Bunuel
Orange08
How many odd integers are greater than the integer x and less than the integer y?
1) There are 12 even integers greater than x and less than y
2) There are 24 integers greater than x and less than y
Sorry, I tried to search the forum for previous explanations. But since the search was too generic, it didn't fetch any results.
(1) Here is the string of 12 even integers and 11 odd integers between them:
eoeoeoeoeoeoeoeoeoeoeoe.
4 cases are possible:
If x and y are both odd then X
eoeoeoeoeoeoeoeoeoeoeoeY then there will be 11 odd integers between them;
If x and y are both even then X
oeoeoeoeoeoeoeoeoeoeoeoeoY then there will be 11+2=13 odd integers between them;
If x is even and y is odd then X
oeoeoeoeoeoeoeoeoeoeoeoeY then there will be 11+1=12 odd integers between them;
If x is odd and y is even then X
eoeoeoeoeoeoeoeoeoeoeoeoY then again there will be 11+1=12 odd integers between them.
Not sufficient.
(2) Out of 24 consecutive integers greater than X and less than Y in any case half will be odd and another half will be even, so there are 12 odd integers greater than X and less than Y. Sufficient.
Answer: B.
P.S. You can try instead of 12 and 24 some smaller numbers to simplify calculations for example 2 even integers for (1) and 4 integers for (2).
Orange08
why are the integers assumed consecutive over here?
Are you talking about (2)? If we are told that there are 4 integers more than X=1 and less than Y=6, then these integers are 2, 3, 4, and 5 - 4 consecutive integers, how else? Note that half are odd and half are even. Or if X=2 and Y=7 then these integers would be 3, 4, 5 and 6 - 4 consecutive integers: half are odd and half are even.
Hope it's clear.
hey bunnel, when you say "4 integers more than X=1 and less than Y=6" why cant it be 1,2,2,2,2,6, or, 1,2,5,5,5,6 this satisfies the statement rather than consecutive integers, right, the question did not say only consecutive or different numbers,,,, ,,iam i missing somethi here,,,,could you explain