Quant - Consecutive Integers

Question 1

In any three (or more) consecutive integers, at least one of the numbers is divisible by _?

Answer 1

3

Question 2

Average of consecutive integers formula

Answer 2

(First term + Last term)/2

Question 3

1) . If n is odd, the sum of consecutive integers is always
2) . If n is even, the sum of consecutive integers is
https: //www.veritasprep.com/blog/2016/08/advanced-number-properties-gmat-part-vi/

Answer 3

1) . divisible by n
2) . never divisible by n

Application -

Question 4

The product of n consecutive integers is always divisible by

Answer 4

n!

Application - If k is a positive integer, what is the remainder when (k + 2)(k^3 – k) is divided by 6 ?

A. 0
B. 1
C. 2
D. 3
E. 4

(k–1)k(k+1)(k+2) .

As we can see we have the product of 4 consecutive integers: (k – 1), k, (k+1), and (k + 2). Thus, the product will always be divisible by 4! = 24, which means that it will be divisible by 6 too.

Question 5

Which of the following must be true?

1) The sum of N consecutive integers is always divisible by N.
2) If N is even then the sum of N consecutive integers is divisible by N.
3) If N is odd then the sum of N consecutive integers is divisible by N.
4) The Product of K consecutive integers is divisible by K.
5) The product of K consecutive integers is divisible by K!

(A) 1, 4, 5
(B) 3, 4, 5
(C) 4 and 5
(D) 1, 2, 3, 4
(E) only 4

Answer 5

Ans = B

Question 6

The sum of all the integers k such that −26 < k < 24 is

Answer 6

ANS = -49

Question 7

The sum of the first n positive integers is given by (EG - 1+ 2= 3…. HAS TO START FROM 1)

Answer 7

N(N+1)/2

Question 8

1) . In any evenly spaced set the arithmetic mean (average) is equal to the
2) . The mean of an odd number of Consecutive Integers will always equal

Answer 8

1) . Median
2) . Middle value - median

Thus -> Mean = Median = (First + Last)/2

Question 9

What is the sum of a certain pair of consecutive odd integers?

(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

What does the question stem mean ?

Answer 9

We are talking about a pair of numbers. This means there are only 2 numbers. One of them is positive and the other negative. Plus, they need to be consecutive odd numbers so they must be -1 and 1 only. Their sum will be 0.

Question 10

The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.

Answer 10

(1) The integers are consecutive odd numbers –> x + (x + 2) + (x + 4) + (x + 6) = 64. We can find x. Sufficient.
(2) Of these integers, the greatest is 6 more than the least –> least = x and greatest = x + 6. Between x and x + 6, there are only 2 odd integers x + 2 and x + 4, so we have the same case as above. Sufficient.

Answer: D.