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145 people were surveyed to find out whether they like or dislike Prod

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145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 21:08
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:28) correct 33% (02:20) wrong based on 33 sessions

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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 21:41
1
Given that 145 people were surveyed to determine whether they like or dislike products A and B. We are to find how many people like product A.

Statement 1: 123 people dislike at least one product.
from this statement we know that 123=Aonly + Bonly + None
Hence we can determine the number, x, who like both products
However, there is no way of determining Those who like Aonly in order to determine A=Aonly + x
Statement 1 is not sufficient on its own.

Statement 2: Aonly = 78
Not sufficient because we need to know the number who like both products, x, and add it to A only to determine the total number who like product A.

1+2 Sufficient. This is because from statement 1 we are able to determine the number of people who like both products, x, and statement 2 gives us the number who like A only.
Hence, the number who like A can be determined by combining both statements.

The answer is C.
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 21:50
2
------------- Like A ----- Dislike A -- Total
Like B -------- ------------- ------
Dislike B ----- ------------- ------
--------------- x ------------- ------ 145

We have to find x

(1) 123 people disliked at least one of the two products
--> 145 - 123 = 22 people liked both the products

------------- Like A ----- Dislike A -- Total
Like B -------- 22 ------------- ------
Dislike B ----- ----------------- ------
--------------- x --------------- ------ 145

--> Insufficient

(2) 78 people liked product A but did not like product B

------------- Like A ----- Dislike A -- Total
Like B -------- ----------------- ------
Dislike B ----- 78 ------------- ------
--------------- x ------------- ------ 145

--> Insufficient

Combining (1) & (2),
------------- Like A ----- Dislike A -- Total
Like B -------- 22 --------------- ------
Dislike B ----- 78 --------------- ------
--------------- x ------------- ------ 145

x = 22 + 78 = 100 --> Sufficient

IMO Option C
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 21:56
1
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

(1) 123 people disliked at least one of the two products

(2) 78 people liked product A but did not like product B
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 22:11
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

(1) 123 people disliked at least one of the two products

(2) 78 people liked product A but did not like product B .....clearly suff


OA:B
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 22:23
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

(1) 123 people disliked at least one of the two products
145-123=22 people like both products
insufficient to find how many like product A

(2) 78 people liked product A but did not like product B
we still don't know how many like both A and B to add with the 78 to be total of people who like A.
insufficient

Together is what we are looking 78+22=100 total number of people who liked product A
therefore, C
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 02 Oct 2019, 23:47
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

No. of people like A only (not B) = x = No. of people who dislike B
No. of people like both A and B product = y
No. of people like B only (not A) = z = No. of people who dislike A
Total = x+y+z+none like any product = 145
Need to find x + y.

(1) 123 people disliked at least one of the two products = x + z + none = 123

Total = x+y+z+none like any product
145 = 123 +y
y (both liked) = 22
Can't know x + y. Hence, insufficient.

(2) 78 people liked product A but did not like product B means x = 78 but we can'g find y.

Combining, we can find x + y = 78 + 22 = 100.
Hence, Ans. C.
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 03 Oct 2019, 03:45
make 2x2 matrix
---------Like A---- Not Like A---- total
Like B--- 22 --- a----------
NotlikeB--78(c)-----b------------
Total----100------45------------145
IMO C ;

145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

(1) 123 people disliked at least one of the two products

(2) 78 people liked product A but did not like product B
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 03 Oct 2019, 05:15
Quote:
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

(1) 123 people disliked at least one of the two products
(2) 78 people liked product A but did not like product B


T=A+B-both+neither

(1) 123 people disliked at least one of the two products: insufic.
123 disliked at least one, then both=145-123=22
145=A+B-22+neither

(2) 78 people liked product A but did not like product B: insufic.
145=A+B-both+neither…145=(78+both)+B-both+neither

(1&2): sufic.
A=78+both…A=78+22=100

Answer (C)
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Re: 145 people were surveyed to find out whether they like or dislike Prod  [#permalink]

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New post 03 Oct 2019, 05:22
145 people were surveyed to find out whether they like or dislike Products A and B. How many like product A?

It is not mentioned whether there are people who didn't opine. Considering that there are some who might not have opined we have to find people who like only A and people who liked both A and B.

(1) 123 people disliked at least one of the two products
It means same 123 people liked at least one of the two products. So, 14-123 = 22 people like both A and B. Hence people who liked A = 22 + 123 - x where x is number of people who liked B.

And 0 ≤ x ≤ 123.

INSUFFICIENT.

(2) 78 people liked product A but did not like product B

People who liked only A = 78. As it is not possible to find people who liked both A and B. Hence
INSUFFICIENT.

Together 1 and 2
Here 123 - x = 78
x = 45

Hence people who like A = 22 + 78 = 100
People who liked only B = 45

SUFFICIENT.

PS: Liking just don't mean people disliked other product or vice-a-versa.
Also, it is assumed that all 145 people surveyed answered positively without any neutral cases.
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Re: 145 people were surveyed to find out whether they like or dislike Prod   [#permalink] 03 Oct 2019, 05:22
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