Iqra has some sweets to put in a pack. If she puts 2, 3 or 4 in a pack, she is left with one sweet and if she puts 7 in a pack, then all sweets are packed. Which of the following is the possible number of sweets she has to pack?
Iqra has some sweets to put in a pack. If she puts 2, 3 or 4 in a pack, she is left with one sweet and if she puts 7 in a pack, then all sweets are packed. Which of the following is the possible number of sweets she has to pack?
Explanation
Let's analyze the situation:
When Iqra puts 2, 3, or 4 sweets in a pack, she is left with 1 sweet. This means the total number of sweets is 1 more than a multiple of 2, 3, and 4.
The least common multiple (LCM) of 2, 3, and 4 is 12. So, the number of sweets can be represented as 12k + 1, where k is an integer.
When she puts 7 sweets in a pack, all sweets are packed, meaning the total number of sweets is a multiple of 7.
Let's check the options:
49 = 12(4) + 1 and 49 = 7 × 7
So, 49 satisfies both conditions.