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Social Security provides about 38 percent of the income for the elderly, but most Americans would likely flunk a test on the program's basic details.

Only one persona retired woman in the Southout of 1,513 surveyed recently by life insurer MassMutual answered all 12 questions right on an elementary test about Social Security retirement benefits. (Tweet This) More than seven out of 10 people received a failing grade.

(Take CNBC's quiz below to see how your Social Security knowledge stacks up.)

Quiz: How much do you know about Social Security?

"Perhaps the greatest Social Security deficit in this country—and what's lost in today's discussions about Social Security—is how little most Americans even know about this retirement benefit," said Michael Fanning, MassMutual's executive vice president of the U.S. insurance group. "While we didn't expect every person to get 100 percent correct, we certainly hoped that more would receive a passing grade."

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Besides not knowing that the full retirement age varies, depending on the year you were born, and that non-U.S. citizens can be eligible for Social Security retirement benefits, 55 percent incorrectly said that they can continue working while collecting full Social Security retirement benefits regardless of their age.

While you can work and receive Social Security retirement benefits, if you have not reached full retirement age, your earnings will be subject to a retirement earnings test. If your income exceeds $15,720 for 2015, for example, the Social Security Administration will deduct $1 from your benefit payments for every $2 you earn above the annual limit.

Lack of knowledge did not diminish Americans optimism about receiving Social Security benefits. Sixty-three percent of people surveyed by MassMutual believe Social Security will be available to them when they retire, but only 45 percent think the program will have sufficient funding.

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An earlier survey by the Pew Research Center found that 41 percent of Americans think there will be no Social Security benefits for them when they retire and nearly a third expect reduced levels of benefits.The Social Security and Medicare trustees' 2014 report projects that all the Social Security trust funds will be depleted by 2033. At that point, the agency will be able to pay out about 77 percent of retirement benefits from payroll taxes collected.

"The Social Security knowledge problem relates to a lack of basic financial literacy," said Anna Rappaport, chair of the Society of Actuaries' Committee on Post-Retirement Needs and Risks.

Since many workers receive retirement information at the workplace, Rappaport said, employers can be a valuable resource in improving financial literacy, including information on Social Security. In fact, more than 90 percent of 250 large employers said they want to introduce or expand their financial wellness programs this year, according to a survey by benefits consulting firm Aon Hewitt.

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People's knowledge of Social Security tends to increase as they approach retirement, Rappaport said. Yet 40 percent of the people surveyed by MassMutual were 50 or older and among this group 62 percent failed the Social Security quiz.

"This is very concerning, as many Americans may be at risk of underutilizing a critical component of their income stream and leaving Social Security retirement benefits they're entitled to on the table," Fanning said. "Many may be putting their retirement plans in jeopardy."