GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 14:28 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If B is a set of real numbers, is there a number in B that

Author Message
TAGS:

### Hide Tags

Intern  Joined: 09 Mar 2013
Posts: 3
If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

1
5 00:00

Difficulty:   55% (hard)

Question Stats: 63% (02:04) correct 37% (01:47) wrong based on 196 sessions

### HideShow timer Statistics

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.

Spoiler: :: OA
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.

Originally posted by battleprof on 23 Apr 2013, 09:38.
Last edited by Bunuel on 23 Apr 2013, 09:46, edited 1 time in total.
RENAMED THE TOPIC.
Manager  Joined: 09 Apr 2013
Posts: 188
Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44 GMAT 2: 740 Q48 V44 GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

battleprof wrote:
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.

Spoiler: :: OA
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.

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.?
Intern  Joined: 09 Mar 2013
Posts: 3
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

dave785 wrote:
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.?

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.
Senior Manager  Joined: 23 Oct 2010
Posts: 318
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

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.
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

battleprof wrote:
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.

Spoiler: :: OA
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.

Every element of a set must be unique. There cannot be two identical members.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 09 Mar 2013
Posts: 3
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

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

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
Quote:
7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}

2) And here is a problem where "set" (not "data set" this time) definitely has identical numbers, as it is the OA!
Quote:
If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S ?

I. Set S contains only one element
II. All elements in set S are equal
III. The median of set S equals the mean of set S

OA: II and III only
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

battleprof wrote:
VeritasPrepKarishma wrote:
Every element of a set must be unique. There cannot be two identical members.

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
Quote:
7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}

2) And here is a problem where "set" (not "data set" this time) definitely has identical numbers, as it is the OA!
Quote:
If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S ?

I. Set S contains only one element
II. All elements in set S are equal
III. The median of set S equals the mean of set S

OA: II and III only

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.

_________________
Karishma
Veritas Prep GMAT Instructor

Manager  Joined: 21 Jan 2010
Posts: 236
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

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.
Senior Manager  P
Joined: 03 Mar 2017
Posts: 373
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

1
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.

_________________
--------------------------------------------------------------------------------------------------------------------------
All the Gods, All the Heavens, and All the Hells lie within you.
Manager  S
Joined: 29 Sep 2017
Posts: 114
Location: United States
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

prerakgoel07 wrote:
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.

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.
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3564
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

strivingFor800 wrote:
prerakgoel07 wrote:
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.

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.

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?
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

prerakgoel07 wrote:
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.

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.

_________________
Karishma
Veritas Prep GMAT Instructor

Intern  B
Joined: 31 May 2018
Posts: 8
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

prerakgoel07 wrote:
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.

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.

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.
thank you
Intern  B
Joined: 20 Sep 2018
Posts: 37
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

battleprof wrote:
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.

Spoiler: :: OA
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.

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 Intern  B
Joined: 20 Sep 2018
Posts: 37
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

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.

Md231 wrote:
battleprof wrote:
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.

Spoiler: :: OA
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.

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 Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

1
abhimanyujain1711 wrote:
prerakgoel07 wrote:
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.

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.

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.
thank you

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If B is a set of real numbers, is there a number in B that  [#permalink]

### Show Tags

1
See this: https://gmatclub.com/forum/if-b-is-a-se ... l#p1216327

Md231 wrote:
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.

Md231 wrote:
battleprof wrote:
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.

Spoiler: :: OA
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.

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 _________________
Karishma
Veritas Prep GMAT Instructor Re: If B is a set of real numbers, is there a number in B that   [#permalink] 01 Oct 2018, 02:40
Display posts from previous: Sort by

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