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B is corrent. Lottery winnings are gambling winnings and must be included in gross income. Gambling losses are deductible from AGI as a miscellaneous deduction (to the extent of winnings) not subject to the 2% of AGI floor if a taxpayer itemizes deduction. Since Jeff elected to take the standard deduction for 2012, the $1,400 spent on lottery tickets is not deductible. All $6,000 of Jeff’s lottery winnings are included in his taxable income.
A is incorrect. Lottery prizes must be included in gross income. 
C is incorrect because $6,000 must be included in gross income. 
D is incorrect. The losses cannot be offset against winnings.