When 24 is divided by the positive integer $n$...... | Free GMAT Practice Question | GMAT Panda

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When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true? I. n is even. II. n is a multiple of 5 . III. n is a factor of 20 .

Explanation	Calculations	Help
$Express the division of 24 by n with remainder 4 using the division statement.$	$24 = n \times q + 4$
$Subtract the remainder from 24 to find a multiple of n .$	$24 - 4 = n \times q$
$Simplify to see that n divides 20.$	$20 = n \times q$
$List the positive divisors of 20 that are greater than the remainder (4).$	$Factors of 20 = 1, 2, 4, 5, 10, 20 Possible values for n : 5, 10, 20$
$Check statement I: Is n always even?$	$n = 5, 10, 20 5 is odd, so I is false.$
$Check statement II: Is n always a multiple of 5?$	$n = 5, 10, 20 5, 10, 20 are all multiples of 5, so II is true.$
$Check statement III: Is n always a factor of 20?$	$n = 5, 10, 20 5, 10, 20 are all factors of 20, so III is true.$

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D. II and III only

When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true? I. n is even. II. n is a multiple of 5 . III. n is a factor of 20 .

Explanation	Calculations	Help
$Express the division of 24 by n with remainder 4 using the division statement.$	$24 = n \times q + 4$
$Subtract the remainder from 24 to find a multiple of n .$	$24 - 4 = n \times q$
$Simplify to see that n divides 20.$	$20 = n \times q$
$List the positive divisors of 20 that are greater than the remainder (4).$	$Factors of 20 = 1, 2, 4, 5, 10, 20 Possible values for n : 5, 10, 20$
$Check statement I: Is n always even?$	$n = 5, 10, 20 5 is odd, so I is false.$
$Check statement II: Is n always a multiple of 5?$	$n = 5, 10, 20 5, 10, 20 are all multiples of 5, so II is true.$
$Check statement III: Is n always a factor of 20?$	$n = 5, 10, 20 5, 10, 20 are all factors of 20, so III is true.$

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D. II and III only