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A market research company surveyed users of the toothpaste industry's 11 Feb 2017, 20:52
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A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
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C
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A market research company surveyed users of the toothpaste industry's 12 Feb 2017, 00:00
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ziyuenlau
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
Show more

Hi..

Info from the Q :- all of the person use ATLEAST one of the brands..

Let's see the statements..


(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
we do not know how many use both so insufficient
Say all using brand Y use brand X then 3:2 or 3z:2z would mean that 2z is part of 3z, that is 2z use both and z use ONLY x..
Ans is 0 for Y..
But say none use both, so 2z out of (3z+2z) use Y, thus %=2z/5z *100=40%..
Different answers possible
Insufficient

(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
So if x use X, then 1/2*x use both, nothing about ONLY y..
Insufficient..

Combined..
3z and 2z is X and Y...
And from II, 3z/2 is common, so total = 3z+2z-3z/2=7z/2..
Only Y =2z-3z/2=z/2..
%=(z/2)/(7z/2) * 100= 100/7%
Suff

C
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A market research company surveyed users of the toothpaste industry's 06 Sep 2017, 22:16
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The question is asking for the ratio Z
Z = (y-only) / (x-only + y-only + both)

1. "Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was 3:2"
=> (y-only + both) / ( x-only + both) = 3/ 2
=> both = 2y - 3x
Insuff.

2. "Among the respondents who reported that they use Brand X, one half also use Brand Y."
=> x-only = both
Insuff.

(1+2) => 2y - 3x = x = both
=> y = 2x = both
=> Z = 2x / ( x + 2x + x) = 1/2
C is suff.

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A market research company surveyed users of the toothpaste industry's 07 Jun 2018, 07:00
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ziyuenlau
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.

Hi..

Info from the Q :- all of the person use ATLEAST one of the brands..

Let's see the statements..


(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
we do not know how many use both so insufficient
Say all using brand Y use brand X then 3:2 or 3z:2z would mean that 2z is part of 3z, that is 2z use both and z use ONLY x..
Ans is 0 for Y..
But say none use both, so 2z out of (3z+2z) use Y, thus %=2z/5z *100=40%..
Different answers possible
Insufficient

(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
So if x use X, then 1/2*x use both, nothing about ONLY y..
Insufficient..

Combined..
3z and 2z is X and Y...
And from II, 3z/2 is common, so total = 3z+2z-3z/2=7z/2..
Only Y =2z-3z/2=z/2..
%=(z/2)/(7z/2) * 100= 100/7%
Suff

C
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I think 3z is supposed to be Y and 2z is supposed to be X

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A market research company surveyed users of the toothpaste industry's 09 Sep 2020, 06:14
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A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
Show more


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?
Bunuel VeritasKarishma Please help me with this.
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A market research company surveyed users of the toothpaste industry's 09 Sep 2020, 07:52
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BillyZ
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?
Bunuel VeritasKarishma Please help me with this.
Show more

IMHO
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A market research company surveyed users of the toothpaste industry's 09 Sep 2020, 08:04
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A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?
Bunuel VeritasKarishma Please help me with this.

IMHO
Show more

I think you didn't understand what I was saying. If, by employing smart numbers strategy, you had taken a value for TOTAL, say 6, you would have been able to find the required answer. A should be sufficient in my view.
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A market research company surveyed users of the toothpaste industry's 09 Sep 2020, 09:27
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BillyZ
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?
Bunuel VeritasKarishma Please help me with this.

IMHO

I think you didn't understand what I was saying. If, by employing smart numbers strategy, you had taken a value for TOTAL, say 6, you would have been able to find the required answer. A should be sufficient in my view.
Show more

Sorry, now i see.
Anyway, good question! :lol:
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A market research company surveyed users of the toothpaste industry's 13 Sep 2020, 23:54
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BillyZ
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?


Bunuel VeritasKarishma Please help me with this.
Show more

Louis14

You know that neither = 0 but you don't know what 'Both' is.
The respondents use at least one of the two brands so they could be using both brands too.

Say there were 100 people.
Using stmnt 1, I know Y:X = 3: 2
Does it mean 60 people use Y and 40 use X? Not necessarily. If you assume that this is the case, you would be assuming that Both = 0. So here 60 would be using only Y.

What if 90 people use Y and 60 use X and 50 use Both? Then 40 use only Y. This is also valid.

This is what we have:
100 = 3a + 2a - Both

Without statement 2, we don't know the value of Both.
Stmnt 2 tells us that half of 2a is Both. So Both = a

100 = 3a + 2a - a
a = 25

People who use Y = 3*25 = 75. People who use only Y = 75 - 25 = 50
Answer (C)
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A market research company surveyed users of the toothpaste industry's 14 Sep 2020, 01:30
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BillyZ
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?


Bunuel VeritasKarishma Please help me with this.

Louis14

You know that neither = 0 but you don't know what 'Both' is.
The respondents use at least one of the two brands so they could be using both brands too.

Say there were 100 people.
Using stmnt 1, I know Y:X = 3: 2
Does it mean 60 people use Y and 40 use X? Not necessarily. If you assume that this is the case, you would be assuming that Both = 0. So here 60 would be using only Y.

What if 90 people use Y and 60 use X and 50 use Both? Then 40 use only Y. This is also valid.

This is what we have:
100 = 3a + 2a - Both

Without statement 2, we don't know the value of Both.
Stmnt 2 tells us that half of 2a is Both. So Both = a

100 = 3a + 2a - a
a = 25

People who use Y = 3*25 = 75. People who use only Y = 75 - 25 = 50
Answer (C)
Show more

Thank you so much, ma'am for this elaborate answer and I do get my mistake. However, I'm still struggling to understand why, when I used the grid matrix, with 60 as total, and neither as 0, did I automatically get 0 for both. So, when total is 60, the 3:2 divide tells us that 36 people use X and the remaining 24 use Y. From here, we can get the values of the negating column and row i.e. Not X and Not Y. The Both column consequently comes out to be 0. I never assumed it to be 0. The grid gave me a O for Both. So, ma'am, where am I going wrong?
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A market research company surveyed users of the toothpaste industry's 16 Nov 2020, 08:16
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A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Why can't we employ 'smart numbers' strategy here? If we pick a number for TOTAL, say, 6, 30 or 60 etc. (any number that is multiple of 2 and 3, for the sake of ease), then we can easily get the percent of respondents who reported that they only use Brand Y using statement 1. The answer would be 60%. We know NEITHER is 0. We can use grid matrix and get the answer.

What am I missing, if I am?


Bunuel VeritasKarishma Please help me with this.

Louis14

You know that neither = 0 but you don't know what 'Both' is.
The respondents use at least one of the two brands so they could be using both brands too.

Say there were 100 people.
Using stmnt 1, I know Y:X = 3: 2
Does it mean 60 people use Y and 40 use X? Not necessarily. If you assume that this is the case, you would be assuming that Both = 0. So here 60 would be using only Y.

What if 90 people use Y and 60 use X and 50 use Both? Then 40 use only Y. This is also valid.

This is what we have:
100 = 3a + 2a - Both

Without statement 2, we don't know the value of Both.
Stmnt 2 tells us that half of 2a is Both. So Both = a

100 = 3a + 2a - a
a = 25


People who use Y = 3*25 = 75. People who use only Y = 75 - 25 = 50
Answer (C)
Show more


Hi Karishma,

Does the stmt 2 imply X+B=1/2(B).
I am not able to understand how X use implies X only. Please help !
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