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06 Jun 2021, 03:34
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:04) correct
38%
(02:14)
wrong
based on 213
sessions
History
Date
Time
Result
Not Attempted Yet
What is the sum of all 4 digit numbers that can be formed by rearranging the digits of the number 3345?
A.99990
B.69994
C.79992
D.49995
E.66660
A.99990
B.69994
C.79992
D.49995
E.66660
06 Jun 2021, 07:09
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With four different nonzero digits, you could make 4! = 24 different numbers in total. Here, since the order of the two 3's won't matter, we need to divide that by 2!, so we can make 12 different four-digit numbers using the digits 3, 3, 4 and 5. The numbers we can make are all clearly less than 5500 (the largest number we can make is 5433), so their sum is certainly less than 12*5500 = 66,000, and only answer D is possible.
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06 Jun 2021, 06:58
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Yogananda
Weird numbers where unique unit digits are in the answer choices indicates that “units digit logic” (for lack of a better term) is the way to go. OP clearly knows how the GMAT works!
.............
Possible formations of 3345 where 5 is the units digit is determined by the possible formations of 334.
Possible formations of a string of N numbers or letters where repeats exist: N!/x!y!etc!
where x, y, and etc = number of repeats.
............
Possible formations of 334: 3!/2! = 3 (three total letters, two repeats).
So possible formations of 3345 where 5 is the units digit = 3
Possible formations of 3345 where 4 is the units digit = 4
...............
Possible formations of 3345 where 3 is the unit digit is a bit different, because it’s determined by the possible formations of 345 = 3! = 6
So possible formations of 3345 where 3 is the units digit = 6
..............
The possible formations of 3345 includes three 5s as the units digit, three 4s as the units digit, and six 3s as the units digit.
5 + 5 + 5 + 4 + 4 + 4 + 3 + 3 + 3 + 3 + 3 + 3 = 3(5) + 3(4) + 6(3) = units digit of 5
Only D fits
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