Is it possible for someone to be exempt from filing a tax return?

Yes, it is possible although age by itself is not a factor. Whether you have to file is determined by a combination of your taxable gross income, filing status, age, if you are someone's dependent and if you have self-employment income. You can find the actual filing requirements in IRS Pub 501 under the heading "Who Must File." You can also use the IRS Interactive Tax Assistant to determine if you have a filing requirement.