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Apr 2808:00 AM PDT
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10 Jan 2023, 11:15
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D
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Difficulty:
95%
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Question Stats:
39% (02:26) correct
61%
(02:20)
wrong
based on 61
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The greatest common factor of two positive integers x and y is 22. What is the value of |x - y| ?
(1) The least common factor of x and y is 66.
(2) x + y is 88.
(1) The least common factor of x and y is 66.
(2) x + y is 88.
10 Jan 2023, 11:33
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The numbers should be 22 and 66. HCF- 22 (11*2 & 11*3*2).
Now (1) says LCM is 66. So |x-y|= 33. A sufficient.
Going for (2) 22+66= 88.
So |22-66|= 33. B is sufficient. So, answer should be D. Each statement alone is sufficient.
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Now (1) says LCM is 66. So |x-y|= 33. A sufficient.
Going for (2) 22+66= 88.
So |22-66|= 33. B is sufficient. So, answer should be D. Each statement alone is sufficient.
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11 Jan 2023, 23:14
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Bunuel
We know that x and y both have 2 * 11 as its factors.
Statement 1
(1) The least common factor of x and y is 66.
x and y combined have 2 * 11 * 3 as its prime factors
Now the possible combinations are
x = 3 * 2 * 11 | y = 2 * 11
or
x = 2 * 11 | y = 3 * 2 * 11
Note, we cannot have x = 3 * 2 * 11 | y = 3 * 2 * 11 as that possibility will change the GCD.
In both cases, |x -y| = 22
Sufficient.
Statement 2
(1) x + y is 88.
Assume
\(x = 22 * p_1\)
\(y = 22 * p_2\)
Given
x + y = 88
\(22 * p_1 + 22 * p_2 = 88\)
\(22(p_1 + p_2) = 88\)
\(p_1 + p_2 = 4\)
Both p_1 & p_2 should be > 0
Possible values
\(p_1 = 1 \quad| \quad p_2 = 3\)
\(p_1 = 2 \quad| \quad p_2 = 2 \) ⇒ Not possible because if \(p_1\) and \(p_2\) are even, the GCD changes.
\(p_1 = 3 \quad| \quad p_2 = 1\)
For the other possibility, |x - y| = 44
Sufficient.
Option D
