If B is a set of real numbers, is there a number in B that

Question

If B is a set of real numbers, is there a number in B that is divisible by seven?

(1) Every number in B is both positive and even.
(2) There are three numbers in set B between 1 and 100 each of whose digits add up to 5.

C. The only numbers that satisfy Statement 2 are 5,14, 23, 32, 41, 50. The only numbers from this set that also satisfy Statement 1 are 14, 32 and 50. Since the question asks is there a number in B that is divisible by seven? we know that with both statements together that number is 14.

Official explanation assumes that the set can't have equal numbers (otherwise there could be 50,50,50 in this set and the answer would be E). 
Why?

I've always thought that a set is something that CAN have identical objects.

dave785 · Answer

I got it right, but only because I wasn't smart enough to think of that. Perhaps if 50 was in there three times, it would be one number (not three) represented three times.?

battleprof · Answer

Well, that's the core of my question. 
And I think official explanation is strange, because there are lots of problems about zero standard deviation, which is zero due to the fact that all the numbers in data set are equal. So it seems to me that GMAT permits a set to have identical elements.

LalaB · Answer

stmnt 1 is not sufficient. there could be 4 6 14 etc (14 is divisible by 7) , or 4 6 10 (none is divisible by 7)

stmnt 2 is insuff. too - there could be 23 41 50 (none is divisible by 7) , or 32 14 50 (14 is divisible by 7)

2 stmnts together are suff, since we have only even integers , the sum of digits of whom is 5
32 14 50.

KarishmaB · Answer

Every element of a set must be unique. There cannot be two identical members.

battleprof · Answer

Well, than I kindly ask you to explain why there are so many problems about standard deviation and those data sets sometimes contain equal numbers. Are "data sets" different from "sets"?

I'm sorry, I can't yet post links, so I copy two problems posted on this forum:

1) posted by Bunuel, there are equal numbers in data sets

2) And here is a problem where "set" (not "data set" this time) definitely has identical numbers, as it is the OA!

KarishmaB · Answer

Yes, I know we see questions with identical elements. Technically, a set has distinct elements. The point is that {1, 2, 3} = {1, 2, 2, 3} so "technically" if you say set S has 3 elements, we would assume they are distinct. That is where this question comes from. We do see deviations in usage though so to avoid confusion, I would hope that if we need to find the number of elements, the word "distinct" will be given. Check out Wikipedia link: https://en.wikipedia.org/wiki/Set_(mathematics) Search for "unique" on this page.

Bluelagoon · Answer

Thanks for the clarification karishma. I hope 'distinct' is mentioned in the question. As for the soln, my 2 cents :

A opens up the can. infinite possibilities.
B says out of 5,14,23,32,41, and 50 - 3 numbers are present on the set.

Combine A and B. We see that number 14 is definitely present. C wins.

warrior1991 · Answer

I still don't get that why the answer is C.

Note:- the set B will have now (32,14,50). If 14 then yes it is divisible by 7 but if 32 then answer will be no.

so E should be the answer. Please help explain C.

ColumbiaEMBA · Answer

You're correct. I think the question is just bad to begin with. This can't be official guide question.

A + B together allow for {14, 32, 50} which means that a number divisible by 7 may exist, but also may not exist.

abhimahna · Answer

Hey  strivingFor800  /  prerakgoel07  ,

I think you guys have not understood the question properly. I don't find anything wrong with the question.

Question says B is a set of some numbers and then ask whether we have a number in this set that is divisible by 7.

By combining the two statement, your set has three elements as 14, 32 and 50. We can see that B does have a number divisible by 7 in it. Hence, C is the answer.

Does that make sense?

KarishmaB · Answer

Question: Is there a number in B that is divisible by 7 ?

If B has a number divisible by 7, answer would be YES
If no number in B is divisible by 7, answer would be NO

Using both statements, set B is defined so we know whether there is a number divisible by 7 or not. Note that every number in B need not be divisible by 7. If we find one, we are good.

Answer (C)

abhimanyujain1711 · Answer

Hello Karishma,

i know the post is rather old but i would still appreciate it if you could answer it for me.
after combining both the statements, we still have the following numbers - 
14,23,32,50.
out of which only 14 is divisible and the rest are not. 
from what i have learnt, we must have either a complete yes or a complete no for a statement to be sufficient.
please let me know your comments.
thank you

Md231 · Answer

Problem with the language here. What is the source? 14, 32, 50 are the numbers that satisfy 1 and 2. 14 may or may not be a part of the set. It is not said that every such number that satisfies the condition is a part of the set. E as per the given language but this language is not convincing. Does GMAT use such ambiguous language? Hopefully not

Md231 · Answer

In other words, I am trying to say that the 3 numbers need not be unique, it is not given in the question.

So it could be a set 32, 32, 50 or 14, 14, 14 leading to different answers.

Thanks.

KarishmaB · Answer

Yes you are right. You must have a yes or a no. The tricky thing about DS is how the question is defined.

Ques 1: How will you answer this question: Is there a number in B that is divisible by seven?
Yes there is a number in B that is divisible by 7. (you need to know at least one number that is divisible by 7)
or
No, there is no number in B that is divisible by 7. (you need to know that all numbers are NOT divisible by 7)
or
May be - there may be a number divisible by 7 or there may be no number divisible by 7. (you don't know any number which is divisible by 7 and there is at least 1 number unknown to you)

First 2 cases are sufficient while the third case gives us not sufficient. 
Do you need to worry whether all numbers in B are divisible by 7? No.

Ques 2: How will you answer this question: Are all numbers in B divisible by 7?
Yes, all number in B are divisible by 7. (you need to know that ALL numbers are divisible by 7)
or
No, not all numbers are divisible by 7 (you need to know at least one number which is NOT divisible by 7)
or
May be - all numbers in B may be divisible by 7 or there may be some numbers which are not. (You don't know any number which is not divisible by 7 and at least one number is unknown to you)

First 2 cases are sufficient while the third case gives us not sufficient.

KarishmaB · Answer

See this: https://gmatclub.com/forum/if-b-is-a-se ... l#p1216327

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If B is a set of real numbers, is there a number in B that

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