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03 Jun 2021, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:38) correct
41%
(01:34)
wrong
based on 93
sessions
History
Date
Time
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Not Attempted Yet
If t is an integer, is 3^t a factor of 21! ?
(1) t is the product of two distinct single-digit prime numbers that are smaller than 7.
(2) 0 < t < 9
(1) t is the product of two distinct single-digit prime numbers that are smaller than 7.
(2) 0 < t < 9
04 Jun 2021, 01:15
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If t is an integer, is 3^t a factor of 21!?
The power of 3 in factorization of 21! is 21/3 + 21/3^2 = 7 + 2 = 9. (Check here: https://gmatclub.com/forum/everything-ab ... 85592.html)
(1) t is the product of two distinct single-digit prime numbers that are smaller than 7. If t = 2*3 = 6 < 9, then 3^t will be a factor of 21! but if t = 3*5 = 15 > 9, then 3^t won't be a factor of 21!. Not sufficient.
(2) 0 < t < 9. For any nonnegative t less than or equal to 9, 3^t is a factor of 21!. Sufficient.
Answer: B.
Check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.
The power of 3 in factorization of 21! is 21/3 + 21/3^2 = 7 + 2 = 9. (Check here: https://gmatclub.com/forum/everything-ab ... 85592.html)
(1) t is the product of two distinct single-digit prime numbers that are smaller than 7. If t = 2*3 = 6 < 9, then 3^t will be a factor of 21! but if t = 3*5 = 15 > 9, then 3^t won't be a factor of 21!. Not sufficient.
(2) 0 < t < 9. For any nonnegative t less than or equal to 9, 3^t is a factor of 21!. Sufficient.
Answer: B.
Check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.
General Discussion
03 Jun 2021, 02:11
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The powers of 3 in 21!:
21/3 = 7
21/9 = 2
7+2 = 9. So up to 3^9 will be a factor of 21!
1) It could be under 9 but it could be over. INSUFFICIENT
2) Tells us 1≤t≤8 which fits into the above range. SUFFICIENT
Answer B
21/3 = 7
21/9 = 2
7+2 = 9. So up to 3^9 will be a factor of 21!
1) It could be under 9 but it could be over. INSUFFICIENT
2) Tells us 1≤t≤8 which fits into the above range. SUFFICIENT
Answer B
