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

 It is currently 17 Oct 2019, 09:09

### 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

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

Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

30 Oct 2013, 20:00
1
fozzzy wrote:
Hi Bunuel,

For this question if the stem stated that all the integers are positive would the answer be A?

Yes, if the integers are positive, the sum would be positive too. Then statement (A) alone would be sufficient.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 09 Mar 2014
Posts: 5
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

15 Apr 2014, 00:21
Brunel,

Thank you for all your help. Brilliant stuff!

I have a concern on this one... I had marked the answer as E on GMATPrep but as per the answers on it the correct answer is A, and obviously the software will consider these answers when calculating your score. How exactly or to what extend can we rely on the score thrown up by the test if they have wrong answers on the software to begin with? It's causing a conflict. Please help.

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

15 Apr 2014, 00:59
Brunel,

Thank you for all your help. Brilliant stuff!

I have a concern on this one... I had marked the answer as E on GMATPrep but as per the answers on it the correct answer is A, and obviously the software will consider these answers when calculating your score. How exactly or to what extend can we rely on the score thrown up by the test if they have wrong answers on the software to begin with? It's causing a conflict. Please help.

Thank you.

Actually there aren't that many flawed questions in GMAT Prep and they remove one when spot it. I remember only 3 or 4 wrong questions in different editions, so generally their score is accurate.
_________________
Intern
Joined: 04 May 2013
Posts: 8
Schools: Yale '17
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

01 Jul 2014, 00:26
Bunuel 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?

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.

I am not understanding, because I got this same question in GMAT prep & ans indicated by them is A. And I am also unclear as why A. So is there something I am missing or the above explanation has something missing??
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

01 Jul 2014, 00:32
patternpandora wrote:
Bunuel 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?

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.

I am not understanding, because I got this same question in GMAT prep & ans indicated by them is A. And I am also unclear as why A. So is there something I am missing or the above explanation has something missing??

As indicated by Bunuel in his post here: the-sum-of-the-integers-in-list-s-is-the-same-as-the-sum-of-127755.html#p1046371
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 28 Apr 2014
Posts: 195
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

01 Jul 2014, 21:39
Bunuel 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?

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.

As always your solutions are elegant and crisp Bunuel. I liked the thought process on 1. Any other way to work on option 2 ? I am a bit wary on putting in values. Any conceptual way to negate this option ?
Intern
Joined: 04 May 2013
Posts: 8
Schools: Yale '17
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

03 Jul 2014, 02:57
VeritasPrepKarishma wrote:
patternpandora wrote:
Bunuel 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?

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.

I am not understanding, because I got this same question in GMAT prep & ans indicated by them is A. And I am also unclear as why A. So is there something I am missing or the above explanation has something missing??

As indicated by Bunuel in his post here: the-sum-of-the-integers-in-list-s-is-the-same-as-the-sum-of-127755.html#p1046371

I am attaching the screenshot indicating OA as A from Gmat Prep test

Attachments

File comment: Screenshot of Q from GMAT prep indicating OA : A

Screenshot 2014-07-03 15.23.16.png [ 498.1 KiB | Viewed 3156 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

03 Jul 2014, 03:36
patternpandora wrote:
VeritasPrepKarishma wrote:
patternpandora wrote:

I am not understanding, because I got this same question in GMAT prep & ans indicated by them is A. And I am also unclear as why A. So is there something I am missing or the above explanation has something missing??

As indicated by Bunuel in his post here: the-sum-of-the-integers-in-list-s-is-the-same-as-the-sum-of-127755.html#p1046371

I am attaching the screenshot indicating OA as A from Gmat Prep test

_________________
Manager
Joined: 22 Jan 2014
Posts: 170
WE: Project Management (Computer Hardware)
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

06 Jul 2014, 08:37
Apex231 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.

My take is E.

1) S = {1,2,3,4} ; avg = 2.5
T = {100,200} ; avg = 150
avg(T) > avg(S) and {S} > {T}

now

S = {1,2,3,4} ; avg = 2.5
T = {100,200,300,400,500} ; avg = 375
avg(T) > avg(S) and {T} > {S}

Hence A is not sufficient.

2) S = {1,2,3} ; median = 2
T = {1,2} ; median = 1.5
{S} > {T}

now

S = {1,2,3} ; median = 2
T = {-5,-4,-3,-2,-1} ; median = -3
{T} > {S}

Hence B is not sufficient

(A) + (B)

S = {1,2,3} ; median = 2
T = {-5,-4,-3,-2,1000} ; median = -3
avg(S) < avg(T) and {T} > {S}

now

S = {1,2,3,4,5,10000} ; median = 4
T = {-100, -3, 1000000} ; median = -3
avg(S) < avg(T) and {S} > {T}

Hence (A)+(B) is insufficient.
_________________
Illegitimi non carborundum.
Intern
Joined: 04 Jun 2014
Posts: 46
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

30 Aug 2014, 06:30
Is it possible to do this in 2 minutes with inserting numbers like in Bunuel's explanation? :S Or is there another approach?
I always prefer to insert numbers, but it seems that it just takes far too long sometimes..
Retired Moderator
Joined: 29 Oct 2013
Posts: 252
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

06 Jan 2016, 06:22
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
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

06 Jan 2016, 22:26
2
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.
_________________
Karishma
Veritas Prep GMAT Instructor

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

19 Jun 2017, 03:51
1
Apex231 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.

Given, Sum of terms in S = Sum of terms in T

Is Number of terms in S > Number of terms in T?

Statement 1: Average of S < Average of T

i.e. (Sum of terms in S)/Number of terms in S < (Sum of terms in T)/Number of terms in T

i.e. (Sum of terms in S)* Number of terms in T < (Sum of terms in T)* Number of terms in S

If sum of terms in S is POSITIVE then it may be cancelled out from both sides and then
Number of terms in T < Number of terms in S

If sum of terms in S is NEGATIVE then it may be cancelled out from both sides but Inequality sign reverses i.e.
Number of terms in T > Number of terms in S

Hence NOT SUFFICIENT

Statement 2: Median of S > Median of T
But median have no relation with the sum of the terms in any set hence
NOT SUFFICIENT

Combining also doesn't give any solution as median has no relation with sum of terms and first statement is Insufficient as we don't know whether Sum of the terms of the Set S and T are positive or negative

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

07 Oct 2017, 00:12
1
Apex231 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.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Sum(S) = Sum(T) ==> Q: #(S) > #(T)

There are 4 variables and 1 equation. Thus the answer E is most likely.

Actually, there is no relation between average and median.
The reason A is not an answer is that the sum could be positive or negative.

Let's consider both conditions 1) and 2) together.

S = { 1, 2, 3, 4 }
T = { 1, 2, 7 }
Sum = 1 + 2 + 3 + 4 = 1 + 2 + 7 = 10
ave(S) = 10/4 and ave(T) = 10/3
med(S) = 2.5 and med(T) = 2
S has more integers than T : Yes

S = { -1, -2, -7 }
T = { -1, -2, -3, -4 }
Sum = (-1)+(-2)+(-7) = (-1)+(-2)+(-3)+(-4) = -10
ave(S) = -10/3 and ave(T) = -10/4
med(S) = -2 and med(T) = -2.5
T has more integers than S : No.

Therefore, the answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

22 Jul 2018, 17:51
chetan2u niks18 gmatbusters KarishmaB Abhishek009 amanvermagmat

Can anyone help with algebraic approach to this Q? I am a bit uncomfortable with
picking numbers to prove statements are not sufficient.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

22 Jul 2018, 21:28
chetan2u niks18 gmatbusters KarishmaB Abhishek009 amanvermagmat

Can anyone help with algebraic approach to this Q? I am a bit uncomfortable with
picking numbers to prove statements are not sufficient.

check this solution by Bunuel. If you have any query, pls let us know -

https://gmatclub.com/forum/the-sum-of-t ... l#p1046371
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

23 Jul 2018, 05:21
chetan2u niks18 gmatbusters KarishmaB Abhishek009 amanvermagmat

Can anyone help with algebraic approach to this Q? I am a bit uncomfortable with
picking numbers to prove statements are not sufficient.

Bunuel has given you the algebraic approach for statement 1 (link given by niks18 above).
When you talk of median, usually you do not have an algebraic approach. You often need to pick numbers to figure out the logic.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 02 Aug 2017
Posts: 52
Concentration: Strategy, Nonprofit
Schools: ISB '20
GPA: 3.71
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

30 Aug 2018, 08:49
1)
Let S= 1,1
T=-1,0,3
Average of S > Average of T

Now let S=1,0,-3
T=-1,-1
Average of S > Average of T

Thus for Average of S > Average of T, # of integers in S can be smaller or greater than those in T.
INSUFFICIENT

2)
Again,
Let S= 1,1
T=-1,0,3
Mean of S(0.5) > Mean of T(0)

Now let S=1,0,-3
T=-1,-1
Mean of S > Mean of T

Thus for Mean of S > Mean of T, # of integers in S can be smaller or greater than those in T.
INSUFFICIENT

As the same examples have been used to show that both options each are insufficient, we can use the same examples to show that both choices together are INSUFFICIENT.

_________________

Everything is in flux, nothing stays still

MGMAT1 :590 Q42 V30 (07/07/18)
VERITAS :660 Q48 V33 (16/07/18)
GMATPREP1 :690 Q46 V36 (22/07/18)
GMATPREP2 :740 Q51 V39 (06/08/18)
ECONOMIST :740 Q49 V44 (11/08/18)
KAPLAN :690 Q49 V36 (17/08/18)
PRINCETON :690 Q48 V38 (26/08/18)
MGMAT2 :720 Q43 V45 (02/09/18)
Manager
Status: wake up with a purpose
Joined: 24 Feb 2017
Posts: 118
Concentration: Accounting, Entrepreneurship
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

26 Apr 2019, 01:28
MathRevolution wrote:
Apex231 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.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Sum(S) = Sum(T) ==> Q: #(S) > #(T)

There are 4 variables and 1 equation. Thus the answer E is most likely.

Actually, there is no relation between average and median.
The reason A is not an answer is that the sum could be positive or negative.

Let's consider both conditions 1) and 2) together.

S = { 1, 2, 3, 4 }
T = { 1, 2, 7 }
Sum = 1 + 2 + 3 + 4 = 1 + 2 + 7 = 10
ave(S) = 10/4 and ave(T) = 10/3
med(S) = 2.5 and med(T) = 2
S has more integers than T : Yes

S = { -1, -2, -7 }
T = { -1, -2, -3, -4 }
Sum = (-1)+(-2)+(-7) = (-1)+(-2)+(-3)+(-4) = -10
ave(S) = -10/3 and ave(T) = -10/4
med(S) = -2 and med(T) = -2.5
T has more integers than S : No.

Therefore, the answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

Why you always say "forget about conventional approach"? Most of you explanation are based on conventional approach. The way you write the explanations makes them boring, dull and eventually no takeaway for the future problems.

Posted from my mobile device
_________________
If people are NOT laughing at your GOALS, your goals are SMALL.
Non-Human User
Joined: 09 Sep 2013
Posts: 13242
Re: The sum of the integers in list S is the same as the sum of the intege  [#permalink]

### Show Tags

15 Jul 2019, 04:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The sum of the integers in list S is the same as the sum of the intege   [#permalink] 15 Jul 2019, 04:08

Go to page   Previous    1   2   [ 40 posts ]

Display posts from previous: Sort by