In the South, before the Civil Rights Act, African-Americans were often excluded from voting on the excuse that they had failed a "literacy test". Were white Southerners ever put through this test,and if so, what proportion of them failed?
It should be understood that literacy tests etc. were tailor-made to exclude African-Americans from polls. Many southern states were clever enough to employ "grandfather clauses" in addition to literacy tests. These clauses essentially ensured that the scenario you pointed out never occurred.
[The grandfather clauses] provided that those who had enjoyed the right to vote prior to 1866 or 1867 or their lineal descendants would be exempt from educational, property, or tax requirements for voting. Because former slaves had not been granted the right to vote until the Fifteenth Amendment was ratified in 1870, these clauses effectively excluded blacks from the vote. At the same time, grandfather clauses assured the right to vote to many impoverished, ignorant, and illiterate whites. In 1915, the U.S. Supreme Court finally declared the grandfather clause unconstitutional because it violated equal voting rights guaranteed by the Fifteenth Amendment.