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Is the positive integer x prime?

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Is the positive integer x prime?  [#permalink]

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New post 31 Jul 2018, 22:03
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:13) correct 39% (00:55) wrong based on 41 sessions

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Re: Is the positive integer x prime?  [#permalink]

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New post 31 Jul 2018, 22:11
1
Bunuel wrote:
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.


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
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Re: Is the positive integer x prime?  [#permalink]

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New post 01 Aug 2018, 00:41
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.
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Re: Is the positive integer x prime? &nbs [#permalink] 01 Aug 2018, 00:41
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