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# A survey asked 1,150 people to choose their favorite laundry detergent

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Math Expert
Joined: 02 Sep 2009
Posts: 55656
A survey asked 1,150 people to choose their favorite laundry detergent  [#permalink]

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23 May 2019, 03:53
00:00

Difficulty:

85% (hard)

Question Stats:

41% (02:23) correct 59% (02:03) wrong based on 46 sessions

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A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?

I. 30
II. 35
III. 45

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

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A survey asked 1,150 people to choose their favorite laundry detergent  [#permalink]

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Updated on: 23 May 2019, 05:42
1
Bunuel wrote:
A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?

I. 30
II. 35
III. 45

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

let's do reverse calculation:

I (30/1150)*100 gives 2.6-> 3

II (35/1150)*100 gives 3.0bc -> 3

III (45/1150)*100 gives 3.9-> 4

D. I and II only.
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Originally posted by LeoN88 on 23 May 2019, 04:35.
Last edited by LeoN88 on 23 May 2019, 05:42, edited 1 time in total.
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Re: A survey asked 1,150 people to choose their favorite laundry detergent  [#permalink]

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23 May 2019, 05:00
(3/100) *1150 ≤ x < (4/100)*1150
34.5 ≤ x < 46

Both 35 and 45 lie in our range.
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Re: A survey asked 1,150 people to choose their favorite laundry detergent  [#permalink]

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28 May 2019, 06:52
Bunuel wrote:
A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?

I. 30
II. 35
III. 45

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

Since 3% can be rounded from as small as 2.5% and as large as 3.5%, we see that at least 29 people could have said brand A is their favorite brand (notice that 0.025 x 1150 = 28.75) and at most 40 people could have said brand A is their favorite brand (notice that 0.035 x 1150 = 40.25).

Therefore, Roman numerals I (30) and II (35) could be the number of people who chose A as their favorite brand.

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Re: A survey asked 1,150 people to choose their favorite laundry detergent   [#permalink] 28 May 2019, 06:52
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