Struggling with this GMAT odd integers question , any idea how to eliminate options fast?

Question

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?

A. –8 
B. 12 
C. 22 
D. 52 
E. 252

Aarushi S · Accepted Answer

This kind of question looks tricky but becomes manageable with a simple pattern. Let the smaller of the two odd integers be 5n, since it has to be a multiple of 5. Then the next consecutive odd number would be 5n + 2. Their sum becomes 10n + 2.
Now check which of the given answer choices can be written in the form 10n + 2. That&rsquo;s the first filter. But that&rsquo;s not enough,  the key is that 5n must be odd, since the question is about odd integers.
For example, if the sum is 22, then 10n + 2 = 22 gives n = 2. But 5n = 10, which is even. That violates the condition. That&rsquo;s the only option where this happens.
So even though 22 fits the math formula, it fails the oddness rule ,  which is why the answer is C.

kritika K · Answer

Best way to crack this is to look for a pattern in the sum formula and use it to eliminate fast.

Let the smaller number be 5n
The next odd number is 5n + 2, so the sum becomes 10n + 2
Test each option by setting 10n + 2 equal to that value, then check if 5n is odd
For A, &ndash;8 means n = &ndash;1, 5n = &ndash;5 which is odd
For B, 12 means n = 1, 5n = 5 which is odd
For C, 22 means n = 2, 5n = 10 which is even
For D, 52 means n = 5, 5n = 25 which is odd
For E, 252 means n = 25, 5n = 125 which is odd

Only 22 leads to an even 5n, which breaks the rule about both numbers being odd.  The final answer is C.