A crate of bananas contains between $30$ and $60$.... | Free GMAT Practice Question | GMAT Panda

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A crate of bananas contains between 30 and 60 bananas. If the bananas are arranged in bunches of 6, there are 4 left over; but if arranged in bunches of 7, there are 3 left over. How many bananas are in the crate?

Explanation	Calculations	Help
$We name n as the number of bananas. Then "If the bananas are arranged in bunches of 6, there are 4 left over" .$	$n = 6 k + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We record the condition "if arranged in bunches of 7, there are 3 left over" .$	$n = 7 m + 3$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We list the numbers between 30 and 60 that fit the first condition.$	$n = 6 k + 4 n = 6 \times 5 + 4 = 34 n = 6 \times 6 + 4 = 40 n = 6 \times 7 + 4 = 46 n = 6 \times 8 + 4 = 52 n = 6 \times 9 + 4 = 58$
$We test 34 against the second condition and rule it out because the remainder is not 3.$	$34 = 7 \times 4 + 6$
$We test 40 against the second condition and rule it out because the remainder is not 3.$	$40 = 7 \times 5 + 5$
$We test 46 against the second condition and rule it out because the remainder is not 3.$	$46 = 7 \times 6 + 4$
$We test 52 against the second condition and find the remainder is 3, so it satisfies both conditions.$	$52 = 7 \times 7 + 3$
$Hence, we find the number of bananas in the crate.$	$n = 52$

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D

A crate of bananas contains between 30 and 60 bananas. If the bananas are arranged in bunches of 6, there are 4 left over; but if arranged in bunches of 7, there are 3 left over. How many bananas are in the crate?

Explanation	Calculations	Help
$We name n as the number of bananas. Then "If the bananas are arranged in bunches of 6, there are 4 left over" .$	$n = 6 k + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We record the condition "if arranged in bunches of 7, there are 3 left over" .$	$n = 7 m + 3$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We list the numbers between 30 and 60 that fit the first condition.$	$n = 6 k + 4 n = 6 \times 5 + 4 = 34 n = 6 \times 6 + 4 = 40 n = 6 \times 7 + 4 = 46 n = 6 \times 8 + 4 = 52 n = 6 \times 9 + 4 = 58$
$We test 34 against the second condition and rule it out because the remainder is not 3.$	$34 = 7 \times 4 + 6$
$We test 40 against the second condition and rule it out because the remainder is not 3.$	$40 = 7 \times 5 + 5$
$We test 46 against the second condition and rule it out because the remainder is not 3.$	$46 = 7 \times 6 + 4$
$We test 52 against the second condition and find the remainder is 3, so it satisfies both conditions.$	$52 = 7 \times 7 + 3$
$Hence, we find the number of bananas in the crate.$	$n = 52$

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D