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

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A survey asked 1,150 people to choose their favorite laundry [#permalink]  05 Mar 2017, 09:14
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Question Stats:

42% (01:14) correct 57% (01:09) wrong based on 147 sessions

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?

Indicate all such numbers.

❑ 20
❑ 25
❑ 30
❑ 35
❑ 40
❑ 45
❑ 50
[Reveal] Spoiler: OA

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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  11 Mar 2017, 20:20
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Expert's post
Explanation

Since x is rounded to the nearest integer (3), the actual percentage could be anything between

2.5% and 3.4999...%, because all of these numbers would round to 3.

Find the number of people that could be represented by these two extremes:

2.5% of 1150 people or $$0.025 \times 1150 = 28.75$$ people
3.4999......% of 1150 people or $$0.03499 \times 1150 = 40.24$$ people.

Hence 30, 35, 40 are possible options. Hence option C, D and E are correct.
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  24 Mar 2017, 14:58
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Expert's post
Carcass 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?
Indicate all such numbers.

❑ 20
❑ 25
❑ 30
❑ 35
❑ 40
❑ 45
❑ 50

[Reveal] Spoiler:
C,D, and E

Since x rounded to the nearest INTEGER is 3, we know that 2.5 ≤ x < 3.5
2.5% of 1150 = 28.75
3.5% of 1150 = 40.25

So, 28.75 ≤ number of people who chose A < 40.25

[Reveal] Spoiler:
C, D, E

Cheers,
Brent
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  14 Aug 2018, 15:16
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As they said X is rounded to the nearest integer, i.e. 3, the range is 2.51<x<3.49
so 2.51% of 1150 = 28.86
3.49% of 1150 = 40.135
SO the answer is 30,35 and 40.
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  15 Aug 2018, 17:53
Creating an inequality equation helps in such questions.
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  14 Oct 2019, 19:37
wouldn't you round 3.49 to 3.5 then to 4?
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  15 Oct 2019, 02:15
Expert's post
Unclear, indeed.

refer to the explanation provided by Brent

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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  15 Oct 2019, 05:49
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Expert's post
lethalasian wrote:
wouldn't you round 3.49 to 3.5 then to 4?

Good idea, but that's not how rounding works.

If we round 3.49 to the nearest tenth, then we get 3.5 (because 3.49 is closer to 3.5 than it is to 3.4)
If we round 3.49 to the nearest unit, then we get 3 (because 3.49 is closer to 3 than it is to 4)

Cheers,
Brent
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  15 Oct 2019, 12:36
Expert's post
Thank you for the spot on clarification Sir.

Regards
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  23 Oct 2019, 09:54
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The values are in ascending order.
Simply pick one value and check what percent is that value of 1150.
I picked 30, 30/1150 * 100 = 2.608.... rounded off to 3
Now check for 40, 40/1150 * 100 = 3.478..... rounded off to 3
Also, check for 45, 45/1150 * 100 = 3.913.... rounded off to 4. Not our answer.

Therefore among the 7 options, 30, 35 and 45 can be 3% of 1150.
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Re: A survey asked 1,150 people to choose their favorite laundry [#permalink]  13 Sep 2020, 02:17
This is very helpful. I was wondering how to solve this since I hadn't read the question properly. Hence, assumed that the question was asking for the percentage and was completely thrown off.
Re: A survey asked 1,150 people to choose their favorite laundry   [#permalink] 13 Sep 2020, 02:17
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