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If a and b are integers, and a is a factor of b, what must be true?
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09 Jul 2021, 08:32
09 Jul 2021, 08:32
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If a and b are integers, and a is a factor of b, what must be true?
I) \(a < b\)
II) The distinct prime factors of \(a^{2}\) are also factors of \(b\).
III) \(0<\frac{a}{b}\leq{1}\)
A) None
B) II only
C) III only
D) I and II only
E) II and III only
I) \(a < b\)
II) The distinct prime factors of \(a^{2}\) are also factors of \(b\).
III) \(0<\frac{a}{b}\leq{1}\)
A) None
B) II only
C) III only
D) I and II only
E) II and III only
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If a and b are integers, and a is a factor of b, what must be true?
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11 Jul 2021, 21:26
11 Jul 2021, 21:26
1
GeminiHeat wrote:
If a and b are integers, and a is a factor of b, what must be true?
I) \(a < b\)
II) The distinct prime factors of \(a^{2}\) are also factors of \(b\).
III) \(0<\frac{a}{b}\leq{1}\)
A) None
B) II only
C) III only
D) I and II only
E) II and III only
I) \(a < b\)
II) The distinct prime factors of \(a^{2}\) are also factors of \(b\).
III) \(0<\frac{a}{b}\leq{1}\)
A) None
B) II only
C) III only
D) I and II only
E) II and III only
I. \(a < b\)
A factor of a number is always less than or equal to the given number for a +ve number
But, A factor of a number can be less than, greater than or equal to the given number for a -ve number
Examples:
\(4 = (2)(2)\) where, \(2 < 4\)
\(-4 = (-2)(2)\) where, \(-2 > -4\)
II. The distinct prime factors of \(a^{2}\) are also factors of \(b\)
The DISTICT prime factors of \(a^2\) will always be same as that of \(a\)
Example:
\(30 = (2)(3)(5)\)
Distinct prime factors are 2, 3, and 5
\(30^2 = (2^2)(3^3)(5^2)\)
Distinct prime factors are 2, 3, and 5
III. \(0 < \frac{a}{b} ≤ 1\)
Take the same example as in I;
\(4 = (2)(2), 0 < \frac{2}{4} ≤ 1\) is True
\(-4 = (-2)(2), 0 < \frac{2}{-4} ≤ 1\) is False
Hence, option B
gmatclubot
If a and b are integers, and a is a factor of b, what must be true? [#permalink]
11 Jul 2021, 21:26
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