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01 Oct 2020, 02:45
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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:
75%
(hard)
Question Stats:
53% (01:49) correct
47%
(01:48)
wrong
based on 251
sessions
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Not Attempted Yet
If a and b are positive integers and k is the greatest common factor of a and b, then k must be the greatest common factor of a and which of the following integers?
A. a + b
B. 3 + b
C. ab
D. 3b
E. b^2
A. a + b
B. 3 + b
C. ab
D. 3b
E. b^2
01 Oct 2020, 10:50
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Bunuel
One way to do this problem is to plug in for a and b. There are many numbers you could use. Let's use a = 4 and b = 2. Then the GCF is k = 2. Now look at the answer choices:
→ A) a + b = 6. The GCD of 4 and 6 is 2. KEEP.
→ B) 3 + b = 5. The GCD of 4 and 5 is 1. ELIMINATE.
→ C) ab = 8. The GCD of 4 and 8 is 4. ELIMINATE.
→ D) 3b = 6. The GCD of 4 and 6 is 2. KEEP.
→ E) b^2 = 4. The GCD of 4 and 4 is 4. ELIMINATE.
Only A and D are left. It's probably safe to eliminate D because the 3 seems pretty random. If you are unsure, you could also plug in again to decide between the two. Try to find numbers that will eliminate D since it is suspect. You could make b one-third of a.
If a = 9 and b = 3, then the GCF is k = 3.
→ A) a + b = 12. The GCD of 9 and 12 is 3. KEEP.
→ D) 3b = 9. The GCD of 9 and 9 is 9. ELIMINATE.
The answer is (A).
01 Oct 2020, 12:03
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a=k*m
b=k*n
where m and n are coprimes
if m is coprime to n, then m or n is coprime to both m+n and m-n.
a+b=k(m+n) and a=k*m; GCD(a+b,a)=k
A
b=k*n
where m and n are coprimes
if m is coprime to n, then m or n is coprime to both m+n and m-n.
a+b=k(m+n) and a=k*m; GCD(a+b,a)=k
A
Bunuel
