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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

Last edited by bkpolymers1617 on 19 Sep 2017, 11:00, edited 1 time in total.

Bunuel : Can you help? I don't have the official explanation, but believe that the answer is C. Please let me know if that is correct. I can prove it, but it would be great if it comes from an expert. Thanks
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

D can not be tge answer. You are assuming that A, B and C are integers which is not true. Can be fractions as well, in which case, we will get scenarios in which they are not integers. So choice d is 100% incorrect
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

1. AB is even- Insufficient. Say AB=2, and C =3/2, then ABC is what ? An odd number. Now take another scenario, take AB=4, C=6. ABC is what? An even number. Hence insufficient. Those who assumed that C is an integer must have believed that A is sufficient.

2. BC is even- Insufficient. Say BC=2, and A = 3/2, then ABC is what ? An odd number. Now take another scenario, take BC=4, A=6. ABC is what? An even number. Hence insufficient. Those who assumed that A is an integer must have believed that B is sufficient.

Now combined, we are sure that one of the 3 numbers is surely an integer. If you multiply ABC in any way, you will have only 2 situations- 1. either ABC is not an integer itself 2. Or ABC is an even integer.

But in no case, would ABC be an odd integer. Hence C is the answer
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

Let us take 2 cases Case 1. a=1/2,b=4, c=1/2 Case 2 a=1/2, b=8., c=1/2

Now use both the statements,

One of the cases will be even integer and other will give odd.

Thanks for posting this. I ll correct this. I had asked the experts, but since there was no revert, I gave my thoughts. I ll change the OA. Thanks
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!