When $63$ is divided by the positive integer $p$, ... | Free GMAT Practice Question | GMAT Panda

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When 63 is divided by the positive integer p, the remainder is 7 . Which of the following statements about p must be true? I. p is even. II. p is a multiple of 7 . III. p is a factor of 112 .

Explanation	Calculations	Help
$We express the condition that "the remainder is 7" using a division statement.$	$63 = p \times q + 7$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We then subtract the remainder to find a multiple of p .$	$63 - 7 = p \times q$
$We simplify to obtain that p divides 56 .$	$56 = p \times q$	Theory & Tactics Method Card DIV0 Click to view full details
$We list all positive factors of 56 that are greater than the remainder.$	$Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56 Possible values for p : 8, 14, 28, 56$
$For I, we check if p is always even by examining the candidates.$	$p = 8, 14, 28, 56 All are even, so I is true.$
$For II, we check if p is always a multiple of 7 .$	$p = 8, 14, 28, 56 8 is not a multiple of 7, so II is false.$
$For III, we check if p is always a factor of 112 .$	$p = 8, 14, 28, 56 All divide 112 evenly, so III is true.$

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E

When 63 is divided by the positive integer p, the remainder is 7 . Which of the following statements about p must be true? I. p is even. II. p is a multiple of 7 . III. p is a factor of 112 .

Explanation	Calculations	Help
$We express the condition that "the remainder is 7" using a division statement.$	$63 = p \times q + 7$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We then subtract the remainder to find a multiple of p .$	$63 - 7 = p \times q$
$We simplify to obtain that p divides 56 .$	$56 = p \times q$	Theory & Tactics Method Card DIV0 Click to view full details
$We list all positive factors of 56 that are greater than the remainder.$	$Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56 Possible values for p : 8, 14, 28, 56$
$For I, we check if p is always even by examining the candidates.$	$p = 8, 14, 28, 56 All are even, so I is true.$
$For II, we check if p is always a multiple of 7 .$	$p = 8, 14, 28, 56 8 is not a multiple of 7, so II is false.$
$For III, we check if p is always a factor of 112 .$	$p = 8, 14, 28, 56 All divide 112 evenly, so III is true.$

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E