Question

A stationery store sells pack of pens, each pack having 45 pens. He wants to pack $100,978$ pens in similiar way. How much pens would be left?

• A. $43$
• B. $34$
• C. $42$

Answer 1

The correct option is A $43$

Concept: A number, divisible by 45, is also divisible by 5 and 9 because 45 is product of two co-prime numbers 5 and 9.

Given that the store sells pack of pens, each pack having 45 pens.

We need to find the greatest number of pens less than $100,978$ that is completely divisible by 45.

Its sum of digits is 25 and last digit is 8, hence on adding 2, the number would be divisible by both 5 and 9.

But, we can't add more pens hence to make the number divisible by 45, we need to subtract 43 from it.

$\because 100,978-43=100,935$

$100,935$ pens can be packed in the way the storekeeper wants.

$43$ pens would be left.