PS - sets ques (with percents) : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 17:12

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# PS - sets ques (with percents)

Author Message
Manager
Joined: 14 May 2007
Posts: 178
Location: India
Followers: 2

Kudos [?]: 70 [0], given: 11

PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 05:31
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hello Everyone,

I came across this question and I am posting it. Though it is a re-post but I need an additional clarification.

Q-1 In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

A) 5
B) 10
C) 15
D) 20
E) 25

OA IS B

My theory: I came across another sets problem where one of the gmatclub member came up with the following formula -

[ OLD SETS QUES SOL
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z
So x+y+z = 27
#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30 ]

Now if I use a similar approach then i should get answer -

solving as per logic mentioned above-
x = 1 IN 2 (IN=intersection)
y = 2 IN 3
z = 1 IN 3

n = none

85 = (50-x-z) + (30-x-y) + (20-z-y) + x+y+z + 5 + n
85 = 50-x-z + 30-x-y + 20-z-y + x+y+z +5 +n
85 = 105 -x - y - z + n
-20 = -x -y -z + n
or 20 = x + y + z - n

Now what should I do ???
Is my approach ok. (gets confused in such type of ques)

Help appreciated,

Cheers,
GR
Manager
Joined: 20 Mar 2008
Posts: 159
Location: USA
Followers: 2

Kudos [?]: 44 [0], given: 0

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 07:08
Here is diagrammatic approach and I get 10 (B).

We could get the same answer by putting 5 in 1 intersection 3 or 3 intersection 2
Attachments

Sets1.doc [24 KiB]

Manager
Joined: 14 May 2007
Posts: 178
Location: India
Followers: 2

Kudos [?]: 70 [0], given: 11

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 07:25
vishy007 wrote:
Here is diagrammatic approach and I get 10 (B).

We could get the same answer by putting 5 in 1 intersection 3 or 3 intersection 2

Sorry, the explanation was not helpful in getting hang of the issue.
Director
Joined: 27 May 2008
Posts: 549
Followers: 8

Kudos [?]: 312 [0], given: 0

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 07:46
greatchap wrote:
Hello Everyone,

I came across this question and I am posting it. Though it is a re-post but I need an additional clarification.

Q-1 In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

A) 5
B) 10
C) 15
D) 20
E) 25

OA IS B

My theory: I came across another sets problem where one of the gmatclub member came up with the following formula -

[ OLD SETS QUES SOL
Set up a venn diagram with the following:
#(all three) = 3
#(soccer and baseball) = z
So x+y+z = 27
#(none) = n

63-x-z + 42-x-y + 39-y-z + x + y + z + 3 + n= 150
147-x-y-z+n= 150
147 - (x+y+z) + n = 150
147 - (27) + n = 150
n = 30 ]

Now if I use a similar approach then i should get answer -

solving as per logic mentioned above-
x = 1 IN 2 (IN=intersection)
y = 2 IN 3
z = 1 IN 3

n = none

85 = (50-x-z) + (30-x-y) + (20-z-y) + x+y+z + 5 + n
85 = 50-x-z + 30-x-y + 20-z-y + x+y+z +5 +n
85 = 105 -x - y - z + n
-20 = -x -y -z + n
or 20 = x + y + z - n

Now what should I do ???
Is my approach ok. (gets confused in such type of ques)

Help appreciated,

Cheers,
GR

You approach is perfect,
we know n = 0, becasue in 85 you are taking only those consumers who like at least one of the products.

x+y+z = 20.

Now we have to find out number of consumers (assuming total is 100) who like more than 2 products.
5 is the number of consumers who like all three, lets call it "t"

Now here is the key, In summation if 1IN2, 2IN3 and 3IN1 (x+y+z) we are actually counting 't' 3 times. while for answer we have to count it only once.

So answer = x+y+z - 2t = 20 - 10 = 10.

HTH.
Manager
Joined: 14 May 2007
Posts: 178
Location: India
Followers: 2

Kudos [?]: 70 [0], given: 11

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 10:23
Thanks a lot, durgesh79. Now I understood the problem. thanks again...

Just one ques, above we got x+y+z = 20 which we got. This 20 is no of people who like at least one product. Am I right?
Director
Joined: 27 May 2008
Posts: 549
Followers: 8

Kudos [?]: 312 [0], given: 0

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 10:57
greatchap wrote:
Thanks a lot, durgesh79. Now I understood the problem. thanks again...

Just one ques, above we got x+y+z = 20 which we got. This 20 is no of people who like at least one product. Am I right?

the no of people who like at least one product is 85.

x+y+z = 20. this is the sum of number of people in 3 groups.
People who like both 1 and 2 - (this group includes some people who like 3 also, we know this number is 5)
people who like both 2 and 3 - (this group includes some people who like 1 also, we know this number is 5)
people who like both 3 and 1 - (this group includes some people who like 2 also, we know this number is 5)

So in the sum 20, we have taken this group of 5 people three times.
Manager
Joined: 11 Apr 2008
Posts: 128
Location: Chicago
Followers: 1

Kudos [?]: 49 [0], given: 0

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 12:11
greatchap wrote:
Hello Everyone,

I came across this question and I am posting it. Though it is a re-post but I need an additional clarification.

Q-1 In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

A) 5
B) 10
C) 15
D) 20
E) 25

OA IS B

Here is an easier way of looking at this problem (and which has many applications toward other problems of the same type). Using the following formula
A + B + C – AB – AC- BC – 2ABC + Neither = Total ...we want to find AB + AC + BC + ABC --> this is the same as the number of participants who liked at least one of the three products.
Interpretation:
AB: # of participants who liked only A and B
AC: # of participants who liked only A and C
BC: # of participants who liked only B and C
ABC: # of participants who liked A, B and C only.

Filling this formula in with the given information we get:
50 + 30 + 20 – AB – AC – BC – 2(5) + 15 = 100
Interpretation:
50 --> A
30 --> B
20 --> C
2(5) --> 2 * ABC
15 --> Neither (which is just 100-85 = neither)

Solving for AB, AC, and BC they all sum to 5 and when you add in the ABC portion, which is 5, we get 10 as the answer.

I hope this makes sense. Let me know if it doesn't.
_________________

Factorials were someone's attempt to make math look exciting!!!

Manager
Joined: 14 May 2007
Posts: 178
Location: India
Followers: 2

Kudos [?]: 70 [0], given: 11

Re: PS - sets ques (with percents) [#permalink]

### Show Tags

16 Jun 2008, 19:38
Allright, now I get it. Earlier on, I made silly mistake.

Thanks a ton guys...
Re: PS - sets ques (with percents)   [#permalink] 16 Jun 2008, 19:38
Display posts from previous: Sort by