GMAT Diagnostic Test Question 42 : Retired Discussions [Locked]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 11:30

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Diagnostic Test Question 42

Author Message
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14421
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3712

Kudos [?]: 22932 [0], given: 4510

GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

07 Jun 2009, 00:07
Expert's post
1
This post was
BOOKMARKED
GMAT Diagnostic Test Question 42
Field: combinations
Difficulty: 750
 Rating:

Set $$X$$ has 5 integers: $$a$$, $$b$$, $$c$$, $$d$$, and $$e$$. If $$m$$ is the mean and $$D$$, where $$D = \sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$, is the standard deviation of the set $$X$$, is $$D \gt 2$$?

(1) $$a$$, $$b$$, $$c$$, $$d$$, and $$e$$ are different integers
(2) $$m$$ is an integer not equal to any elements of the set $$X$$

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient
_________________

Founder of GMAT Club

US News Rankings progression - last 10 years in a snapshot - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [0], given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

08 Jul 2009, 03:32
Explanation:
 Rating:

Statement 1 is not sufficient. The answer to the question might be YES or NO depending on the numbers in the set. Any set with significant range will have $$D \gt 2$$ (e.g. 1, 2, 3, 4, 100). On the other hand, $$D$$ can be as low as $$\sqrt{2}$$ for a set consisting of 1, 2, 3, 4, and 5 (mean of this set equals 3):

$$D = \sqrt{\frac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}$$

The answer to the question can be either YES or NO. Not sufficient.

Statement 2 is not sufficient by itself either. Again, $$D$$ can be very big if the range is great (see an example frm S1). Consider this set for $$D$$ to be as low as 2: 1, 1, 1, 1, 6. The mean is 2, $$D$$ is calculated as follows:

$$D = \sqrt{\frac{(1-2)^2+(1-2)^2+(1-2)^2+(1-2)^2+(6-2)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2$$

The answer to the question can be either YES or NO. Not sufficient.

Combining both statements, we have enough information to answer the question. The answer is YES. To prove that we have to think of a set with minimum possible range under restrictions of S1 and S2. We will use this set: 1, 2, 3, 6, 8. Its mean is 4. The standard deviation is calculated as follows:

$$D = \sqrt{\frac{(1-4)^2+(2-4)^2+(3-4)^2+(6-4)^2+(8-4)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2$$

S2+S1 is sufficient.
_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 02 Jul 2009
Posts: 6
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

28 Jul 2009, 16:59
The different elements of the set are a,b,c,d,e.
The standard deviation is d.
So, I actually got confused if the question asks to find if - both the standard deviation and the fourth element - are greater than 2.

Harry
CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [0], given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

28 Jul 2009, 23:51
The question was meant to ask if the standard deviation was greater than 2. I'll put a "D" to stand for standard deviation to avoid confusion. Thanks!
charimaalu wrote:
The different elements of the set are a,b,c,d,e.
The standard deviation is d.
So, I actually got confused if the question asks to find if - both the standard deviation and the fourth element - are greater than 2.

Harry

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [0], given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

29 Jul 2009, 23:04
I've updated the PDF and the question above to avoid confusion.
_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 14 Aug 2009
Posts: 123
Followers: 2

Kudos [?]: 103 [1] , given: 13

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

23 Aug 2009, 08:58
1
KUDOS
dzyubam wrote:
Explanation:
 Rating:

Statement 1 is not sufficient. The answer to the question might be YES or NO depending on the numbers in the set. Any set with significant range will have $$d \gt 2$$ (e.g. 1, 2, 3, 4, 100). On the other hand, $$d$$ can be as low as $$\sqrt{2}$$ for a set consisting of 1, 2, 3, 4, and 5 (mean of this set equals 3):

$$d = \sqrt{\frac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}$$

The answer to the question can be either YES or NO. Not sufficient.

Statement 2 is not sufficient by itself either. Again, we $$d$$ can be very big if the range is great (see an example frm S1). Consider this set for $$d$$ to be as low as 2: 1, 1, 1, 1, 6. The mean is 2, $$d$$ is calculated as follows:

$$d = \sqrt{\frac{(1-2)^2+(1-2)^2+(1-2)^2+(1-2)^2+(6-2)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2$$

The answer to the question can be either YES or NO. Not sufficient.

Combining both statements, we have enough information to answer the question. The answer is YES. To prove that we have to think of a set with minimum possible range under restrictions of S1 and S2. We will use this set: 1, 2, 3, 6, 8. Its mean is 4. The standard deviation is calculated as follows:

S2+S1 is sufficient.

$$d = \sqrt{\frac{(1-4)^2+(2-4)^2+(3-4)^2+(6-4)^2+(8-4)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2$$
can't prove "S2+S1 is sufficient", it is only one example.
_________________

Kudos me if my reply helps!

Manager
Joined: 22 Jul 2009
Posts: 191
Followers: 4

Kudos [?]: 259 [0], given: 18

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

23 Aug 2009, 14:44
Could somebody prove that the answer is C?

An example is not enough to prove it.

I can't find a counterexample, most likely because the answer is indeed C, but would be good if it could be proved.

BTW, shouldn't this question be on the "statistics" field?
_________________

Please kudos if my post helps.

Intern
Joined: 21 Aug 2009
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 19

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

23 Aug 2009, 22:16
I guess the answer could be B, but can anyone give a prove? Thanks.
Manager
Joined: 22 Jul 2009
Posts: 191
Followers: 4

Kudos [?]: 259 [0], given: 18

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

23 Aug 2009, 23:12
defeatgmat wrote:
I guess the answer could be B, but can anyone give a prove? Thanks.

Its already been proved. Look at the official explanation above; dzyubam provided a counterexample that makes statement 2 not sufficient.
_________________

Please kudos if my post helps.

Manager
Joined: 14 Aug 2009
Posts: 123
Followers: 2

Kudos [?]: 103 [0], given: 13

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

24 Aug 2009, 00:11
powerka wrote:
defeatgmat wrote:
I guess the answer could be B, but can anyone give a prove? Thanks.

Its already been proved. Look at the official explanation above; dzyubam provided a counterexample that makes statement 2 not sufficient.

The example only proves 2) individually is insufficient;

The example after it gave only one instance, can't prove S1+S2 are always correct.
_________________

Kudos me if my reply helps!

CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [0], given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

24 Aug 2009, 04:27
In my proof that C is the correct option I've used the numbers that produce the least standard deviation given the conditions in S1 and S2. I can't think of a better way to prove it. You're welcome to come up with one if you can. Anybody?
_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 14 Aug 2009
Posts: 123
Followers: 2

Kudos [?]: 103 [1] , given: 13

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

25 Aug 2009, 16:18
1
KUDOS
If D=2 is the minimum, we can say D>2.
can anyone prove this?
_________________

Kudos me if my reply helps!

Intern
Joined: 21 Aug 2009
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 19

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

25 Aug 2009, 17:54
flyingbunny wrote:
If D=2 is the minimum, we can say D>2.
can anyone prove this?

Yep, I believe this would be the key.
Director
Joined: 11 Jun 2007
Posts: 931
Followers: 1

Kudos [?]: 175 [0], given: 0

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

07 Sep 2009, 11:46
Think it should be E. Please let me know where my logic is incorrect.

What I did first to breakdown this problem is in order for std D> 2, have to find out the mininum the numerator should be
D = $$\sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$

next step, I squared both sides for D > 2:
2^2 > $$\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}$$

2^2 * 5 > $$(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2$$

20 > sum of numerator

Combining information from the two statements together, this is my counterexample:
I used this for my set: 1, 2, 4, 5, 6. Its mean is 3.6. The standard deviation is calculated as follows:

is numerator greater than 20?
= $$\sqrt{\frac{(1-3.6)^2+(2-3.6)^2+(4-3.6)^2+(5-3.6)^2+(6-3.6)^2}{5}}$$
= $$\sqrt{\frac{(2.6)^2+(1.6)^2+(0.4)^2+(1.4)^2+(2.4)^2}{5}}$$
= 6.76 + 2.56 + 0.16 + 1.96 + 5.76
= 17.xx

in this case, it is a NO, D < 2
CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [1] , given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

07 Sep 2009, 13:35
1
KUDOS
There's one problem with your counter example. $$m$$ should be an integer according to S2.
beckee529 wrote:
Think it should be E. Please let me know where my logic is incorrect.

What I did first to breakdown this problem is in order for std D> 2, have to find out the mininum the numerator should be
D = $$\sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$
...

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 67

Kudos [?]: 734 [0], given: 19

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

09 Sep 2009, 07:58
bb wrote:
GMAT Diagnostic Test Question 42
Field: combinations
Difficulty: 750
 Rating:

Set $$X$$ has 5 integers: $$a$$, $$b$$, $$c$$, $$d$$, and $$e$$. If $$m$$ is the mean and $$D$$, where $$D = \sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$, is the standard deviation of the set $$X$$, is $$D \gt 2$$?

(1) $$a$$, $$b$$, $$c$$, $$d$$, and $$e$$ are different integers
(2) $$m$$ is an integer not equal to any elements of the set $$X$$

Sticking to the question and the conditions above suffices to say that D>2.

Things to be noted:

1. a, b, c, d, and e, Elements of the set X, are different integers.
2. m is different from the above 5 elements of the set X.
3. Calcualation of D is only using the given formula i.e.

$$D = \sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$

Statements 1 and 2 are sufficient and therefore C is correct.

dzyubam wrote:
Explanation:
 Rating:

Statement 1 is not sufficient. The answer to the question might be YES or NO depending on the numbers in the set. Any set with significant range will have $$D \gt 2$$ (e.g. 1, 2, 3, 4, 100). On the other hand, $$D$$ can be as low as $$\sqrt{2}$$ for a set consisting of 1, 2, 3, 4, and 5 (mean of this set equals 3):

$$D = \sqrt{\frac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}$$

The answer to the question can be either YES or NO. Not sufficient.

Statement 2 is not sufficient by itself either. Again, $$D$$ can be very big if the range is great (see an example frm S1). Consider this set for $$D$$ to be as low as 2: 1, 1, 1, 1, 6. The mean is 2, $$D$$ is calculated as follows:

$$D = \sqrt{\frac{(1-2)^2+(1-2)^2+(1-2)^2+(1-2)^2+(6-2)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2$$

The answer to the question can be either YES or NO. Not sufficient.

Combining both statements, we have enough information to answer the question. The answer is YES. To prove that we have to think of a set with minimum possible range under restrictions of S1 and S2. We will use this set: 1, 2, 3, 6, 8. Its mean is 4. The standard deviation is calculated as follows:

$$D = \sqrt{\frac{(1-4)^2+(2-4)^2+(3-4)^2+(6-4)^2+(8-4)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2$$

S2+S1 is sufficient.

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Intern
Joined: 01 Sep 2009
Posts: 4
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

15 Sep 2009, 15:05
edit: nvm, got it. the restriction that m is an integer is key.
Intern
Joined: 24 Nov 2009
Posts: 27
Location: ny, ny
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

25 Nov 2009, 16:06
I have a question about the OE for this problem. You have assumed that the integers in set X to be 1,1,1,1,6 which gives us m=2. however, this satisfies only S2. S1 says that all the elements of set X must be "Different Integers" or as I assumed to be "Distinct Integers".
The smallest set I came up with was x = {1,2,3,4,15} gives us m = 5 and SD = 26^1/2
Ofcourse, after the test, I realized that I never considered negative integers.
I came up with choice C as a calculated guess since thats all I could manage in 2 mins
CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 911 [0], given: 334

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

26 Nov 2009, 01:59
I assumed that when I was explaining why S2 ONLY can't be sufficient. We have to be sure to regard information presented in S1 and S2 separately as long as we consider A or B as possible answers.

I hope this helps .
amittilak wrote:
I have a question about the OE for this problem. You have assumed that the integers in set X to be 1,1,1,1,6 which gives us m=2. however, this satisfies only S2. S1 says that all the elements of set X must be "Different Integers" or as I assumed to be "Distinct Integers".
The smallest set I came up with was x = {1,2,3,4,15} gives us m = 5 and SD = 26^1/2
Ofcourse, after the test, I realized that I never considered negative integers.
I came up with choice C as a calculated guess since thats all I could manage in 2 mins

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 08 Jul 2009
Posts: 171
Followers: 0

Kudos [?]: 25 [0], given: 26

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

05 Jan 2010, 17:06
Oh, that's what i missed too. Thanks.

dzyubam wrote:
There's one problem with your counter example. $$m$$ should be an integer according to S2.
beckee529 wrote:
Think it should be E. Please let me know where my logic is incorrect.

What I did first to breakdown this problem is in order for std D> 2, have to find out the mininum the numerator should be
D = $$\sqrt{\frac{(a-m)^2+(b-m)^2+(c-m)^2+(d-m)^2+(e-m)^2}{5}}$$
...
Re: GMAT Diagnostic Test Question 42   [#permalink] 05 Jan 2010, 17:06

Go to page    1   2    Next  [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
7 GMAT Diagnostic Test Question 42 4 29 Sep 2013, 21:00
16 GMAT Diagnostic Test Question 4 37 06 Jun 2009, 20:06
23 GMAT Diagnostic Test Question 3 33 06 Jun 2009, 18:33
9 GMAT Diagnostic Test Question 2 26 06 Jun 2009, 18:03
36 GMAT Diagnostic Test Question 1 30 05 Jun 2009, 21:30
Display posts from previous: Sort by

# GMAT Diagnostic Test Question 42

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.