Question:medium

The smallest number that should be subtracted from 2085, so that the new number is completely divisible by 23 is

Updated On: Jul 15, 2026
  • 9
  • 15
  • 20
  • 19
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The Correct Option is B

Approach Solution - 1

Step 1: Understanding the Question.
We need the smallest number that, when subtracted from 2085, leaves a number exactly divisible by 23.

Step 2: Key Formula or Approach.
The smallest number to subtract to make a number divisible by another is simply the remainder left when we divide the first number by the second.

Step 3: Detailed Explanation.
Divide 2085 by 23:
\[ 23 \times 90 = 2070 \]
\[ 2085 - 2070 = 15 \]
So 2085 leaves a remainder of 15 when divided by 23.
Subtracting this remainder gives a number exactly divisible by 23:
\[ 2085 - 15 = 2070 = 23 \times 90 \]

Step 4: Final Answer.
The smallest number to subtract is 15. \[ \boxed{15} \]
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Approach Solution -2

The goal is to find the smallest amount to take away from 2085 so that what remains splits evenly by 23. Rather than dividing 2085 itself, check each option by subtracting it from 2085 and testing whether that specific result sits on a multiple of 23.

  1. Option (A): 9: \( 2085 - 9 = 2076 \). Checking against the nearby multiples \( 23 \times 90 = 2070 \) and \( 23 \times 91 = 2093 \), 2076 falls strictly between these two, so it is not divisible by 23.
  2. Option (B): 15: \( 2085 - 15 = 2070 \). This is exactly \( 23 \times 90 \), a whole multiple of 23 with nothing left over.
  3. Option (C): 20: \( 2085 - 20 = 2065 \). Checking against the nearby multiples \( 23 \times 89 = 2047 \) and \( 23 \times 90 = 2070 \), 2065 sits in between, so it is not divisible by 23.
  4. Option (D): 19: \( 2085 - 19 = 2066 \). This also falls between \( 23 \times 89 = 2047 \) and \( 23 \times 90 = 2070 \), so it too fails to divide evenly.

Only subtracting 15 lands exactly on a multiple of 23, and since it is also the smallest option that does so, it is the answer being sought.

Therefore, the correct answer is 15.

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