In a five digit number, the digit at the hundreds place is three-fourth of the digit at ten thousands place and the digit at tens place is two-third of the digit at hundreds place. The digit at tens place is square of the smallest prime number and the digit at thousands place is the largest single digit prime number. If the digit at unit place is the largest single digit odd number, then the number is
CTET - 2021,
Answer: A
The number is 87649.
Fill in the digits from the clues, starting with the ones that are fixed directly:
\[ \begin{aligned} \text{tens} &= 2^{2} = 4 \\ \text{hundreds} &: \tfrac{2}{3} \times h = 4,\ h = 6 \\ \text{ten thousands} &: \tfrac{3}{4} \times t = 6,\ t = 8 \\ \text{thousands} &= 7,\quad \text{units} = 9 \end{aligned} \]
The smallest prime is 2, so the tens digit is 4. The largest single-digit prime is 7 and the largest single-digit odd number is 9. Reading from the ten thousands place: 8, 7, 6, 4, 9, giving 87649.
The other numbers fail at once: 49327 and 42937 have the wrong tens digit, and 83419 has 4 in the hundreds place, which is not three-fourths of 8.
Please log in or register to report this question.