Let $2 and $1 be the determining factor and let $0.50 to mark up the sum to $100.
When $2 x 50, $1 x 0 and $ 0.50 x 0~~~~~this is one way
When $2 x 49, $1 can be x1 or x2 or x0 and let $0.50 to mark up to the sum
Then this will be 3 way. $ 1 x0 would mean than no one dollar is used, only two dollar and 50p will be used.
When $2 x 48, $1 can be x1 or x2 or x3 or x4 or x0. Therefore, there are 5 ways
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when $2 x 1, $1 can be x0 or x1 or .... or x 98, a total of 99 ways
when $2 x 0, $1 can be x0 or x1 or .... or x 98 or x 99 or x 100, a total of 101 ways
As you can see , this is an arithmatic progression. To find possible way to make a sum of $ 100, apply arithmatic summation.
It will be 1+3+5+...+101=2601
I don't get answer from the option. Maybe there is some mistake in my calculation? Please kindly point out.