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

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When 50 is divided by the positive integer n, the remainder is 10. 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 30.

Explanation	Calculations	Help
$We express the division with remainder.$	$50 = n \times q + 10$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We subtract the remainder to find a multiple of n .$	$50 - 10 = n \times q$
$We simplify to see that n divides 40.$	$40 = n \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$We list all positive divisors of 40 that exceed the remainder 10.$	$Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40 Possible values for n : 20, 40$
$We check "n is even" and see that both possible values of n are even, so statement I is true.$	$n = 20, 40$
$We check "n is a multiple of 5" and see that both possible values of n are multiples of 5, so statement II is true.$	$n = 20, 40$
$We check "n is a factor of 30" and see that neither 20 nor 40 is a factor of 30, so statement III is false.$	$n = 20, 40$

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C

When 50 is divided by the positive integer n, the remainder is 10. 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 30.

Explanation	Calculations	Help
$We express the division with remainder.$	$50 = n \times q + 10$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We subtract the remainder to find a multiple of n .$	$50 - 10 = n \times q$
$We simplify to see that n divides 40.$	$40 = n \times q$	Theory & Tactics Method Card TRANS5-E Click to view full details
$We list all positive divisors of 40 that exceed the remainder 10.$	$Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40 Possible values for n : 20, 40$
$We check "n is even" and see that both possible values of n are even, so statement I is true.$	$n = 20, 40$
$We check "n is a multiple of 5" and see that both possible values of n are multiples of 5, so statement II is true.$	$n = 20, 40$
$We check "n is a factor of 30" and see that neither 20 nor 40 is a factor of 30, so statement III is false.$	$n = 20, 40$

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C