Question

here are the clues for a mystery number. the number is 760,000 when rounded to the nearest ten thousand the number is 765,000 when rounded to the nearest thousand. which number could be the mystery number? 765,321 762,321 763,981 764,981

Explanation:

Step1: Check rounding to nearest ten thousand

For a number to round to 760,000 to the nearest ten thousand, it must satisfy $755,000 \leq n < 765,000$.

• $765,321$: $765,321 \geq 765,000$ → rounds to 770,000 (invalid)
• $762,321$: $755,000 \leq 762,321 < 765,000$ → rounds to 760,000 (valid)
• $763,981$: $755,000 \leq 763,981 < 765,000$ → rounds to 760,000 (valid)
• $764,981$: $755,000 \leq 764,981 < 765,000$ → rounds to 760,000 (valid)

Step2: Check rounding to nearest thousand

For a number to round to 765,000 to the nearest thousand, it must satisfy $764,500 \leq n < 765,500$.

• $762,321$: $762,321 < 764,500$ → rounds to 762,000 (invalid)
• $763,981$: $763,981 < 764,500$ → rounds to 764,000 (invalid)
• $764,981$: $764,500 \leq 764,981 < 765,500$ → rounds to 765,000 (valid)

Answer:

764,981