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    [Solved] The sum of three consecutive integers is always divisib

    Sum of three consecutive integers is always divisible by 6. For ex: Let three consecutive integers be 21, 22 and 23. Sum = 66, which is divisible by 6.

    Home Quantitative Aptitude Number System Divisibility and Remainder

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    The sum of three consecutive integers is always divisible by ____.

    This question was previously asked in

    SSC CPO Tier- I Previous Paper 8 (Held on: 4th July 2017 Shift 2)

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    12 6 18 24

    Answer (Detailed Solution Below)

    Option 2 : 6 Crack Railway with

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    Detailed Solution

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    Sum of three consecutive integers is always divisible by 6.

    For ex:

    Let three consecutive integers be 21, 22 and 23.

    Sum = 66, which is divisible by 6.

    Download Solution PDF

    Share on Whatsapp

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    More Divisibility and Remainder Questions

    Q1. If an 8-digit number 1862383A is divisible by 22, find the value of A.Q2. Find the greatest value of k for which the 6-digit number 24312k is divisible by 6.Q3. If an 8-digit number 256139A4 is divisible by 11, find the value of A.Q4. Find the greatest value of (a + b) such than an 8-digit number 4523a60b is divisible by 15.Q5. Given below are two statements Statement I: If two numbers divided by a third number give the same remainder, their difference is exactly divisible by that number. Statement II: Least common multiple of two or more given numbers is the largest number which is exactly divisible by each of them. In light of the above statements, choose the correct answer from the options given belowQ6. Let p = 22n + 2 + m and q = 24n - m (where n is even natural number). What should be the least value of m such that p as well as q is divisible by 5?Q7. 275 + 313 is divisible byQ8. 461 + 462 + 463 + 464 is divisible byQ9. 4143 + 4343 is divisible byQ10. What is the number of divisors of 1000 (excluding 1 and 1000)?

    More Number System Questions

    Q1. If an 8-digit number 1862383A is divisible by 22, find the value of A.Q2. The least number by which 72 must be multiplied in order to produce a multiple of 112 isQ3. In a school there are 360, 520 and 280 students in classes 5, 6 and 7 respectively. Buses are to be hired to take these students for a trip. Find the maximum number of students who can be accommodated in each bus if each bus must take same number of students, and each bus should have students from the same class.Q4. Find the greatest value of k for which the 6-digit number 24312k is divisible by 6.Q5. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?Q6. If an 8-digit number 256139A4 is divisible by 11, find the value of A.Q7. If 23.5% of a number is 11.75, then what is the number?Q8. If x =

    2+32−3

    , then the value of (x - 7)2 is

    Q9. Find the greatest value of (a + b) such than an 8-digit number 4523a60b is divisible by 15.Q10. If the square of a positive number is 6 more than five times the number, what is the number?

    स्रोत : testbook.com

    The sum of three consecutive numbers is always divisible by 4. Ver

    The sum of three consecutive numbers is always divisible by 4. Verify this statement with the help of some examples.

    Previous Question Next Question Question :

    The sum of three consecutive numbers is always divisible by 4. Verify this statement with the help of some examples.

    Answer :

    3 + 5 = 8 and 8 is divisible by 4.5 + 7 = 12 and 12 is divisible by 4.7 + 9 = 16 and 16 is divisible by 4.9 + 11 = 20 and 20 is divisible by 4.

    Related Answer

    The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

    More Related Question & Answers

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    स्रोत : www.doubtnut.com

    The sum of three consecutive odd numbers is always class 8 maths CBSE

    The sum of three consecutive odd numbers is always divisible by A 1 B 3 C 5 D 6

    The sum of three consecutive odd numbers is always divisible by

    A) 1 B) 3 C) 5 D) 6 Answer Verified 201.6k+ views

    Hint: The consecutive odd numbers refer to the numbers taken in a continuous manner skipping events in between. We can assume 3 such numbers using a variable, take their sum and see what number can we get common because that will be the one by which the sum will always be divisibleComplete step-by-step answer:

    Some consecutive odd numbers are:

    1, 3, 5, 7

    We can see that the gap between two consecutive odd numbers is 2. Let us assume three consecutive numbers to be:

    n n+2 n+2+2 ⇒(n,n+2,n+4)

    nn+2n+2+2⇒(n,n+2,n+4)

    The sum of these three odd consecutive numbers is given as:

    n+n+2+n+4=3n+6 n+n+2+n+4=3n+6

    From this sum, we can take number 3 as common:

    (3n+6)⇒3(n+2) (3n+6)⇒3(n+2)

    This shows that the answer will be a product of 3, n be any number. Thus, the same will be divisible by 3.

    Therefore, the sum of three consecutive odd numbers is always divisible by 3 and the correct answer is

    3 3 .

    So, the correct answer is “Option B”.Note: The natural numbers (greater than 1) are odd and even in an alternative manner and thus consecutive events and odds respectively are at a gap of two.

    We can check if the answer obtained is correct or not by taking an example.

    If the three consecutive integers are 3, 5, 7, their sum will be:

    3+5+7=15 3+5+7=15

    And 15 is the product of 3 and 5 and thus is divisible by both.

    If the three consecutive integers are 11, 13, 15, their sum will be:

    11+13+15=39 11+13+15=39

    And 39 is the product of 3 and 11 and thus is divisible by both.

    The common number by which both the sums are divisible is 3 so the answer we obtained is correct.

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    Mohammed 6 day ago
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