PQID = PS91602.01 | 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.
Takeaway(s):
If k is an odd number, then the next consecutive odd number will be k + 2.
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