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08 Feb 2021, 09:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:37) correct
34%
(01:27)
wrong
based on 129
sessions
History
Date
Time
Result
Not Attempted Yet
How many odd numbers less than 1000 can be formed using the digits 0, 1, 4 and 7 if repetition of digits is allowed?
A. 12
B. 14
C. 16
D. 24
E. 32
A. 12
B. 14
C. 16
D. 24
E. 32
08 Feb 2021, 09:25
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How many odd numbers less than 1000 can be formed using the digits 0, 1, 4 and 7 if repetition of digits is allowed?
A. 12
B. 14
C. 16
D. 24
E. 32
I used the dumb way to solve this, "less than 1000" means the number can range from single digit to 3 digits, and the numbers can be re0used according to prompt. I list them below ranging by value (small to big) so we don't miss any
single digit odd number: 1,7
double digit odd number: 11,17, 41,47,71,77
Triple digit odd number (A lot of this kind): 101, 107, 111, 117, 141, 147, 171,177, 401, 407,411,417,441,447,471,477,701,707,711,717,741,747,771,777
I believe the answer is 24, hence D
A. 12
B. 14
C. 16
D. 24
E. 32
I used the dumb way to solve this, "less than 1000" means the number can range from single digit to 3 digits, and the numbers can be re0used according to prompt. I list them below ranging by value (small to big) so we don't miss any
single digit odd number: 1,7
double digit odd number: 11,17, 41,47,71,77
Triple digit odd number (A lot of this kind): 101, 107, 111, 117, 141, 147, 171,177, 401, 407,411,417,441,447,471,477,701,707,711,717,741,747,771,777
I believe the answer is 24, hence D
To form an off number the last digit should be an odd digit.
Therefore, number responsible to create odd are \(1,7\) from the list \(0,1,4,7\).
Now we have, 1 digit, 2 digit and 3-digit numbers;
Case 1: Three-digit number \(3 \times 4 \times 2 = 24\)
Case 2: Two-digit number \(3\times 2 = 6\)
Case 3: One digit \(2\)
Please refer to the attachment below for better visualization of ways to select numbers.
\(Total = 32\)
ANS E
Therefore, number responsible to create odd are \(1,7\) from the list \(0,1,4,7\).
Now we have, 1 digit, 2 digit and 3-digit numbers;
Case 1: Three-digit number \(3 \times 4 \times 2 = 24\)
Case 2: Two-digit number \(3\times 2 = 6\)
Case 3: One digit \(2\)
Please refer to the attachment below for better visualization of ways to select numbers.
\(Total = 32\)
ANS E
Attachments
Untitled2.png [ 6.47 KiB | Viewed 2305 times ]
