Question
Download Solution PDFLet x and y be the largest four-digit and the smallest five-digit numbers, respectively, that when divided by 789 leaves a remainder of 7 in each case. What is the value of |x — y]?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Let x and y be the largest four-digit and the smallest five-digit numbers, respectively, that when divided by 789 leave a remainder of 7.
Formula used:
Number = Divisor × Quotient + Remainder
Calculation:
Largest four-digit number: 9999
⇒ Find x such that 9999 = 789 × Quotient + 7
⇒ Quotient = ⌊(9999 - 7) ÷ 789⌋ = ⌊9992 ÷ 789⌋ = 12
⇒ x = 789 × 12 + 7
⇒ x = 9468 + 7 = 9475
Smallest five-digit number: 10000
⇒ Find y such that 10000 = 789 × Quotient + 7
⇒ Quotient = ⌊(10000 - 7) ÷ 789⌋ = ⌊9993 ÷ 789⌋ = 13
⇒ y = 789 × 13 + 7
⇒ y = 10257 + 7 = 10264
⇒ |x - y| = |9475 - 10264|
⇒ |x - y| = 789
∴ The correct answer is option (2).
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