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06 Sep 2020, 09:52
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Difficulty:
15%
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Question Stats:
80% (01:04) correct
20%
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wrong
based on 94
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If x is a positive integer, is x^2 divisible by 24?
(1) x is divisible by 4
(2) x is divisible by 6
(1) x is divisible by 4
(2) x is divisible by 6
06 Sep 2020, 11:04
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for 24 number should be divisible by 8 and 3
case1: It is divisible by 4 but what about 3 so not sufficient.
case 2: It is divisible by 6 but about divisibility of 8 so not sufficient.
case 3: Combining both we find 4*6=24 which is divisible by both 8 and 3 so sufficient.
case1: It is divisible by 4 but what about 3 so not sufficient.
case 2: It is divisible by 6 but about divisibility of 8 so not sufficient.
case 3: Combining both we find 4*6=24 which is divisible by both 8 and 3 so sufficient.
07 Sep 2020, 21:11
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This is a YES/NO type of question, where plugging in of values will help.
Question: Is x^2[/m] is divisible by 24
Constraint: x is a positive integer (x \(\neq 0\))
Statement 1: x is divisible by 4.
If x = 4 (which is divisible by 4), then x^2[/m] = 16 (which is not divisible by 24) . Therefore NO.
If x = 12 (which is divisible by 4), then x^2[/m] = 144 (which is divisible by 24). Therefore YES.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E.
Statement 2: x is divisible by 6.
If x = 6 (which is divisible by 6), then x^2[/m] = 36 (which is not divisible by 24) . Therefore NO.
If x = 12 (which is divisible by 6), then x^2[/m] = 144 (which is divisible by 24). Therefore YES.
Therefore Statement 2 Alone is Insufficient. Answer Options could be C or E.
Combining Both Statements: x is divisible by 4 and 6, which means x is divisible by 12
The minimum value of x here is 12 = 4 * 3 = \(2^2 * 3\). The square will be \(2^4 * 3^2\)
For a number to be divisible by 24, we need an 8 = \(2^3\) and a \(3\), which will always be there in the squares of multiples of 12.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
Question: Is x^2[/m] is divisible by 24
Constraint: x is a positive integer (x \(\neq 0\))
Statement 1: x is divisible by 4.
If x = 4 (which is divisible by 4), then x^2[/m] = 16 (which is not divisible by 24) . Therefore NO.
If x = 12 (which is divisible by 4), then x^2[/m] = 144 (which is divisible by 24). Therefore YES.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E.
Statement 2: x is divisible by 6.
If x = 6 (which is divisible by 6), then x^2[/m] = 36 (which is not divisible by 24) . Therefore NO.
If x = 12 (which is divisible by 6), then x^2[/m] = 144 (which is divisible by 24). Therefore YES.
Therefore Statement 2 Alone is Insufficient. Answer Options could be C or E.
Combining Both Statements: x is divisible by 4 and 6, which means x is divisible by 12
The minimum value of x here is 12 = 4 * 3 = \(2^2 * 3\). The square will be \(2^4 * 3^2\)
For a number to be divisible by 24, we need an 8 = \(2^3\) and a \(3\), which will always be there in the squares of multiples of 12.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
