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03 Aug 2022, 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:
95%
(hard)
Question Stats:
41% (02:38) correct
59%
(02:14)
wrong
based on 119
sessions
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What is the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9, which are divisible by 11 and no digit is repeated ?
A. 72
B. 60
C. 48
D. 36
E. 24
Are You Up For the Challenge: 700 Level Questions
A. 72
B. 60
C. 48
D. 36
E. 24
Are You Up For the Challenge: 700 Level Questions
03 Aug 2022, 08:23
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Bunuel
A number is divisible by 11 if the sum of the digits in the odd places of the number minus the sum of the digits in the even places of the number is either a multiple of 11 or zero.
Let's label the places of the number by calling it ABCDEF. (A+C+E)-(B+D+F) has to be either a multiple of 11 or zero.
The sum of all the available digits is 24. If one group is even, the other will be even; if one group is odd, the other will be odd. If we subtract an even from an even, we get an even, so can't be 11. If we subtract an odd from an odd, we get an even, so can't be 11. We also can't get a multiple of 11, as that would require us to have 23 in the first group and 1 in the second, but the minimum sum for a group is 3: {0,1,2}.
Soooo, we must have two groups that sum to the same amount, and since both groups combined sum to 24, each group sums to 12.
There are two ways to make a group that sums to 12: {0,5,7} and {1,2,9}.
If we distribute one of those groups to ACE and distribute the other to BDF, (A+C+E)-(B+D+F) will equal 0. There are two possible cases.
Case 1: ACE is {0,5,7} and BDF is {1,2,9}
How many ways are there to choose A? It can't be 0 or we would have a 5-digit number, so there are two options. 2.
How many ways are there to choose B? 3.
How many ways are there to choose C? 2.
How many ways are there to choose D? 2.
How many ways are there to choose E? 1.
How many ways are there to choose F? 1.
2*3*2*2*1*1 = 24
Case 2: ACE is {1,2,9} and BDF is {0,5,7}
How many ways are there to choose A? 3.
How many ways are there to choose B? 3.
How many ways are there to choose C? 2.
How many ways are there to choose D? 2.
How many ways are there to choose E? 1.
How many ways are there to choose F? 1.
3*3*2*2*1*1 = 36
Add those together and we have our total.
24+36 = 60
Answer choice B.
General Discussion
14 Jul 2025, 06:28
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