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Number of ways to pay a bill with given currency denominations

CAT 2007 Slot 1 · Quantitative Ability · Easy · Permutations and Combinations

This is an easy Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Permutations and Combinations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?

  1. A.

    17

  2. B.

    16

  3. C.

    18

  4. D.

    15

  5. E.

    19

Answer

C

Explanation

Let x,y,zx, y, z be the number of 1, 10, and 50 Misos coins/notes respectively. x+10y+50z=107x + 10y + 50z = 107. Possible values of zz: 0, 1, 2.

  • If z=0z = 0, x+10y=107x + 10y = 107, yy can range from 0 to 10 →11\rightarrow 11 ways.
  • If z=1z = 1, x+10y=57x + 10y = 57, yy can range from 0 to 5 →6\rightarrow 6 ways.
  • If z=2z = 2, x+10y=7x + 10y = 7, y=0→1y = 0 \rightarrow 1 way. Total ways =11+6+1=18= 11 + 6 + 1 = 18.

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