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If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers? – OGQR 2020 Question #86 with Solution

OGQR 2020: Question No. 86

If the smaller of 2 consecutive odd integers is a multiple of 5, which of the following could NOT be the sum of these 2 integers?

Source OGQR 2020
Type Problem Solving
Topic Number Property
Sub-Topic Even – Odd
Difficulty Medium

Solution

Given

In this question, we are given

  • The smaller of 2 consecutive odd integers is a multiple of 5.

To Find

We need to determine

  • Among the given options, which one could not be the sum of those 2 consecutive odd integers.

Approach & Working

Let us assume that the smaller of the 2 consecutive odd number is 5k, where k is an odd number.

  • Therefore, the other integer must be 5k + 2.
  • And, their sum is 5k + 5k + 2 = 10k + 2

Now, let’s check the options individually.

  • If 10k + 2 = -8, then 10k = -10 or, k = -1, which is an odd number
  • If 10k + 2 = 12, then 10k = 10 or, k = 1, which is an odd number
  • If 10k + 2 = 22, then 10k = 20 or, k = 2, which is an even number
  • If 10k + 2 = 52, then 10k = 50 or, k = 5, which is an odd number
  • If 10k + 2 = 252, then 10k = 250 or, k = 25, which is an odd number

As k is an odd number, k cannot be equal to 2.

Hence, the correct answer is option C.

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