Data Sufficiency

Set S consists of 20 different positive numbers. How many of the intergers in S are odd?

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

I went to D ( wrong answer )
(1) I said that if 10 are even than teh remaining is odd so I got (A)
+
(2) I said that if 10 are multiples of 4 than for sure they are even again, so I got the same info as (1)
result:
each one of them is sufficient alone !! ==> D
but the OG went for (A)
don't understand that !!!!!!

there can be even integers which are not multiple of 4.
so ans is A

Yes answer A is correct
as the no of even numbers is given,so the rest is odd

A is only correct if the numbers are consecutive, but it doesn't say that.

A is correct as there are even numbers which are not multiples of 4. If the questions says multiples of 2 then it would have been D.

B isn't correct because:

Yes, Multiples of 4 means that the number is even. However, there could be multiples of 2 in the remaining 10 numbers that could be even.

For example,
10 numbers could be multiples of 4: 4, 8, 12, 16, 32...
10 numbers could be multiples of 2: 2, 6, 10, ....
In the end, all 20 numbers could be even.

marouan wrote:Set S consists of 20 different positive numbers. How many of the intergers in S are odd?

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

I would go for (E).

Please follow the question carefully. The stem says that S consists of 20 different numbers. It does not say whether the 20 numbers are integers or a mixture of integers and fractions. Until that information is given, we can not determine the number of odd integers in the set.

Please rectify me if I am wrong.

marouan, Could you please specify the source of this question?

I thought it was E too. I would be assuming there are 10 even and 10 odd numbers.


Please give me an odd number that is a Multiple of 4?

The answer should be (A)

The Question clearly states that there are 20 positive numbers.So,if 10 are even the rest of them have to be odd.

Ian Stewart wrote:I agree with Uri that we need to know that all of the numbers in the set are integers in order for the first statement to be sufficient. I've seen the question before, and I think it does say 'positive integers' rather than 'positive numbers', so I expect that's a transcription error in the original post.

griscomtestprep wrote:A is only correct if the numbers are consecutive, but it doesn't say that.

We certainly don't need to know whether the numbers are consecutive here; we only need to know that they are all integers.

You are right Ian. The actual question is as follows:

Set S consists of 20 different positive integers. How many of the integers in S are odd?
(1) 10 of the integers in S are even.
(2) 10 of the integers in S are multiples of 4.

Now QA should be A

what if the set was:

1 6 8 10 11 12 13 15 18 20 22 24.... etc

where you can have X amount of even integers and Y amount of odd integers.. it doesnt state if its a consecutive set.

Being x diff to y.

Thats why I chose E

This question states only set which can contain ANY values (suppose, whole numbers) with the condition of positiveness (>0). We even don't have a sequence condition here, so there might be no functional relationship among the values as such... Only 20 different positive numbers are given in set S. Question: how many integers are odd? Now it's clear that this is some mis-translated/mis-spelled/paraphrased version of DS. Because we have never been told that set S contains integers, am I right?

By knowing this, we should refrain from answering this question at all.

marouan wrote:Set S consists of 20 different positive numbers. How many of the integers in S are odd?

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

Ian Stewart wrote:I agree with Uri that we need to know that all of the numbers in the set are integers in order for the first statement to be sufficient. I've seen the question before, and I think it does say 'positive integers' rather than 'positive numbers', so I expect that's a transcription error in the original post.

griscomtestprep wrote:A is only correct if the numbers are consecutive, but it doesn't say that.

We certainly don't need to know whether the numbers are consecutive here; we only need to know that they are all integers.

Sorry to dig up this old thread but could you please explain this? If the set isn't consecutive, then you could easily have 20 even integers in the set. Where is the contraint that they all don't have to be odd? Couldn't they all be even?