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26 Feb 2021, 04:00
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C
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:
63% (02:27) correct
37%
(02:29)
wrong
based on 317
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Number of 5 digit numbers divisible by 25 that can be formed using only the digits 1, 2, 3, 4, 5, & 0 taken five at a time is
(A) 2
(B) 32
(C) 42
(D) 52
(E) 62
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 2
(B) 32
(C) 42
(D) 52
(E) 62
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
26 Feb 2021, 04:12
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Bunuel
For a number to be divisible by 25, its last two digits must be 25 or 50.
Case 1: Last two digits are 25
Number of options for the ten-thousands digit = 3. (1, 3 or 4)
Number of options for the thousands digit = 3. (Any of the 3 remaining digits)
Number of options for the hundreds digit = 2. (Either of the 2 remaining digits)
To combine these options, we multiply:
3*3*2 = 18
Case 2: Last two digits are 50
Number of options for the ten-thousands digit = 4. (Any of the 4 remaining digits)
Number of options for the thousands digit = 3. (Any of the 3 remaining digits)
Number of options for the hundreds digit = 2. (Either of the 2 remaining digits)
To combine these options, we multiply:
4*3*2 = 24
Total ways = Case 1 + Case 2 = 18+24 = 42
26 Feb 2021, 05:44
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Bunuel
CONCEPT
: For a number to be divisible by 25, Last two digits of number must be either 00, 25, 50 or 75Digits to be used are 1, 2, 3, 4, 5, & 0 and we need to use 5 digits at a time out of them to make 5 digit numbers i.e. repetition of digits is NOT allowed
Last two digits can only be {25, and 50}
Case 1: _ _ _ 2 5
Left most place can be filled in 3 ways (except using digits 0, 2 and 5}
Second Left most place can be filled in 3 ways (except using digits 2, 5 and used at ten thousands place}
Third Left most place can be filled in 2 ways (except using digits 2, 5 and used at ten thousands and thousands place}
Total Numbers = 3*3*2 = 18
Case 2: _ _ _ 5 0
Left most place can be filled in 4 ways (except using digits 0 and 5}
Second Left most place can be filled in 3 ways (except using digits 0, 5 and used at ten thousands place}
Third Left most place can be filled in 2 ways (except using digits 0, 5 and used at ten thousands and thousands place}
Total Numbers = 4*3*2 = 24
Total Favorable numbers = 18+24 = 42
Answer: Option C
