Hydrochlorothiazide is a thiazide diuretic => thiazide diuretics are associated with hypokalemia.
What other diuretics are associated with hypokalemia? Loop diuretics.
Inhibition of Na+ reabsorption occurs in both loop diuretics (inhibit NKCC cotransporter) and thiazide diuretics (inhibit NaCl cortransporter). All of this increased Na+ increases Aldosterone activity.
Relevant to this problem, Aldosterone upregulates expression of the Na+/K+ ATP antiporter (reabsorb Na+ into body, expel K+ into lumen). This results in hypokalemia in the body.
Hang on, there's more high yield info!
Aldosterone does one other important thing - activation of a H+ channel that expels H+ into the lumen.
So, given that this patient has hypokalemia, you know there is upregulation of Aldosterone. Do you think her pH would be high, or low? Exactly, it would be high because inc. Aldosterone => inc. H+ expelled into the lumen => metabolic akalosis.
Now you understand why both loop diuretics and thiazide diuretics can cause what's called "hypokalemic metabolic alkalosis."
Thiazide diuretics are the class with the largest risk of hypokalemia.
If both HCTZ and loop diuretics were provided as an answer choice, further clue that hctz would be the answer choice is the presentation of the patient "feeling funny". This suggests hypercalcemia (psychiatric overtones) which is a side effect unique to HCTZ.