Question

Krishnan bought chocolates for his brothers. When he grouped the chocolates in groups of 4, 1 chocolate was left, if grouped in 5, 4 chocolates were left, if grouped in 6, 1 chocolate was left and if grouped in 7, no chocolate was left ungrouped. If the total number of chocolates bought was less than 50, find the number of chocolates Krishnan bought.

• A. 49
• B. 35
• C. 45
• D. 29

Answer 1

The correct option is A

49

Number of chocolates = 4a + 1
(as when they are grouped in 4, 1 is left)
Number of chocolates = 5b + 4
(as when they are grouped in 5, 4 are left)
Number of chocolates = 6c + 1
(as when they are grouped in 6, 1 is left)
And number of chocolates = 7d + 0
(as when grouped in 7, 0 is left)

It is clear that the number must be a multiple of seven.
The multiples of seven below 50 are:
7, 14, 21, 28, 35, 42 and 49
$49=4\times 12+1$
$49=5\times 9+4$
$49=6\times 8+1$
$49=7\times 7+0$
Thus, the correct answer is 49.