CAT 2007 — QA Question 20
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
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?
Answer & solution
- A
17
- B
16
18
- D
15
- E
19
Let number of 50, 10 and 1 miso notes used is x, y and z respectively.
⇒ 50x + 10y + z = 107
Now, since x, y and z are whole numbers x can take only three values i.e., 0, 1 and 2.
Case 1: x = 0
⇒ 10y + z = 107
⇒ y can take values from 0 till 10 i.e., 11 values
∴ 11 ways to pay bill of 107 misos.
Case 2: x = 1
⇒ 10y + z = 57
⇒ y can take values from 0 till 5 i.e., 6 values
∴ 6 ways to pay bill of 107 misos.
Case 3: x = 2
⇒ 10y + z = 7
⇒ y can take only 1 value i.e., 0
∴ 1 way to pay bill of 107 misos.
⇒ Total ways the bill can be paid = 11 + 6 + 1 = 18 ways,
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The bill can be paid in 18 ways as shown in the above table.
Hence, option (c).