No group immediately claimed responsibility for the attacks but the bombings bore the hallmarks of an al-Qaeda-inspired group and other Sunni insurgents, who frequently use suicide and car bombs to target public areas and government buildings in their bid to undermine confidence in the Shiite-led government.
The explosions also coincided with the anniversary of the 2003 fall of Baghdad in the hands of US troops.
Earlier in the day, a car bomb in Baghdad's central Nidhal Street killed four people and wounded 11, while three people died and nine were wounded in a car bombing in the northern Kazimiyah district.
Car bombs also exploded in the areas of Shaab, Shammaiya, Karrada and Maamil, killing a total of seven people and wounding 30, police officials added.
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Medical officials confirmed the causality figures. All officials spoke on condition of anonymity because they were not authorised to talk to the media.
Violence has surged in Iraq since last year, with the country weathering its deadliest bout of violence since it pulled back from the brink of civil war in 2008. UN figures showed that last year, Iraq saw the highest death toll in attacks, with 8,868 people killed.
Today's attacks came as Iraq is heading toward a crucial election on April 30, its first vote since the 2011 US troop pullout.