passpadi

2015

Mathematics

POST UTME

If 1P1223=98101P122_3 = 98_{10} , where P is a digit, find the value of P

A.

3

B.

2

C.

1

D.

0

Correct Answer: 0

Explanation

Convert to base 10

given: 1P1223=98101P122_3 = 98_{10}

14P3122120=98101^4P^31^22^12^0 = 98_10

1×34+P×33+1x32+2x31+2=981 × 3^4 + P × 3^3 + 1 x 3^2 + 2 x 3^1 + 2 = 98

81+27P+9+6+2=9881 + 27P + 9 + 6 + 2 = 98

98+27P=9898 + 27P = 98

27P=027P = 0

P=027=0P = \frac{0}{27} = 0

Convert to base 10

given: 1P1223=98101P122_3 = 98_{10}

14P3122120=98101^4P^31^22^12^0 = 98_10

1×34+P×33+1x32+2x31+2=981 × 3^4 + P × 3^3 + 1 x 3^2 + 2 x 3^1 + 2 = 98

81+27P+9+6+2=9881 + 27P + 9 + 6 + 2 = 98

98+27P=9898 + 27P = 98

27P=027P = 0

P=027=0P = \frac{0}{27} = 0

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