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07 Dec 2021, 03:30
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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:
55%
(hard)
Question Stats:
53% (01:42) correct
47%
(02:00)
wrong
based on 75
sessions
History
Date
Time
Result
Not Attempted Yet
Each of the following numbers has two digits blotted out. Which of the numbers could be the number of hours in x days, where x is an integer?
(A) \(25\blacksquare,\blacksquare06\)
(B) \(50\blacksquare ,\blacksquare 26\)
(C) \(56\blacksquare ,\blacksquare 02\)
(D) \(62\blacksquare ,\blacksquare 50\)
(E) \(65\blacksquare ,\blacksquare 20\)
Are You Up For the Challenge: 700 Level Questions
(A) \(25\blacksquare,\blacksquare06\)
(B) \(50\blacksquare ,\blacksquare 26\)
(C) \(56\blacksquare ,\blacksquare 02\)
(D) \(62\blacksquare ,\blacksquare 50\)
(E) \(65\blacksquare ,\blacksquare 20\)
Are You Up For the Challenge: 700 Level Questions
07 Dec 2021, 12:16
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Bunuel
We know that 1 day has 24 hours, so x days will have x * 24 hours
A multiple of 24 means, the number must be divisible by 4 & 3
If last two digits of a number are divisible by 4, whole number is divisible by 4
Scanning through the options, only option E holds true!
armaankumar
Joined: 10 Jun 2020
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08 Dec 2021, 06:05
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Bunuel
The correct answer must be a multiple of 24.
Prime Factorization of 24 = 2^3 * 3
The correct answer will be divisible 2^3 and 3.
Since we don't know the entire number, we can't use the divisibility rules of 3 and 8.
Therefore, we'll use the divisibility rule of 4 (Any number divisible by 8 is also divisible by 4)
Divisibility Rule of 4: Last two digits are divisible by 4
Only option (e) meets the condition.
Alternative Solution:
Divisibility Rule for 8: Last 3 digits are divisible by 8 or the number can be halved thrice.
(A) \(25\blacksquare,\blacksquare06\) This option can halved only once because then it will have 3 in the unit's digit.
(B) \(50\blacksquare ,\blacksquare 26\) This option can halved only once because then it will have 3 in the unit's digit.
(C) \(56\blacksquare ,\blacksquare 02\) This option can halved only once because then it will have 1 in the unit's digit.
(D) \(62\blacksquare ,\blacksquare 50\) This option can halved only once because then it will have 5 in the unit's digit.
(E) \(65\blacksquare ,\blacksquare 20\) This option is the only option left which can be halved thrice
