Set S consists of 20 different positive integers. How many

Question

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

I chose D, in that each stmt. is sufficient but the answer is A. Can someone explain why stmt. 2 is not sufficient? All multiples of 4 are even (such as 4, 8, 12, 16, 20, 24, 28, 32....), so if we have 10, the other ten integers must be odd...am I missing something?

Any help is appreciated, thx!

Any help is appreciated, thx!

anandsebastin · Answer

Clear  A 

Statement 1:
10 are odd and all are positive integers. 
SUFF

Statement 2:
10 are multiples of 4. There could be others that are even but not multiples of 4. eg. 6

INSUFF

mukeshnathani · Answer

anandsebastin - Can you pls. explain how did u conclude from (1) that "10 are odd and all are positive integers."

I was thinking on the lines that all 20 can be also even ?Hence we cannot say for sure from (1) that "10 are odd and all are positive integers." Am I missing something ? :oops:

yezz · Answer

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

all intigers are either even or odd ( as long as they are positive)

FROM ONE .....SUFF

FROM TWO
10 OF THE INTIGERS ARE MULTIPLES OF 4 ( EVEN) AND WE HAVE NO CLUE ABOUT THE OTHERS

WHERE SOME MIGHT BE EVEN BUT NOT MULTIPLES OF 4 (EG: 2,0)

MY ANSWER IS A

cmugeria · Answer

Please help explain how statement 1 is sufficient. I had this question on GMAT Prep and answered as E. Statement 1 does not emphasize that ONLY 10 Integers are even

saxenashobhit · Answer

dont forget - whatever data is given , IS true -
in A - 10 are even, that means others are odd - Suff

B - insuff 
Ans is A

Bunuel · Answer

In this case saying that "10 of the integers in S are even" means that EXACTLY 10 are even, as if there were more than 10 even numbers in the set, say 15, then it would make no sense to say that there are 10 even numbers.

So as there are 20 integers and out of them 10 are even then the rest must be odd.

On the other hand statement (2) just tells us that there are at least 10 even numbers in the set, so number of odd numbers in the set could vary from 0 (if all numbers are even) to 10 (if these 10 multiples of 4 are the only even numbers in the set).

Answer A is correct.

anairamitch1804 · Answer

We are told the numbers are positive integers so that leaves out zero.

All positive integers are either odd or even. If 10 of 20 are odd, the rest are even. (Assuming the statement means exactly 10 are even. If it means at least ten are even we don't have an answer.)

B doesn't work because we could have even numbers (e.g.2, 6, 10) that are not multiples of 4 so that there might be more than 10 even integers. Insufficient.

Hence A.

Jashan25 · Answer

I don't think that answer should be A as it is not written that only 10 are even.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Set S consists of 20 different positive integers. How many

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Set S consists of 20 different positive integers. How many

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards