When 50 is divided by the positive integer $p$, th... | Free GMAT Practice Question | GMAT Panda

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When 50 is divided by the positive integer p, the remainder is 8 . 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 21 .

Explanation	Calculations	Help
$We express the fact "50 is divided by p, the remainder is 8" as a division statement.$	$50 = p \times q + 8$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We then subtract 8 from both sides to find a multiple of p.$	$50 - 8 = p \times q$
$We simplify to see that p divides 42.$	$42 = p \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$We list the positive divisors of 42 that could equal p given p must exceed the remainder.$	$Divisors of 42 = 1, 2, 3, 6, 7, 14, 21, 42 Possible values for p : 14, 21, 42$
$We check statement I by seeing if p must be even.$	$p = 14, 21, 42 21 is odd$
$We check statement II by seeing if p must be a multiple of 7.$	$p = 14, 21, 42 All are multiples of 7$
$We check statement III by seeing if p must be a factor of 21.$	$p = 14, 21, 42 14 and 42 are not factors of 21$

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B

When 50 is divided by the positive integer p, the remainder is 8 . 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 21 .

Explanation	Calculations	Help
$We express the fact "50 is divided by p, the remainder is 8" as a division statement.$	$50 = p \times q + 8$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We then subtract 8 from both sides to find a multiple of p.$	$50 - 8 = p \times q$
$We simplify to see that p divides 42.$	$42 = p \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$We list the positive divisors of 42 that could equal p given p must exceed the remainder.$	$Divisors of 42 = 1, 2, 3, 6, 7, 14, 21, 42 Possible values for p : 14, 21, 42$
$We check statement I by seeing if p must be even.$	$p = 14, 21, 42 21 is odd$
$We check statement II by seeing if p must be a multiple of 7.$	$p = 14, 21, 42 All are multiples of 7$
$We check statement III by seeing if p must be a factor of 21.$	$p = 14, 21, 42 14 and 42 are not factors of 21$

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B