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# The sum of the integers in list S is the same as the sum of

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The sum of the integers in list S is the same as the sum of [#permalink]

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18 Feb 2012, 09:09
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The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T?

(1) The average (arithmetic mean) of the integers in S is less than the average of the integers in T.
(2) The median of the integers in S is greater than the median of the integers in T.
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Re: The sum of the integers in list S is the same as the sum of [#permalink]

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18 Feb 2012, 11:24
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The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T?

Given: $$sum(S)=sum(T)$$. Question: is $$t<s$$, where $$s$$ and $$t$$ are # of integers in lists S and T respectively.

(1) The average (arithmetic mean) of the integers in S is less than the average of the integers in T --> $$\frac{sum}{s}<\frac{sum}{t}$$ --> cross multiply: $$sum*t<sum*s$$. Now, if $$sum<0$$ then $$t>s$$ (when reducing by negative flip the sign) but if $$sum>0$$ then $$t<s$$. not sufficient.

(2) The median of the integers in S is greater than the median of the integers in T. If S={1, 1} and T={0, 0, 2} then the median of S (1) is greater than the median of T (0) and S contains less elements than T but if S={-1, -1, -1} and T={-3, 0} then the median of S (-1) is greater than the median of T (-1.5) and S contains more elements than T. Not sufficient.

(1)+(2):
If S={-1, 2, 2} and T={1, 2} then the sum is equal (3), the average of S (1) is less than the average of T (1.5), the median of S (2) is greater than the median of T (1.5) and S contains more elements than T.

If S={-2, -1} and T={-2, -2, 1} then the sum is equal (-3), the average of S (-1.5) is less than the average of T (-1), the median of S (-1.5) is greater than the median of T (-2) and S contains less elements than T.

Not sufficient.

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Re: List S and T [#permalink]

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17 Sep 2012, 21:35
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Bunuel wrote:
enigma123 wrote:
The sum of the integers in list S is same as the sum of the integers in list T. Does S contains more integers than T?

1. The average (arithmetic mean) of the integers in S is less than the average of the integers in T.

2. The median of the integers in S is greater than the median of the integers in T.

Any idea how to get A?

Dear Bunuel

I ran into this question in a Gmat Prep exam and the OA is A. It works with positive integers, but it doesn't with negatives. My pick was C, but after a closer look I ended up with E as you.

My deduction is that the mean is a function of the number of items in each set. As the number of items increases, the mean decreases. In statament 1 we are told that the mean of S is smaller than that of T, but that only work for positives.

Have you ever ran into a GMAT Prep OA that is disputable?

I considered the following

S = 1, 2, 3, 4, 5
Sum is 15
Mean is 3

T = 7, 8
Sum is 15
Mean is 7.5

Therefore if mean of S < mean of T, then S must have more items than T, only if the Sum of the sets is possitive.

Considering two sets that Sum a negative number

S = -4, -3, -2, -1
Sum is -10
Mean -2.5

T = -9, -1
Sum is - 10
Mean -5

Different answer for positives and negatives, therefore not sufficient

We can not take a set that Sums 0, as the medians would be the same

2) The median of integers in S is greater than the median in integers in T.

For positives

S = 1, 2, 3, 4, 5
Sum is 15
Median is 3

T = 7, 8
Sum is 15
Median is 7.5

or

S= 1, 1, 1, 2, 2, 3
Sum 10
Median 1.5

T = 2, 2, 2, 4
Sum 10
Median 2

Seems sufficient but considering two sets that Sum a negative number

S = -4, -3, -2, -1
Sum is -10
Mean -2.5
Median -2.5

T = -9, -1
Sum is - 10
Mean -5
Median -5

Therefore Insufficient

I chosed C as I believed the two statements force the Sum of both sets to be positve, but I guess it was a poorly analyzed deduction.

I have never runed into a question where the OA was open to dispute, have you?

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Crazy sets S and T.JPG [ 76.13 KiB | Viewed 24512 times ]

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Re: The sum of the integers in list S is the same as the sum of [#permalink]

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18 Feb 2012, 10:53
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A is clearly sufficient.

Statement two is insufficient-e.g consider the following sets:

S- 2,3,5
T- 1,2,3,4
S has fewer numbers than T

Now,let S-1,3,4,5
T- 1,3,9

S has more numbers
In each case median of S is greater
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Re: The sum of the integers in list S is the same as the sum of [#permalink]

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21 Feb 2012, 05:23
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Expert's post
prashantbacchewar wrote:
Is the approach to solve such questions is come up with sets which satisfy and dont satisfy the conditions.

Is there any other way we can solve this type of questions.

Generally on DS questions when using plug-in method, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

Of course algebra/math or conceptual/pure logic approach is also applicable to prove that the statement is not sufficient. It really depends on the particular problem and personal preferences to choose which approach to take.

Hope it helps.
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Re: average of integers in a list [#permalink]

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09 Oct 2013, 20:31
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The sum of integers in list S is the same as sum of integers in T. Does S contains more integers than T?

1. the average of integers in S is less than average of integers in T.
2. the median of the integers in S is greater than the median of the integers in T.

Solution :

Statement 1 : Average of S (A1) is less than average of T(A2)

A1<A2

S1 / n1 < S2 / n2

Since S1 = S2 (given)

We can surely find out whether n1 > n2 or not. Sufficient

Statement 2 :

Knowing the median of 2 sets will not let us know the number of integers in each set. (Insufficient)

Option A

Hope it helped.

Cheers
Qoofi
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Re: The sum of the integers in list S is the same as the sum of [#permalink]

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06 Jan 2016, 22:26
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Expert's post
NoHalfMeasures wrote:
The sum of integers in list S is the same as the sum of the integers in T. Does S contain more integers than T?
can we also interpret the above statement to mean that " s and t may also contain decimals along with integers but only sum of their integers is equal?" I am just trying to see how closely we should adhere to the language of the GMAC questions. Thanks

Yes, S and T may contain non-integers too. The question is only concerned about integers (Does S contain more INTEGERS that T?) and hence we don't really care about the other elements. The statements also only talk about integers.

Had the question been: "Does S contain more elements than T?"
we would have had to consider the possibility of non integer elements too.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 16 Jan 2012 Posts: 30 Followers: 0 Kudos [?]: 7 [1] , given: 0 Re: The sum of the integers in list S is the same as the sum of [#permalink] ### Show Tags 18 Feb 2012, 11:26 1 This post received KUDOS clearly, as explained by bunel..ans is E... I did not consider negative sum in A Math Expert Joined: 02 Sep 2009 Posts: 37619 Followers: 7406 Kudos [?]: 99707 [1] , given: 11035 Re: List S and T [#permalink] ### Show Tags 18 Sep 2012, 01:08 1 This post received KUDOS Expert's post Bull78 wrote: Dear Bunuel I ran into this question in a Gmat Prep exam and the OA is A. It works with positive integers, but it doesn't with negatives. My pick was C, but after a closer look I ended up with E as you. I chosed C as I believed the two statements force the Sum of both sets to be positve, but I guess it was a poorly analyzed deduction. I have never runed into a question where the OA was open to dispute, have you? Thanks in advance Yes, there are several questions in GMAT Prep with incorrect answers. This question is one of them. A is not correct, answer should be E. _________________ Math Expert Joined: 02 Sep 2009 Posts: 37619 Followers: 7406 Kudos [?]: 99707 [1] , given: 11035 Re: List S and T [#permalink] ### Show Tags 03 Nov 2012, 09:49 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED srikanthsharma wrote: Bunuel wrote: Bull78 wrote: Dear Bunuel I ran into this question in a Gmat Prep exam and the OA is A. It works with positive integers, but it doesn't with negatives. My pick was C, but after a closer look I ended up with E as you. I chosed C as I believed the two statements force the Sum of both sets to be positve, but I guess it was a poorly analyzed deduction. I have never runed into a question where the OA was open to dispute, have you? Thanks in advance Yes, there are several questions in GMAT Prep with incorrect answers. This question is one of them. A is not correct, answer should be E. Bunuel, I guess A sufficiently works. Because, after reviewing your answer, I tried doing the question again with both positive and negative integers Please see the explanation below and suggest if i went wrong anywhere. Data Sufficiency: 1. Arithmetic mean of list S is less than Arithmetic mean of list T Basic formula used --> Sum = mean * Number of integers in the set Given condition in the question: Sum of the integers in the list S = Sum of the integers in the list T Integers can be both positive and negative. Let the List S = {3,-3,10,2,13} Sum = (3-3+10+2+13) = 25 Number of integers = 5 Mean = 5 (Substitute in the formula) Then List T would be Sum = 25 (Condition given in the question) Number of integers = ? Mean of List T Should be more than mean of List S assume mean = 6 then number of integers in the List T = (25/6) = 4.166 Of course, Number of integers in a List is a number we can still conclude that List T will always be less in the number of integers with Same sum and With more mean. Again, answer to this question is E, not A. There are two examples in my post satisfying both statements and giving different answers. _________________ Manager Status: Pushing Hard Affiliations: GNGO2, SSCRB Joined: 30 Sep 2012 Posts: 89 Location: India Concentration: Finance, Entrepreneurship GPA: 3.33 WE: Analyst (Health Care) Followers: 1 Kudos [?]: 83 [1] , given: 11 Re: sum of integers in list S [#permalink] ### Show Tags 07 May 2013, 08:55 1 This post received KUDOS rochak22 wrote: . The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T? (1) The average (arithmetic mean) of the integers in S is less than the average of the integers in T. (2) The median of the integers in S is greater than the median of the integers in T. Okay the Question asks if the integers in set S is more than the integers in set T ?? Statement1 :: The average (arithmetic mean) of the integers in S is less than the average of the integers in T. Now, use smart number plugin ..... lets say if S = 2, 2, 2 and T = 3, 3, then the sums for both is 6, & the average of S is less than T and S has more integers than T. similarly, if S = -3, -3 and T = -2, -2, -2, then the sums for both is -6, the average of S is less than T and S has fewer integers than T. Therefore, Insufficient Statement 2 :: If T = 2, 2, 2 and S = 3, 3, then the sums for both is 6 & the median of S is greater than median of T and S has fewer integers than T. & If T = -3, -3 and S = -2, -2, -2, then the sums for both -6 & the median of S is greater than median of T and S has more integers than T. Therefore, Insufficient. 1+2 .......... Lets say If S = -7, 9, 10 and T = 6, 6, then the sums for both is 12 & the average of S is less than the average pf T & the median of S is greater than the median of T and S has more integers than T. if S = -6, -6 and T = -10, -9, 7, then the sums for both is -12 & the average of S is less than the average of T & the median of S is greater than the median of T and S has fewer integers than T. Therefore, Insufficient. Hence, E ................. _________________ If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake. Manager Joined: 20 Apr 2010 Posts: 210 Schools: ISB, HEC, Said Followers: 4 Kudos [?]: 81 [0], given: 28 Re: The sum of the integers in list S is the same as the sum of [#permalink] ### Show Tags 21 Feb 2012, 00:30 Is the approach to solve such questions is come up with sets which satisfy and dont satisfy the conditions. Is there any other way we can solve this type of questions. Intern Joined: 29 Sep 2012 Posts: 20 Location: United States Concentration: Finance, Strategy WE: Corporate Finance (Investment Banking) Followers: 0 Kudos [?]: 8 [0], given: 68 Re: List S and T [#permalink] ### Show Tags 03 Nov 2012, 08:49 Bunuel wrote: Bull78 wrote: Dear Bunuel I ran into this question in a Gmat Prep exam and the OA is A. It works with positive integers, but it doesn't with negatives. My pick was C, but after a closer look I ended up with E as you. I chosed C as I believed the two statements force the Sum of both sets to be positve, but I guess it was a poorly analyzed deduction. I have never runed into a question where the OA was open to dispute, have you? Thanks in advance Yes, there are several questions in GMAT Prep with incorrect answers. This question is one of them. A is not correct, answer should be E. Bunuel, I guess A sufficiently works. Because, after reviewing your answer, I tried doing the question again with both positive and negative integers Please see the explanation below and suggest if i went wrong anywhere. Data Sufficiency: 1. Arithmetic mean of list S is less than Arithmetic mean of list T Basic formula used --> Sum = mean * Number of integers in the set Given condition in the question: Sum of the integers in the list S = Sum of the integers in the list T Integers can be both positive and negative. Let the List S = {3,-3,10,2,13} Sum = (3-3+10+2+13) = 25 Number of integers = 5 Mean = 5 (Substitute in the formula) Then List T would be Sum = 25 (Condition given in the question) Number of integers = ? Mean of List T Should be more than mean of List S assume mean = 6 then number of integers in the List T = (25/6) = 4.166 Of course, Number of integers in a List is a number we can still conclude that List T will always be less in the number of integers with Same sum and With more mean. _________________ Learn the Values. Knowledge comes by itself. Intern Joined: 29 Sep 2012 Posts: 20 Location: United States Concentration: Finance, Strategy WE: Corporate Finance (Investment Banking) Followers: 0 Kudos [?]: 8 [0], given: 68 Re: List S and T [#permalink] ### Show Tags 03 Nov 2012, 10:40 Thank you Bunuel. You are a good teacher. Attention to detail is what i have learnt from your explanations. _________________ Learn the Values. Knowledge comes by itself. Intern Joined: 05 May 2013 Posts: 12 Followers: 0 Kudos [?]: 2 [0], given: 6 Re: sum of integers in list S [#permalink] ### Show Tags 07 May 2013, 08:44 S1 sufficient. Since sum S = sum T, as mean for S is less than mean for T, sum/s < sum/t => t<s where s and t are respective number of integers in S and T. S2 insufficient. Answer is A. EDIT: those numbers below zero complicate things. Last edited by AbuRashid on 07 May 2013, 10:58, edited 1 time in total. Intern Joined: 14 Feb 2013 Posts: 32 Schools: Duke '16 Followers: 1 Kudos [?]: 50 [0], given: 14 Re: sum of integers in list S [#permalink] ### Show Tags 08 May 2013, 02:13 Let average of Set S = A1 , Sum = S1 and number of integers in the list = n1 Let average of Set T = A2, Sum = S2 and number of integers in the list = n2 (1) We know, S = A * n A1 = S1/n1 A2 = S2/n2 Acc to statement 1, A1 < A2, so $$\frac{S1}{n1} < \frac{S2}{n2}$$ Given, The sum of the integers in list S is the same as the sum of the integers in list T So, S1 = S2 $$\frac{1}{n1} < \frac{1}{n2}$$ n2 < n1 (2) The median of the integers in S is greater than the median of the integers in T. - Not Sufficient Can someone explain why, Answer is E and not A _________________ Consider giving +1 Kudo when my post helps you. Also, Good Questions deserve Kudos..! Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 630 Followers: 82 Kudos [?]: 1149 [0], given: 136 Re: sum of integers in list S [#permalink] ### Show Tags 08 May 2013, 05:11 Quote: Can someone explain why, Answer is E and not A We know that $$\frac{S}{s}<\frac{S}{t}$$ , where S ,s,t are the sum and no of integers in the list S and T respectively. Thus, s>t for S>0 and t>s for S<0. Insufficient.Remember that the sum of the integers can be negative also. _________________ Intern Joined: 01 May 2013 Posts: 6 Followers: 0 Kudos [?]: 0 [0], given: 12 Re: List S and T [#permalink] ### Show Tags 09 May 2013, 19:54 ChallengeAnything wrote: Bunuel wrote: Bull78 wrote: Dear Bunuel I ran into this question in a Gmat Prep exam and the OA is A. It works with positive integers, but it doesn't with negatives. My pick was C, but after a closer look I ended up with E as you. I chosed C as I believed the two statements force the Sum of both sets to be positve, but I guess it was a poorly analyzed deduction. I have never runed into a question where the OA was open to dispute, have you? Thanks in advance Yes, there are several questions in GMAT Prep with incorrect answers. This question is one of them. A is not correct, answer should be E. Bunuel, I guess A sufficiently works. Because, after reviewing your answer, I tried doing the question again with both positive and negative integers Please see the explanation below and suggest if i went wrong anywhere. Data Sufficiency: 1. Arithmetic mean of list S is less than Arithmetic mean of list T Basic formula used --> Sum = mean * Number of integers in the set Given condition in the question: Sum of the integers in the list S = Sum of the integers in the list T Integers can be both positive and negative. Let the List S = {3,-3,10,2,13} Sum = (3-3+10+2+13) = 25 Number of integers = 5 Mean = 5 (Substitute in the formula) Then List T would be Sum = 25 (Condition given in the question) Number of integers = ? Mean of List T Should be more than mean of List S assume mean = 6 then number of integers in the List T = (25/6) = 4.166 Of course, Number of integers in a List is a number we can still conclude that List T will always be less in the number of integers with Same sum and With more mean. but please tell me why did you consider statements 1 and 2 together..... when statement 1 alone is suffiecient : statement 1 talks about the sum as a whole so : as per the basic formula : sum/num of numbers gives mean and as given sum is equal for both sets and mean of s is less than t clearly says s has more num of integers. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7252 Location: Pune, India Followers: 2205 Kudos [?]: 14355 [0], given: 222 Re: List S and T [#permalink] ### Show Tags 10 May 2013, 08:30 dyuthi92 wrote: but please tell me why did you consider statements 1 and 2 together..... when statement 1 alone is suffiecient : statement 1 talks about the sum as a whole so : as per the basic formula : sum/num of numbers gives mean and as given sum is equal for both sets and mean of s is less than t clearly says s has more num of integers. Consider this: S = {-1, 0, 1} T = {-2, -1, 0, 1, 2} Sum of both the sets is 0. T has more integers. or S = {-2, -1, 0, 1, 2} T = {-1, 0, 1} Sum of both the sets is 0. S has more integers. Similarly, think what happens when the sum is negative. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: average of integers in a list [#permalink]

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10 Oct 2013, 01:36
Qoofi wrote:
The sum of integers in list S is the same as sum of integers in T. Does S contains more integers than T?

1. the average of integers in S is less than average of integers in T.
2. the median of the integers in S is greater than the median of the integers in T.

Solution :

Statement 1 : Average of S (A1) is less than average of T(A2)

A1<A2

S1 / n1 < S2 / n2

Since S1 = S2 (given)

We can surely find out whether n1 > n2 or not. Sufficient

Statement 2 :

Knowing the median of 2 sets will not let us know the number of integers in each set. (Insufficient)

Option A

Hope it helped.

Cheers
Qoofi

The correct answer is E, not A. Check here: the-sum-of-the-integers-in-list-s-is-the-same-as-the-sum-of-127755.html#p1046371

Hope it helps.
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Re: average of integers in a list   [#permalink] 10 Oct 2013, 01:36

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