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GMAT Quant — Applied Mathematics (Word Problems)

A boardwalk is made up of n wooden planks of equal length, with an unpainted gap between each pair of consecutive planks. Each gap is \frac{2}{5} as long as one plank. The total length from the beginning of the first plank to the end of the last plank is 356 inches. If n is an integer and each gap length, in inches, is an integer greater than 3, what is the value of n ?

Explanation	Calculations	Help
$We name p as the length of each plank in inches.$	$p = length of each plank$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "the total length from the beginning of the first plank to the end of the last plank is 356 inches" into an equation by adding the lengths of all planks and gaps.$	$n p + (n - 1) \times \frac{2}{5} p = 356$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We combine like terms by factoring out p .$	$\frac{( 7 n - 2 ) p}{5} = 356$
$We clear the fraction by multiplying both sides by 5.$	$(7 n - 2) p = 1780$
$We name g as the length of each gap in inches and translate "each gap is 2/5 as long as one plank" into an equation.$	$g = \frac{2}{5} p$	Theory & Tactics Method Card TRANS1-A Click to view full details Theory & Tactics Method Card TRANS2-B Click to view full details
$We solve for p in terms of g and substitute into the cleared equation.$	$p = \frac{5}{2} g (7 n - 2) \times \frac{5}{2} g = 1780 (7 n - 2) g = 712$
$We factor 712 to find its integer factors.$	$712 = 8 \times 89$	Theory & Tactics Method Card DIV4-C Click to view full details
$We test factor pairs and choose the one where g is an integer greater than 3, then solve for n .$	$7 n - 2 = 89 7 n = 91 n = 13$

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C

GMAT Quant — Applied Mathematics (Word Problems)

A boardwalk is made up of n wooden planks of equal length, with an unpainted gap between each pair of consecutive planks. Each gap is \frac{2}{5} as long as one plank. The total length from the beginning of the first plank to the end of the last plank is 356 inches. If n is an integer and each gap length, in inches, is an integer greater than 3, what is the value of n ?

Explanation	Calculations	Help
$We name p as the length of each plank in inches.$	$p = length of each plank$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "the total length from the beginning of the first plank to the end of the last plank is 356 inches" into an equation by adding the lengths of all planks and gaps.$	$n p + (n - 1) \times \frac{2}{5} p = 356$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We combine like terms by factoring out p .$	$\frac{( 7 n - 2 ) p}{5} = 356$
$We clear the fraction by multiplying both sides by 5.$	$(7 n - 2) p = 1780$
$We name g as the length of each gap in inches and translate "each gap is 2/5 as long as one plank" into an equation.$	$g = \frac{2}{5} p$	Theory & Tactics Method Card TRANS1-A Click to view full details Theory & Tactics Method Card TRANS2-B Click to view full details
$We solve for p in terms of g and substitute into the cleared equation.$	$p = \frac{5}{2} g (7 n - 2) \times \frac{5}{2} g = 1780 (7 n - 2) g = 712$
$We factor 712 to find its integer factors.$	$712 = 8 \times 89$	Theory & Tactics Method Card DIV4-C Click to view full details
$We test factor pairs and choose the one where g is an integer greater than 3, then solve for n .$	$7 n - 2 = 89 7 n = 91 n = 13$

Scroll horizontally to view all columns

C