The picture above is a chart of all of the sales in the Katy area, from hwy 6 to 1463, and from Clay Rd to the Seven Lakes area in the south.  The dots are plotted at the final sales price and days on the market (DOM) at which the house closed.  The size of the dots are represent the cumualative days on the market (CDOM), which includes all of the time since the house was first listed.   DOM just represents time since last status change, eg a price reduction.  

There were 442 closings from March 4th until April 11th, and you can see the rising trend of days until closing versus price.  In general higher price points leads to more days on the market as illustrated by the trend line fitted to the points.   The biggest cluster of points are the ones that sold immediately (the very tiny dots at the left edge of the plot).  Surprisingly, those small dots are present at all price ranges, but the biggest cluster is the below $250,000 price, and that agrees with what I've seen personally, lower priced homes that look move in ready and aren't overpriced sell pretty quickly.  The houses that sell within the first 10 days have an average price of $250k, and an average discount from list price of $2500.  There are plenty of more expensive houses that sold quickly as well, represented by the small dots in the upper half of the left edge of the chart.   These were mostly sold at asking price, or a little above or below asking, with 2 outliers that sold for 10% and 20% below asking.

Of the 442 properties, 75% sold within the first 90 days. All of the houses priced below $200k sold within 90 days. (except one).    There is a cluster of bigger dots from $220k to $350k that plot around 25 days DOM.  These houses were all repriced, (thus resetting the days on market and moved them to the left edge of the chart), then quickly sold, and the size of the dots indicate that they were around 200 days CDOM.

We can try and generalize that the lower priced market is still moving pretty well.  For higher priced houses it is possible to sell quickly, but it has to be priced correctly, otherwise the house can sit on the market for 5-7 months before dropping the price to the price it should have had, then it sells.  Houses are still moving, but accurate pricing is key to selling before you've paid another 6 month of mortgage, taxes and insurance.

From a C21 pricing presentation I saw recently:

If a listing is overpriced... Lost time, and delays have consequences,  Lost Money, Lost Opportunity to move to the new home and emotional stress.

It's better to avoid those problems and price the house accurately using the correct comparable properties.