Eat your fruits and veggies: a meta-analysis study of Fruit and vegetable intake and the risk of cardiovascular disease, total cancer and all-cause mortality. Key takeaway:

Reductions in risk were observed up to 800 g/day [fruit and vegetable intake] for all outcomes except cancer (600 g/day). Inverse associations were observed between the intake of apples and pears, citrus fruits, green leafy vegetables, cruciferous vegetables, and salads and cardiovascular disease and all-cause mortality, and between the intake of green-yellow vegetables and cruciferous vegetables and total cancer risk. An estimated 5.6 and 7.8 million premature deaths worldwide in 2013 may be attributable to a fruit and vegetable intake below 500 and 800 g/day, respectively, if the observed associations are causal.

It’s a bit old, and it is a study of studies, but the findings match your grandmother’s admonitions. Personally, I prefer apricots, which are high in potassium and therefore helpful in lowering blood pressure.