, group1 or grpup2 doesn't exclude the possibilities where people can use both brands. You can see this arrangement as inclusive OR. When you select gorup1 (brand A) chances are still there that, some customers using brand B are also counted. When you select brand B, as before, chances are still there that, some customers using Brand A, are counted. thus, to avoid the double counting, "both" is subtracted once. As I mentioned earlier, since it is inclusive OR, "both" is counted once. So, when you say "A + B", it means A, and B, or both. now if you want to use this formula, you have do so as under 200 = (60 + x) + (3x + x)  x + 80 =) x = 15 so, as you can see, the formula doesn't intend to mean, group1 = only A and group2 = only B, but rather, it means group1 = only A + those who are using A and B both OR you can simply solve the problem as follows 120 = 60 + 3x + x =) x =15 since, 80 uses neither, total is 120, 60 uses only A, 3x uses only B, and x uses both hope this helps and is clear! thanks and cheers! Hi gmatcracker2018, many thanks for taking time to explain:) did you finally crack GMAT ? I have one question regarding this expression: and for every household that used both brands of soap, 3 used only Brand B soap.why are you writing as 3x instead of just 3. it says 3 used only Brand B soap so if those who use both A and B both is denoted as X hence if i break down the wording of question shouldnt we get this > \(60+x = A\) means households that used only soap A only as well as+ those who use both soaps A with B \(3+x= B\) means households that used only soap B as well as+ those who use both soaps B with A \(X= both\) means households that used both A and B soaps \(80 = neither\) households that used neither A nor B



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A marketing firm determined that, of 200 households surveyed [#permalink]
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23 Mar 2018, 03:24
dave13 wrote: Hi gmatcracker2018, many thanks for taking time to explain:) did you finally crack GMAT ? I have one question regarding this expression: and for every household that used both brands of soap, 3 used only Brand B soap.why are you writing as 3x instead of just 3. it says 3 used only Brand B soap so if those who use both A and B both is denoted as X hence if i break down the wording of question shouldnt we get this > \(60+x = A\) \(3+x= B\) \(X= both\) \(80 = neither\) Hey dave13 , You didn't understand the meaning of the sentence "for every household that used both brands of soap, 3 used only Brand B soap. " correctly. This means if they were X households who used both the brands, there were 3X households that used only Brand B. Thus, the calculation you did is incorrect because of the wrong meaning you took. It's a 1 to 3 relationship. Does that make sense?
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]
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23 Mar 2018, 17:36
abhimahna wrote: dave13 wrote: Hi gmatcracker2018, many thanks for taking time to explain:) did you finally crack GMAT ? I have one question regarding this expression: and for every household that used both brands of soap, 3 used only Brand B soap.why are you writing as 3x instead of just 3. it says 3 used only Brand B soap so if those who use both A and B both is denoted as X hence if i break down the wording of question shouldnt we get this > \(60+x = A\) \(3+x= B\) \(X= both\) \(80 = neither\) Hey dave13 , You didn't understand the meaning of the sentence "for every household that used both brands of soap, 3 used only Brand B soap. " correctly. This means if they were X households who used both the brands, there were 3X households that used only Brand B. Thus, the calculation you did is incorrect because of the wrong meaning you took. It's a 1 to 3 relationship. Does that make sense? hi dave13 as you can see abhimahna the boss has already replied to your question very elegantly anyway, please note that, we have got a relationship between "both" and "only B". Thus, if you don't attach a variable to the ratio, given, you won't get any hard number thanks



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Re: A marketing firm determined that, of 200 households surveyed [#permalink]
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26 Mar 2018, 11:05
Solution: Given:• Number of households surveyed = 200
• Households who used only Brand A soaps = 60
• Households who used only Brand B soaps = 3* Households who used both soaps.
• Households who used neither Brand A nor Brand B soaps = 80 Working out: We need to find out the number of households which used soaps of both the brands. To understand the solution, let us draw a 2set Venn diagram Since the total households surveyed were 200 and 80 of them used no soaps, (20080) households used at least one of Brand A or Brand B soaps. • Thus, \(3x +x +60 = 120\)
• Or, \(x =15\).
Thus, 15 households used both the brands of the soaps. Answer: Option A
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