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A
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Difficulty:
35%
(medium)
Question Stats:
60% (01:08) correct
40%
(01:08)
wrong
based on 151
sessions
History
Date
Time
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Not Attempted Yet
x and y are two positive integers. Is x divided by y an integer?
(1) All of y's factors are also factors of x.
(2) Each prime factor of y is also a prime factor of x.
(1) All of y's factors are also factors of x.
(2) Each prime factor of y is also a prime factor of x.
23 Jul 2019, 01:21
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kavach
Given: x and y are two positive integers.
Asked: Is x divided by y an integer?
(1) All of y's factors are also factors of x.
If All of y's factors are also factors of x. => x is divisible by y => x divided by y is an integer
Take for example x=12 y=3 => all factors of 3 are also factors of 12 => 12 is divisible by 3.
SUFFICIENT
(2) Each prime factor of y is also a prime factor of x.
Take for example, \(y=p_1^3p_2^4\) and \(x=p_1p_2\) where\(p_1 & p_2\) are prime numbers
Each prime factor of y is also a prime factor of x
But x is NOT divisible by y => x/y is not an integer.
But if \(x=p_1^3p_2^4\) and \(y=p_1p_2\) where\(p_1 & p_2\) are prime numbers
Each prime factor of y is also a prime factor of x
And x is divisible by y => x/y is an integer.
NOT SUFFICIENT
IMO A
26 Jul 2019, 12:38
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kavach
Sometimes I myself don't understand how I get some questions right so quickly.
Anyway,
Basically question is asking if remainder is 0.
A. It basically assures everything in the denominator will cancel out with numerator which means remainder will be 0 no matter what. Sufficient.
B. It says all prime factors of denominator are present in numerator too. which is fine but what if numerator is 3*4 and denominator is 3*4*4*4*4. It won't work then even though both 2 and 3 are present in numerator.
I hope it makes sense! I am always open to criticism. Thank you and do not forget kudos.!
