This is a tricky question for sure. I suggest using the following examples as n and t for each condition:
1)
n =1 and
t =5 (answer is 1),
n =5 and
t =5 (answer is 5), NOT SUFFICIENT.
2)
n =5 and
t =105, (answer is 7),
n =105 and
t =105 (answer is 7),
n = 210 and
t = 105 (answer is 7), etc., SUFFICIENT.
Yes, the values for nt will eventually become quite large, but they are essentially pointless to calculate by hand, because the building blocks aka prime factorials of each multiplied number are always the same. Thus, the greatest common prime factor (GCPF) of
nt never increases.
Pro Tips for GCF and LCM:The GCF (greatest common factor) will never be LARGER than the SMALLEST number.
THE LCM (least common multiple) will never be SMALLER than the LARGEST number.
_________________
My name is Brian McElroy, founder of McElroy Tutoring (https://www.mcelroytutoring.com). I'm a 42 year-old Providence, RI native, and I live with my wife, our three daughters, and our two dogs in beautiful Colorado Springs, Colorado. Ever since graduating from Harvard with honors in the spring of 2002, I’ve worked as a private tutor, essay editor, author, and admissions consultant.
I’ve taken the real GMAT 6 times — including the GMAT online — and have scored in the 700s each time, with personal bests of 770/800 composite, Quant 50/51, Verbal 48/51, IR 8 (2 times), and AWA 6 (4 times), with 3 consecutive 99% scores on Verbal. More importantly, however, I’ve coached hundreds of aspiring MBA students to significantly better GMAT scores over the last two decades, including scores as high as 720 (94%), 740 (97%), 760 (99%), 770, 780, and even the elusive perfect 800, with an average score improvement of over 120 points.
I've also scored a verified perfect 340 on the GRE, and 179 (99%) on the LSAT.