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14 Oct 2022, 01:26
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Difficulty:
85%
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Question Stats:
51% (02:48) correct
49%
(02:41)
wrong
based on 114
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Q. How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 such that the number is a multiple of 4? (Repetitions of digits not allowed)
A.72
B.63
C.60
D.36
E.27
A.72
B.63
C.60
D.36
E.27
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14 Oct 2022, 13:52
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Snehaaaaa
Number will be divisible by four if its last two digits are divisible by 4. So possible values of last two digits are 04,12,20,24,32,40,52
Now these number can be divided into two groups
a) when last two digits contain zero
b) when last two digits doesn't contain zero
a) when last two digit contains zero, let 4 digit number be abcd. now since cd are fixed. A, can take 4 values from the balance 4 numbers, and B can take 3 values from the remaining 3 numbers. Additionally, since 3 cases exists in which 0 comes in the last two digits. so total number of cases are
4.3.3 = 36 (first 4 for a, second 3 for b, and last 3 for remaining 2 digits)
b) when last two digits doesn't contains zero. In this case A can take 3 values (as zero cannot appear in the A, Why ? if we have zero in first place then number will become 3 digit number). B can have 3 values (as zero can come in this position), and there are 4 such cases in which 0 doesn't come in the last two digits. so total number of cases are
3.3.4 = 36
so overall cases = 36+36 = 72 hence A
14 Oct 2022, 21:20
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A number is divisible by 4 if the last 2 digits are a multiple of 4, ie xx04, xx08, xx12, etc.
Unique endings of the tens digit and ones digit from these 6 numbers are the following:
12, 24, 32, 20, 04, 52, 40
no 4 digit number can start with zero and there are no repetitions, so 3 digits can fill the thousands spot and 3 digits (include zero now) can fill the hundreds spot.
For example, look at xx12, we will count the permutations
3012
4012
5012
3412
3512
4312
4512
5412
5312
If zero is in the tens or ones spot, as in xx04, xx20 and xx40, then there are 12 permutations each for a total of 36.
Total is 72.
Unique endings of the tens digit and ones digit from these 6 numbers are the following:
12, 24, 32, 20, 04, 52, 40
no 4 digit number can start with zero and there are no repetitions, so 3 digits can fill the thousands spot and 3 digits (include zero now) can fill the hundreds spot.
For example, look at xx12, we will count the permutations
3012
4012
5012
3412
3512
4312
4512
5412
5312
If zero is in the tens or ones spot, as in xx04, xx20 and xx40, then there are 12 permutations each for a total of 36.
Total is 72.
