Data Sufficiency

Q: Set S consists of 20 different positive integers. How many of the integers in set S are odd?

1. 10 of the integers in S are even.
2. 10 of the integers in S are multiples of 4.


My answer was D but it was incorrect. How? Can anyone please explain.


Cheers!

Should be A IMO.

(2) can have cases where numbers are even but not multiples of 4. For e.g. (2,6,10 and so on)

(1) since 10 Nos are even the other 10 should be odd. Sufficient

statement 1:10 of them are even integers

out of the othe 10,
any one might be 0

which is neither even nor odd


same goes for statement 2


so the ans should be E

The question mentions +ve integers, so zero would not be possible,

rijul007 wrote:statement 1:10 of them are even integers

out of the othe 10,
any one might be 0

which is neither even nor odd


same goes for statement 2


so the ans should be E

As option 2 says 10 numbers in set S are multiples of 4 that means all 10 multiple numbers are even. Multiple of 4 cannot be an odd number. So rest of the 10 numbers are odd as the numbers in the set are positive and consecutive.

Then answer should be D. Correct me if I am wrong.

Consecutive?? I don't see that word

Ahmed MS wrote:As option 2 says 10 numbers in set S are multiples of 4 that means all 10 multiple numbers are even. Multiple of 4 cannot be an odd number. So rest of the 10 numbers are odd as the numbers in the set are positive and consecutive.

Then answer should be D. Correct me if I am wrong.

Pardon me. Was it right without the consecutive numbers?

I am not sure how the question would be framed for consecutive, for Statement 2 says 10 multiples of 4 which would be (4 to 40) but we can only have the first 20 numbers if they are consecutive. If it was multiples of 2 in (B) what you say makes sense.

Ahmed MS wrote:Pardon me. Was it right without the consecutive numbers?

IMO: A.

For the exactly same reasons as mentioned by Ashwin.

What is the OA?

Thanks.

Hey guys,

Love the discussion...just want to clarify a few things here:

0 is an even number. Even means "integer that is divisible by 2", and 0/2 = 0, which means since there is nothing after the decimal point that 0 is even. Shankar is right that the question says positive (and 0 is neither positive nor negative), but since it came up I wanted to clarify.

Statement 2 - consider the set 2, 4, 6, 8, 10. Only two of these are divisible by 4 (4 and 8) but all are even. So statement 2 is not sufficient. We know that 10 of the values are divisible by 4, and therefore even. But even numbers like 2 and 6 that are not divisible by 4 can still be even, and we don't know anything about the 10 numbers that aren't divisible by 4. All could be even or all could be odd.

___________________________________

Now, I'd go A on this one but I'd also be surprised if this one passed the "experimental phase" of the GMAT's testing system. Statement 1 says that 10 of the integers are even, and I think it's reasonable to say that, since the set has been defined at 20 total integers, the others are odd. But statement 1 doesn't say "exactly" 10 integers, so logically you could probably construct an argument that, if all 20 of them are even, you're still not wrong in saying "10 are even". You could quite easily say "Bill Gates has a million dollars" and not be wrong...even though he has considerably more than just a million.

So my hypothesis on this one is that it's written to elicit the answer A, but were it in the experimental phase of the official GMAT enough "high ability" users would pick E that they'd have to investigate the question and throw it out. That "10 but not necessarily EXACTLY 10" logic isn't the GMAT's typical style on Data Sufficiency...it's a lot more LSAT or Philosophy than GMAT.

Brian@VeritasPrep wrote:Hey guys,

Love the discussion...just want to clarify a few things here:

Thanks a lot for the detailed post Brian. Appreciate it ! But when GMAT says '10 of the integers in S are even',does it not mean 'Exactly 10 of the integers in S are even' ?

I feel that if the characteristic of the entity is dual such as A group of students which can speak english and french. In this case '10 of the students speak english' differs from '10 of the students speak only English'.

My 2 cents !