NECO Mathematics 2024 Objective — Question 27
Question 27 of 50 from the National Examinations Council (NECO) Mathematics 2024 Objective paper, with the correct answer and a full explanation.
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The number 1621 was subtracted from 6244 in base x. If the result is 4323, find x.
- A. (a) seven
- B. (b) eight
- C. (c) nine
- D. (d) ten
Explanation
Converting to base 10: 6244ₓ=6x³+2x²+4x+4; 1621ₓ=x³+6x²+2x+1; 4323ₓ=4x³+3x²+2x+3. (6244−1621)ₓ: (6x³+2x²+4x+4)−(x³+6x²+2x+1)=5x³−4x²+2x+3. Setting equal to 4323ₓ: 5x³−4x²+2x+3=4x³+3x²+2x+3 → x³−7x²=0 → x²(x−7)=0 → x=7 (rejecting 0). Answer: seven.
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