Chem solution question, pls help?

Mass of the solution = (35 g) + (1.5 × 10² g) = 185 g
Volume of the solution = (185 g) / (1.57 g/mL) = 117.8 mL = 0.118 L

Molar mass of NaOH = (23.0 + 16.0 + 1.0) g/mol = 40.0 g/mol
No. of moles of NaOH = (35 g) / (40.0 g/mol) = 0.875 mol

Molarity = (0.875 mol) / (0.118 L) = 7.4 M (to 2 sig. fig.)

I continue to be puzzled by the strange density values given frequently in Y!A. I do not know where these density values come from . But they make no logic:
Read the data given and some of the solutions calculated
35g NaOH dissolved in 1.5x10^2g water,
That is 35g NaOH dissolved in 150g or 150mL water
It is logical to expect the volume of the final solution to be in excess if 150mL
But we are told: Density = 1.57g/mL
By calculation , the volume is 118 mL
How is it possible that you take 150g or 150mL of water , add 35g of NaOH to this water and then the total volume is 118mL ?
There is no logic in this question - or unhappily the answers submitted.
I have checked my density data for NaOH solutions.
We have 35g NaOH in a total of 185g solution = 18.9%m/m
Density of NaOH solutions
19.16%m/m: density = 1.210g/mL
18.26%m/m: density = 1.200g/mL
We can approximate the density of a 18.9%m/m NaOH solution to be 1.208g/mL
Now do the calculation
185 g / 1.208 g/mL = 153.1mL ( which is what we can expect)

35 g of NaOH = 0.875 mole

molarity =moles / volume in L
Molarity = 0.875 mol / 0.1531L
Molarity = 5.7mol /L or 5.7M
Do some “ crude “ chemistry:
You have 35g NaOH in 150mL water
This is APPROXIMATELY 35*1000/150 = 233g NaOH /L
Mol NaOH / L = 233/40 = 5.8mol /L
Which allowing for the “crude” calculation: Checks my above reasoning.

Incidentally , an NaOH solution with density = 1.530 g/mL has a concentration of 50.50%m/m
This density is less than the submitted 1.57g/mL