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Updated on: 26 Jul 2020, 11:23
Originally posted by sarphant123 on 26 Jul 2020, 11:20.
Last edited by Bunuel on 26 Jul 2020, 11:23, edited 1 time in total.
Last edited by Bunuel on 26 Jul 2020, 11:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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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:
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69% (01:28) correct
31%
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If x is a positive integer, is x^4 divisible by 16?
(1) x^2 is divisible by 20.
(2) x is divisible by 25.
(1) x^2 is divisible by 20.
(2) x is divisible by 25.
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26 Jul 2020, 12:46
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If x is a positive integer, is x^4 divisible by 16?
(1) x^2 is divisible by 20.
x^2 has to be a multiple of 20 = 20n (N is an integer
since X is an integer,
the minimum value of x = √20n
x = √2*2*5*n
n has to be 5 for x to be integer.
x = 10
other values will be multiple of 10, so 10m
therefore 10m^4 will never be divisible by 16
(Sufficient)
(2) x is divisible by 25.
X = 25n
now n can be any integer, 1,2,3,4,.........16..32.....
for which X^4 is not always divisible by 16
(insufficient)
Answer is A
(1) x^2 is divisible by 20.
x^2 has to be a multiple of 20 = 20n (N is an integer
since X is an integer,
the minimum value of x = √20n
x = √2*2*5*n
n has to be 5 for x to be integer.
x = 10
other values will be multiple of 10, so 10m
therefore 10m^4 will never be divisible by 16
(Sufficient)
(2) x is divisible by 25.
X = 25n
now n can be any integer, 1,2,3,4,.........16..32.....
for which X^4 is not always divisible by 16
(insufficient)
Answer is A
Updated on: 27 Sep 2020, 06:02
Originally posted by CrackverbalGMAT on 26 Jul 2020, 13:24.
Last edited by CrackverbalGMAT on 27 Sep 2020, 06:02, edited 1 time in total.
Last edited by CrackverbalGMAT on 27 Sep 2020, 06:02, edited 1 time in total.
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Constraint: x is a positive Integer
To Answer: is \(x^4\), divisible by 16
Statement (1): \(x^2\) is divisible by 20.
For \(x^2\) to be divisible by 20, x has to be any 2 digit number ending in 0, x = 10, 20, 30 and so on
If x = 10, \(x^2\) = 100 which is divisible by 20 and \(x^4\) = 1 * 10,000 which is divisible by 16.
If x = 20, \(x^2\) = 400 which is divisible by 20 and \(x^4\) = 16 * 10,000 which is divisible by 16.
If x = 30, \(x^2\) = 900 which is divisible by 20 and \(x^4\) = 81 * 10,000 which is divisible by 16.
\(x^4 \) for any of the values of x will have a minimum of 4 zeroes in the end and hence will always be divisible by 16.
Statement (1) is Sufficient.
The answer could be A or D
Statement (2): x is divisible by 25.
For x to be divisible by 25. x = 25, 50, 75, 100, 150, 200, 400, 800 and so on.
If x = 25, \(x^4 \) = 390625 and this is not divisible by 16.
If x = 50, \(x^4 \) = 625 * 10,000 and this is divisible by 16.
\(x^4 \) for numbers ending 5 are odd and can never be divisible by 16, whereas \(x^4 \) for x ending with a 0 will always be divisible by 16.
Since we have 2 conflicting statements , Statement (2) is Insufficient.
Option A
Arun Kumar
To Answer: is \(x^4\), divisible by 16
Statement (1): \(x^2\) is divisible by 20.
For \(x^2\) to be divisible by 20, x has to be any 2 digit number ending in 0, x = 10, 20, 30 and so on
If x = 10, \(x^2\) = 100 which is divisible by 20 and \(x^4\) = 1 * 10,000 which is divisible by 16.
If x = 20, \(x^2\) = 400 which is divisible by 20 and \(x^4\) = 16 * 10,000 which is divisible by 16.
If x = 30, \(x^2\) = 900 which is divisible by 20 and \(x^4\) = 81 * 10,000 which is divisible by 16.
\(x^4 \) for any of the values of x will have a minimum of 4 zeroes in the end and hence will always be divisible by 16.
Statement (1) is Sufficient.
The answer could be A or D
Statement (2): x is divisible by 25.
For x to be divisible by 25. x = 25, 50, 75, 100, 150, 200, 400, 800 and so on.
If x = 25, \(x^4 \) = 390625 and this is not divisible by 16.
If x = 50, \(x^4 \) = 625 * 10,000 and this is divisible by 16.
\(x^4 \) for numbers ending 5 are odd and can never be divisible by 16, whereas \(x^4 \) for x ending with a 0 will always be divisible by 16.
Since we have 2 conflicting statements , Statement (2) is Insufficient.
Option A
Arun Kumar
