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SQL Server join query to get row with latest date closest to another date

I have looked through a lot of pages and can't find quite what I want to achieve. I have a select statement that I want to get the latest date that it is greater than so for example:

If I have two dates of 2015/06/01, 2015/07/01 and in my table I have one record with the date 2015/05/01 and another with the date 2015/06/20.

For the 2015/06/01 I want to have the max date that it is greater than in this case would be 2015/05/01.

For the 2015/07/01, I want to have the max date that it is greater than, in this case it would be 2015/06/20.

I want only the one option to return not all the matches which is what I currently get.

There are other joins etc to other tables and it would use all of them but for this purpose I have taken that information out because it is irrelevant to what I'm trying to achieve. If you require any more information just comment.

After comments I have created a Fiddle db structure, http://sqlfiddle.com/#!6/2738f/2/0 .

So here is my current query:

With IptBandRates as (
    select 
    ibr.ipt_band_code,
    ibr.ipt_rate,
    ibr.concessionary_date,
    max(ibr.concessionary_date) as concessionary_date2
    from product.ipt_band_rates ibr
    inner join quote.quote qu on '4' = qu.quote_id 
    where ibr.concessionary_date <= qu.[effective_date]
    group by ibr.concessionary_date, ibr.ipt_rate, ipt_band_code
)

select 

IptBandRates.ipt_rate as ipt_rate

from quote.premium
inner join quote.cover on quote.premium.cover_id = quote.cover.cover_id
inner join quote.quote qu on quote.cover.quote_id = qu.quote_id 

inner join product.premium_class on
 quote.cover.product_code = product.premium_class.product_code and
 quote.cover.product_ver_no = product.premium_class.product_ver_no and
 quote.cover.class_type_code = product.premium_class.class_type_code

 inner join product.ipt_band on  
 product.premium_class.ipt_band_code = product.ipt_band.ipt_band_code 

 inner join IptBandRates on 
 product.ipt_band.ipt_band_code = IptBandRates.ipt_band_code
 inner join product.ipt_band_rates ibrs on 
 ibrs.ipt_band_code = IptBandRates.ipt_band_code and
 ibrs.concessionary_date = IptBandRates.concessionary_date

where qu.quote_id  = '4'

do you need somethin like this?

x is the table with your dates and y is only a reference to get dates of the 1st day of each month to extract the maximum date lesser than..

;with 
x as (
    select 1 id, '2015/05/01' d
    union all
    select 2 id, '2015/06/20' d
    union all
    select 3 id, '2015/06/15' d
    union all
    select 4 id, '2015/05/10' d
    union all
    select 5 id, '2015/07/02' d
    union all
    select 6 id, '2015/04/02' d
),
y as (
    select '2015/05/01' ref_month
    union all
    select '2015/06/01' 
    union all
    select '2015/07/01' 
)
SELECT * 
FROM y
    outer apply (
        select MAX(d) max_date
        from x
        where d < y.ref_month
    ) z

result will be:

ref_month   max_date
2015/05/01  2015/04/02
2015/06/01  2015/05/10
2015/07/01  2015/06/20

I know this is old, but this is a way of doing it.

IF OBJECT_ID('tempdb..#FilteringDates') IS NOT NULL
    DROP TABLE #FilteringDates

CREATE TABLE #FilteringDates (filterDate DATE)

INSERT INTO #FilteringDates (
    filterDate)
VALUES
    ('2018-01-01'),
    ('2018-02-15'),
    ('2018-03-20')

IF OBJECT_ID('tempdb..#DataDates') IS NOT NULL
    DROP TABLE #DataDates

CREATE TABLE #DataDates (
    dataDate DATE,
    otherValue INT)

INSERT INTO #DataDates (
    dataDate,
    otherValue)
VALUES
    ('2017-06-01', 1),
    ('2018-01-03', 90),
    ('2018-01-15', 150),
    ('2018-01-20', 35),
    ('2018-02-20', 400),
    ('2018-03-10', 425),
    ('2018-04-20', 3)


;WITH DateRankings AS
(
    SELECT
        F.filterDate,
        D.dataDate,
        D.otherValue,
        MostRecentRanking = ROW_NUMBER() OVER (
            PARTITION BY
                F.filterDate
            ORDER BY
                D.dataDate DESC)
    FROM
        #FilteringDates AS F
        INNER JOIN #DataDates AS D ON D.dataDate <= F.filterDate
)
SELECT
    D.filterDate,
    MostRecentDate = D.dataDate,
    D.otherValue
FROM
    DateRankings AS D
WHERE
    D.MostRecentRanking = 1

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