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happypuppy
GMAT 1: 720 Q50 V38 (Online)
Posts: 203
18 Sep 2022, 20:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:36) correct
46%
(02:40)
wrong
based on 166
sessions
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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
(Repetitions of digits not allowed)
A. 72
B. 63
C. 60
D. 36
E. 27
19 Sep 2022, 00:06
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happypuppy
Solution:
- A number is a multiple of 4 when the last 2 digits of the number are divisible by 4
- Based on the digits available, a 4-digit number can be divisible by 4 when the last two digits are 04, 12, 20, 24, 32, 40 and 52
- Number of 4 digit number with last digit 04 \(= 4 (1, 2, 3, 5)\times 3(\text{remaining from 1, 2, 3, 5})\times 1(0)\times 1(4)=12\)
- Number of 4 digit number with last digit 12 \(= 3 (3, 4, 5)\times 3(\text{remaining from 3, 4, 5 and 0})\times 1(1)\times 1(2)=9\)
- Number of 4 digit number with last digit 20 \(= 4 \times 3\times 1\times 1=12\)
- Number of 4 digit number with last digit 24 \(= 3 \times 3\times 1\times 1=9\)
- Number of 4 digit number with last digit 32 \(= 3 \times 3\times 1\times 1=9\)
- Number of 4 digit number with last digit 40 \(= 4 \times 3\times 1\times 1=12\)
- Number of 4 digit number with last digit 52 \(= 3 \times 3\times 1\times 1=9\)
- So, the total number of 4-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5 such that the number is a multiple of 4
\(=12+9+12+9+9+12+9=72\)
Hence the right answer is Option A
21 Sep 2022, 06:17
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I'm a little on the slow side in calculating all permutations listed in the explanation. Can anybody offer a quicker, more pragmatic approach?
