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When 45 is divided by the positive integer m, the remainder is 3. Which of the following statements about m must be true? I. m is even. II. m is a multiple of 7. III. m is a factor of 42.

Explanation	Calculations	Help
$Express the division of 45 by m with remainder 3 using the division statement.$	$45 = m \times q + 3$	Theory & Tactics Method Card TRANS5-F Click to view full details
$Subtract the remainder from 45 to find a multiple of m .$	$45 - 3 = m \times q$
$Simplify to see that m divides 42.$	$42 = m \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$List the positive divisors of 42 that are greater than the remainder (3).$	$Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42$
$Filter the factors to only those greater than the remainder (3).$	$Possible values for m : 6, 7, 14, 21, 42$
$Check statement I: Is m always even?$	$m = 6, 7, 14, 21, 42$
$Since 7 and 21 are odd, statement I is false.$	$7 and 21 are odd, so I is false.$
$Check statement II: Is m always a multiple of 7?$	$m = 6, 7, 14, 21, 42$
$Since 6 is not a multiple of 7, statement II is false.$	$6 is not a multiple of 7, so II is false.$
$Check statement III: Is m always a factor of 42?$	$m = 6, 7, 14, 21, 42$
$All possible values of m are factors of 42, so statement III is true.$	$All are factors of 42, so III is true.$

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A

When 45 is divided by the positive integer m, the remainder is 3. Which of the following statements about m must be true? I. m is even. II. m is a multiple of 7. III. m is a factor of 42.

Explanation	Calculations	Help
$Express the division of 45 by m with remainder 3 using the division statement.$	$45 = m \times q + 3$	Theory & Tactics Method Card TRANS5-F Click to view full details
$Subtract the remainder from 45 to find a multiple of m .$	$45 - 3 = m \times q$
$Simplify to see that m divides 42.$	$42 = m \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$List the positive divisors of 42 that are greater than the remainder (3).$	$Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42$
$Filter the factors to only those greater than the remainder (3).$	$Possible values for m : 6, 7, 14, 21, 42$
$Check statement I: Is m always even?$	$m = 6, 7, 14, 21, 42$
$Since 7 and 21 are odd, statement I is false.$	$7 and 21 are odd, so I is false.$
$Check statement II: Is m always a multiple of 7?$	$m = 6, 7, 14, 21, 42$
$Since 6 is not a multiple of 7, statement II is false.$	$6 is not a multiple of 7, so II is false.$
$Check statement III: Is m always a factor of 42?$	$m = 6, 7, 14, 21, 42$
$All possible values of m are factors of 42, so statement III is true.$	$All are factors of 42, so III is true.$

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A