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31 Jul 2018, 22:03
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E
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Difficulty:
25%
(medium)
Question Stats:
69% (01:15) correct
31%
(01:03)
wrong
based on 334
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Is the positive integer x prime?
(1) The Greatest Common Factor of x and y is 1.
(2) The Least Common Multiple of x and y is xy.
(1) The Greatest Common Factor of x and y is 1.
(2) The Least Common Multiple of x and y is xy.
31 Jul 2018, 22:11
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Bunuel
Is the positive integer x prime?
(1) The Greatest Common Factor of x and y is 1.
(2) The Least Common Multiple of x and y is xy.
(1) The Greatest Common Factor of x and y is 1.
(2) The Least Common Multiple of x and y is xy.
Statement 1:
Suppose x=9 ,y=2 GCF = 1 . X is not prime
If x=2, y=9 GCF = 1 . X is prime
Insufficient
Statement2:
Suppose x=9 ,y=2 LCM = xy = 18 . X is not prime
If x=2, y=9 LCM = xy = 18 . X is prime
Insufficient
1&2: Give same data
Hence E
General Discussion
01 Aug 2018, 00:41
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Hi,
Again this question, if we know the below simple properties then it’s just a 20-sec problem.
Product of two numbers = Products of their HCF and LCM
• If two numbers are m and n, then HCF of m and n cannot be larger than the difference between m and n
• Two consecutive numbers (x and x+1) can share no factors other than 1, HCF will be 1 and LCM will be x(x + 1).
Two numbers are called co-prime(relatively prime) if HCF of two numbers is 1 and LCM is product of two numbers.
For two numbers to be co-prime not necessary that numbers has to be prime.
If you don’t know the below above rule, then don’t hesitate plug in numbers.
Question is “x” prime ?
That’s is, whether x = 2,3,5,7,11, ….
Statement I is insufficient:
The Greatest Common Factor of x and y is 1.
If x = 2 and y =3 , then G.C.F is 1 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then G.C.F is 1 and answer to the question is NO(x is not prime).
Statement II is insufficient:
The Least Common Multiple of x and y is xy.
We can take the same examples,
If x = 2 and y =3 , then L.C.M is 6 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then L.C.M is 12 and answer to the question is NO(x is not prime).
Together also we can use the same numbers,
So not sufficient.
Answer is E.
Again this question, if we know the below simple properties then it’s just a 20-sec problem.
Product of two numbers = Products of their HCF and LCM
• If two numbers are m and n, then HCF of m and n cannot be larger than the difference between m and n
• Two consecutive numbers (x and x+1) can share no factors other than 1, HCF will be 1 and LCM will be x(x + 1).
Two numbers are called co-prime(relatively prime) if HCF of two numbers is 1 and LCM is product of two numbers.
For two numbers to be co-prime not necessary that numbers has to be prime.
If you don’t know the below above rule, then don’t hesitate plug in numbers.
Question is “x” prime ?
That’s is, whether x = 2,3,5,7,11, ….
Statement I is insufficient:
The Greatest Common Factor of x and y is 1.
If x = 2 and y =3 , then G.C.F is 1 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then G.C.F is 1 and answer to the question is NO(x is not prime).
Statement II is insufficient:
The Least Common Multiple of x and y is xy.
We can take the same examples,
If x = 2 and y =3 , then L.C.M is 6 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then L.C.M is 12 and answer to the question is NO(x is not prime).
Together also we can use the same numbers,
So not sufficient.
Answer is E.
