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Apr 2808:00 AM PDT
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11 Jun 2020, 02:55
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D
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Difficulty:
45%
(medium)
Question Stats:
60% (01:30) correct
40%
(01:45)
wrong
based on 148
sessions
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If a and b are positive integers, what is the greatest common factor of a and b?
(1) The greatest common factor of half of a and half of b is 7.
(2) a is 14 and b is an even multiple of 21
Are You Up For the Challenge: 700 Level Questions
(1) The greatest common factor of half of a and half of b is 7.
(2) a is 14 and b is an even multiple of 21
Are You Up For the Challenge: 700 Level Questions
11 Jun 2020, 03:05
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St. 1:
If GCD of a/2 and b/2 is 7
=> GCD of a and b = 14
=> St.1 is sufficient
St. 2:
a = 14 = 2*7
b = 21*2*n = 2*7*3*n
So, GCD = 2*7 = 14
=> St.2 is sufficient
=> Answer: D
Posted from my mobile device
If GCD of a/2 and b/2 is 7
=> GCD of a and b = 14
=> St.1 is sufficient
St. 2:
a = 14 = 2*7
b = 21*2*n = 2*7*3*n
So, GCD = 2*7 = 14
=> St.2 is sufficient
=> Answer: D
Posted from my mobile device
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11 Jun 2020, 03:28
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IMO D
Statement 1: The greatest common factor of half of a and half of b is 7.
Therefore both a and b are multiple of 7
A = 7x
B = 7y
Since both are divisible by 2, and it leaves only 7 as other common factor so the value of no. Has to be 14*prime no. Such as (14*2,14*3,14*5......)
The only common no. Is 14
Therefore HCF is 14
(Sufficient)
Statement 2: a is 14 and b is an even multiple of 21
A = 14
B = 42,84,126........
When we take HCF of both no. A and B = 14(7*2*1)
(Sufficient)
Posted from my mobile device
Statement 1: The greatest common factor of half of a and half of b is 7.
Therefore both a and b are multiple of 7
A = 7x
B = 7y
Since both are divisible by 2, and it leaves only 7 as other common factor so the value of no. Has to be 14*prime no. Such as (14*2,14*3,14*5......)
The only common no. Is 14
Therefore HCF is 14
(Sufficient)
Statement 2: a is 14 and b is an even multiple of 21
A = 14
B = 42,84,126........
When we take HCF of both no. A and B = 14(7*2*1)
(Sufficient)
Posted from my mobile device
