Question

a, b, c, d, and e are five consecutive integers in increasing order of size. Which one of the following expressions is not odd?

Answer 1

Answer:

b and d

Step-by-step explanation:

in alphabetical order

a=1,b=2,c=3,d=4,e=5

so...here not odd are b and d

Answer 2

The correct options are (A), (B), and (E).

Given:

a, b, c, d, and e are five consecutive increasing integers.

To Find:

Which among the below expressions is not odd.

(A) a + b + c

(B) ab + c

(C) ab + d

(D) ac + d

(E) ac + e

Solution:

To solve this problem, we need to use the concepts given below:

1) Sum of even numbers is even.

2) Product of even numbers is even.

3) Sum of two odd numbers is even.

4) Product of two odd numbers is odd.

5) Sum of an odd and even number gives an odd number.

6) Product of an odd and even number gives an even number.

We are given that a, b, c, d, and e are five consecutive numbers. Consecutive numbers are alternately even and odd.

Case 1: If a = an even number.

⇒ b = odd , c = even, d = odd, e = even.

Now let us analyze each of our given options:

(A) a + b + c = even + odd + even

⇒ a + b + c = (even + odd) + even =  odd + even = an even number.

(B) ab + c = (even x odd) + even = even + even = an even number

(C) ab + d =  (even x odd) + odd = even + odd = an odd number

(D) ac + d = (even x even) + odd = even + odd = an odd number

(E) ac + e = (even x even) + even = even + even = an even number.

From the above calculations, we obtain that options (A), (B), and (E) are even.

Case 2: If a = an odd number.

⇒ b = even , c = odd, d = even, e = odd

Now let us analyze each of our given options:

(A) a + b + c = odd + even + odd

⇒ a + b + c = (odd + even ) + odd = odd + odd = an even number.

(B) ab + c = (odd x even ) + odd = even + even = an even number

(C) ab + d = (odd + even ) + even = odd + even = an odd number.

(D) ac + d = ( odd x odd) + even = odd + even = an odd number.

(E) ac + e =  ( odd x odd) + odd = odd + odd = an even number

From the above calculations, we obtain that options (A), (B), and (E) are even.

Hence from the above two cases, we observe that options (A), (B), and (E) are not odd.

∴ The correct options are (A), (B), and (E).

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