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# Of the people surveyed last Monday, 60% were homeowners. Of the people

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Re: Of the people surveyed last Monday, 60% were homeowners. Of the people [#permalink]
Mvkumar86
HarveyKlaus
Of the people surveyed last Monday, 60% were homeowners. Of the people surveyed last Tuesday, 40% were homeowners. Was the number of homeowners surveyed last Tuesday greater than the number of homeowners surveyed last Monday?

1) The number of people surveyed last Tuesday was 55% greater than the number of people surveyed last Monday
2) 300 people were surveyed last Monday

1) In this case, The least possible number of people surveyed on Monday is always >=100 and Tuesday >=155

so the (least possible) number of homeowners surveyed on Mondays (60) < number of homeowners surveyed on Tuesday(62)
Sufficient

2) NS. No info about Tuesday's numbers

Excellent, I was thinking the same thing. Is there a shortcut for finding out the least number of people surveyed? A lot of work to find out if 20 (monday) & 31 (tuesday 55% greater) does not yield an integer when you take 40% of 31. Same for 40 & 62, (40% of 6.2 is 6.2 * 4 ) .... until we get to 100 - 155.
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Re: Of the people surveyed last Monday, 60% were homeowners. Of the people [#permalink]
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Hi HarveyKlaus,

While dealing with DS questions on percentages, ratios and word problems it is always recommended that you 'deconstruct the question'. Doing so will provide clarity on why a statement will be sufficient or insufficient.

Of the people surveyed last Monday, 60% were homeowners. Of the people surveyed last Tuesday, 40% were homeowners. Was the number of homeowners surveyed last Tuesday greater than the number of homeowners surveyed last Monday?

Let the number of people surveyed last Monday be 'x' and let the number of people surveyed last Tuesday be 'y'.

The number of homeowners surveyed last Monday will be (60/100) * x
The number of homeowners surveyed last Tuesday will be (40/100) * y

Now the question asks us 'Was the number of homeowners surveyed last Tuesday greater than the number of homeowners surveyed last Monday'. Putting this into an equation form we get

Is (40/100) * y > (60/100) * x

(60/100) * y < (40/100) * x, simplifying we get

Is 3x - 2y < 0

Statement 1 : The number of people surveyed last Tuesday was 55% greater than the number of people surveyed last Monday

If the number of people surveyed last Monday is 'x' and the number of people surveyed last Tuesday is 'y' then y = 1.55x

Substituting y - 1.55x in 3x - 2y < 0 we get

3x - 2(1.55x) < 0 -----> 3x - 3.10x < 0. This will give us a definite YES since x and y are always positive. Sufficient.

Statement 2 : 300 people were surveyed last Monday

Here we have x = 300 but do not have a definite value for y, so depending on whatever value of y we take we can either get a YES or a NO. Insufficient.

OA : A

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Re: Of the people surveyed last Monday, 60% were homeowners. Of the people [#permalink]
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Re: Of the people surveyed last Monday, 60% were homeowners. Of the people [#permalink]
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