Author 
Message 
Founder
Joined: 04 Dec 2002
Posts: 15148
Location: United States (WA)

GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
07 Jun 2009, 01:07
GMAT Diagnostic Test Question 42Field: combinations Difficulty: 750
Set \(X\) has 5 integers: \(a\), \(b\), \(c\), \(d\), and \(e\). If \(m\) is the mean and \(D\), where \(D = \sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\), 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
Coauthor of the GMAT Club tests



CIO
Joined: 02 Oct 2007
Posts: 1218

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
08 Jul 2009, 04:32
Explanation:
Official Answer: CStatement 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): \(D = \sqrt{\frac{(13)^2+(23)^2+(33)^2+(43)^2+(53)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}\) 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: \(D = \sqrt{\frac{(12)^2+(12)^2+(12)^2+(12)^2+(62)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2\) 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: \(D = \sqrt{\frac{(14)^2+(24)^2+(34)^2+(64)^2+(84)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2\) S2+S1 is sufficient.
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
28 Jul 2009, 17:59
I had confusion here... 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
29 Jul 2009, 00:51
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: I had confusion here... 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. Please read this before posting in GMAT Club Tests forum 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
30 Jul 2009, 00:04



Manager
Joined: 14 Aug 2009
Posts: 123

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
23 Aug 2009, 09:58
1
This post received KUDOS
dzyubam wrote: Explanation:
Official Answer: CStatement 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): \(d = \sqrt{\frac{(13)^2+(23)^2+(33)^2+(43)^2+(53)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}\) 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: \(d = \sqrt{\frac{(12)^2+(12)^2+(12)^2+(12)^2+(62)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2\) 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. \( d = \sqrt{\frac{(14)^2+(24)^2+(34)^2+(64)^2+(84)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2\) 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
23 Aug 2009, 15:44
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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
23 Aug 2009, 23:16
I guess the answer could be B, but can anyone give a prove? Thanks.



Manager
Joined: 22 Jul 2009
Posts: 191

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
24 Aug 2009, 00:12
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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
24 Aug 2009, 01:11
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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
24 Aug 2009, 05:27



Manager
Joined: 14 Aug 2009
Posts: 123

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
25 Aug 2009, 17:18
1
This post received 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
25 Aug 2009, 18:54
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: 914

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
07 Sep 2009, 12:46
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 = \(\sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\)
next step, I squared both sides for D > 2: 2^2 > \(\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}\)
2^2 * 5 > \((am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2\)
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? = \(\sqrt{\frac{(13.6)^2+(23.6)^2+(43.6)^2+(53.6)^2+(63.6)^2}{5}}\) = \(\sqrt{\frac{(2.6)^2+(1.6)^2+(0.4)^2+(1.4)^2+(2.4)^2}{5}}\) = 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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
07 Sep 2009, 14:35
1
This post received 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 = \(\sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\) ...
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum 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: 2473

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
09 Sep 2009, 08:58
bb wrote: GMAT Diagnostic Test Question 42Field: combinations Difficulty: 750
Set \(X\) has 5 integers: \(a\), \(b\), \(c\), \(d\), and \(e\). If \(m\) is the mean and \(D\), where \(D = \sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\), 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. \(D = \sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\) Statements 1 and 2 are sufficient and therefore C is correct. dzyubam wrote: Explanation:
Official Answer: CStatement 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): \(D = \sqrt{\frac{(13)^2+(23)^2+(33)^2+(43)^2+(53)^2}{5}} = \sqrt{\frac{4 + 1 + 0 + 1 + 4}{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}\) 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: \(D = \sqrt{\frac{(12)^2+(12)^2+(12)^2+(12)^2+(62)^2}{5}} = \sqrt{\frac{1 + 1 + 1 + 1 + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2\) 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: \(D = \sqrt{\frac{(14)^2+(24)^2+(34)^2+(64)^2+(84)^2}{5}} = \sqrt{\frac{9 + 4 + 1 + 4 + 16}{5}} = \sqrt{\frac{34}{5}} = \sqrt{6.8} > 2\) S2+S1 is sufficient.
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Intern
Joined: 01 Sep 2009
Posts: 4

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
15 Sep 2009, 16:05
edit: nvm, got it. the restriction that m is an integer is key.



Intern
Joined: 24 Nov 2009
Posts: 27
Location: ny, ny

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
25 Nov 2009, 17:06
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

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
26 Nov 2009, 02:59
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. Please read this before posting in GMAT Club Tests forum 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: 170

Re: GMAT Diagnostic Test Question 42 [#permalink]
Show Tags
05 Jan 2010, 18:06
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 = \(\sqrt{\frac{(am)^2+(bm)^2+(cm)^2+(dm)^2+(em)^2}{5}}\) ...




Re: GMAT Diagnostic Test Question 42
[#permalink]
05 Jan 2010, 18:06



Go to page
1 2
Next
[ 23 posts ]




