## 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__

__Given__

In this question, we are given

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

__To Find__

__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__

__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.

Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you

try out our FREE Trial?We are themost reviewed online GMAT Preparation company in GMATClubwith more than 2500 reviews as of February 2023.