There are between $39$ and $50$ coins in a jar. If... | Free GMAT Practice Question | GMAT Panda

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There are between 39 and 50 coins in a jar. If they are counted out 6 at a time, there are 4 left over, but if they are counted out 7 at a time, there are 5 left over. How many coins are in the jar?

Explanation	Calculations	Help
$We let n be the number of coins and translate "If they are counted out 6 at a time, there are 4 left over" into an equation.$	$n = number of coins n = 6 k + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We translate "If they are counted out 7 at a time, there are 5 left over" into an equation.$	$m = number of full groups of 7 n = 7 m + 5$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We find values of n between 39 and 50 that satisfy the first equation.$	$6 \times 6 + 4 = 40 6 \times 7 + 4 = 46$
$We test 40 in the second equation and find that it leaves the correct remainder.$	$40 = 7 \times 5 + 5$
$We test 46 and find that it leaves the wrong remainder, so we reject it.$	$46 = 7 \times 6 + 4$

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A

There are between 39 and 50 coins in a jar. If they are counted out 6 at a time, there are 4 left over, but if they are counted out 7 at a time, there are 5 left over. How many coins are in the jar?

Explanation	Calculations	Help
$We let n be the number of coins and translate "If they are counted out 6 at a time, there are 4 left over" into an equation.$	$n = number of coins n = 6 k + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We translate "If they are counted out 7 at a time, there are 5 left over" into an equation.$	$m = number of full groups of 7 n = 7 m + 5$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We find values of n between 39 and 50 that satisfy the first equation.$	$6 \times 6 + 4 = 40 6 \times 7 + 4 = 46$
$We test 40 in the second equation and find that it leaves the correct remainder.$	$40 = 7 \times 5 + 5$
$We test 46 and find that it leaves the wrong remainder, so we reject it.$	$46 = 7 \times 6 + 4$

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A