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26 Jun 2023, 08:17
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C
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54% (01:53) correct
46%
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based on 129
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If q is a positive integer, does q^2 have exactly 3 positive factors?
(1) LCM of q and 7 is 14.
(2) GCD of q and 7 is 7.
(1) LCM of q and 7 is 14.
(2) GCD of q and 7 is 7.
26 Jun 2023, 08:30
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RenB
If q is a positive integer, does q^2 have exactly 3 positive factors?
(1) LCM of q and 7 is 14.
(2) GCD of q and 7 is 7.
(1) LCM of q and 7 is 14.
(2) GCD of q and 7 is 7.
Question: does \(q^2 \) have exactly 3 positive factors
Inference: Is q prime ?
Statement 1
(1) LCM of q and 7 is 14
Case 1: q = 2; LCM (2,7) = 14
Is q prime → Yes
Case 2: q = 14; LCM (14,7) = 14
Is q prime → No
As we have contradictory answers to the question, this statement alone is not sufficient. We can eliminate A and D.
Statement 2
(2) GCD of q and 7 is 7
Case 1: q = 7; GCD (7,7) = 7
Is q prime → Yes
Case 2: q = 14; GCD (14,7) = 7
Is q prime → No
As we have contradictory answers to the question, this statement alone is not sufficient. We can eliminate B.
Combined
LCM * GCD = Product of two numbers
q * 7 = 14 * 7
q = 14
Is q prime → No
We have a definite answer, Option C
18 Aug 2024, 07:22
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