📚 Part of: Constitutional Law And Number Theory Mcqs

Largest 3-digit number completely divided by 7 is?

Category: Miscellaneous Indian Gk

Correct Answer: D) 994.

Exam Relevance: CAT, GMAT, GRE, Bank PO, SSC CGL

Difficulty: Easy

Concept notes:

To find the largest 3-digit number completely divisible by 7, we need to identify the largest 3-digit number and then determine the largest multiple of 7 that is less than or equal to this number. This involves understanding the concept of division and remainders.

Common Mistakes:
  • Students might incorrectly assume that the largest 3-digit number (999) is divisible by 7.
  • Students might not correctly perform the division to find the remainder.
  • Students might not understand how to adjust the number to find the largest multiple of 7.
Explanation:

To find the largest 3-digit number completely divisible by 7, we start by identifying the largest 3-digit number, which is 999. We then need to determine the largest multiple of 7 that is less than or equal to 999.

First, we perform the division of 999 by 7:

\[ 999 \div 7 = 142.7142857 \]

The quotient is 142 and the remainder is 5. This means that 999 is not completely divisible by 7, as there is a remainder of 5.

To find the largest multiple of 7 that is less than or equal to 999, we take the quotient 142 and multiply it by 7:

\[ 142 \times 7 = 994 \]

This means that 994 is the largest 3-digit number that is completely divisible by 7.

To verify, we can perform the division of 994 by 7:

\[ 994 \div 7 = 142 \]

The quotient is 142 and the remainder is 0, confirming that 994 is completely divisible by 7.

Therefore, the largest 3-digit number completely divisible by 7 is 994.

This problem involves understanding the concept of division and remainders, and how to find the largest multiple of a given number within a specified range. It is a fundamental concept in number theory and arithmetic, often tested in various competitive examinations.

Option Analysis:
  • Option A: 991 is not the correct answer because when we divide 991 by 7, we get a remainder. The quotient is 141 and the remainder is 4, meaning 991 is not completely divisible by 7.
  • Option B: 992 is not the correct answer because when we divide 992 by 7, we get a remainder. The quotient is 141 and the remainder is 5, meaning 992 is not completely divisible by 7.
  • Option C: 993 is not the correct answer because when we divide 993 by 7, we get a remainder. The quotient is 141 and the remainder is 6, meaning 993 is not completely divisible by 7.
  • Option D: 994 is the correct answer because when we divide 994 by 7, we get a quotient of 142 and no remainder, meaning 994 is completely divisible by 7.
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