Last visit was: 19 Nov 2025, 16:33 It is currently 19 Nov 2025, 16:33
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
User avatar
zisis
Joined: 16 Feb 2010
Last visit: 01 Jul 2012
Posts: 122
Own Kudos:
1,724
 [38]
Given Kudos: 16
Posts: 122
Kudos: 1,724
 [38]
4
Kudos
Add Kudos
34
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,368
 [9]
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
 [9]
5
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
zisis
Joined: 16 Feb 2010
Last visit: 01 Jul 2012
Posts: 122
Own Kudos:
Given Kudos: 16
Posts: 122
Kudos: 1,724
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zisis
the OA is def the one posted....double checked it.....
will let more people get involved and then post the OA explanation.....your post supports my view that this question is not phrased correclt (ie is open to misinterpetation).....

the bigger question is how can we make sure that the practise we get is up to the test's standard if massive companies like Kaplan cannt phrase their questions correctly....

Check the statements not the OA (placement of negative/positive in 1 and 2). There is nothing wrong with the question.
User avatar
zisis
Joined: 16 Feb 2010
Last visit: 01 Jul 2012
Posts: 122
Own Kudos:
Given Kudos: 16
Posts: 122
Kudos: 1,724
Kudos
Add Kudos
Bookmarks
Bookmark this Post
you were right......I AM going mental.... just edited my post....hope this makes more sense
User avatar
zisis
Joined: 16 Feb 2010
Last visit: 01 Jul 2012
Posts: 122
Own Kudos:
Given Kudos: 16
Posts: 122
Kudos: 1,724
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zisis
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive
(2) The fourth term in S is negative


The book claims this is one of the most diff questions GMAT can produce which I believe it is a joke....nevertheless got it wrong because I mis-interpreted the question. I am posting to see if more people will mis-interpret or if it is just me that is going *o*kers


One final question:
I misinterpreted the If each term in S after the second part....thought that the "formula"/instructions (\(An= An-1 * An-2\) is only for the third onwards, thus we know nothing for the first two terms thus it is not possible to answer the question.....is that a valid conclusion....?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zisis
zisis
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive
(2) The fourth term in S is negative


The book claims this is one of the most diff questions GMAT can produce which I believe it is a joke....nevertheless got it wrong because I mis-interpreted the question. I am posting to see if more people will mis-interpret or if it is just me that is going *o*kers


One final question:
I misinterpreted the If each term in S after the second part....thought that the "formula"/instructions (\(An= An-1 * An-2\) is only for the third onwards, thus we know nothing for the first two terms thus it is not possible to answer the question.....is that a valid conclusion....?

You interpreted correctly: \(a_n=a_{n-1}*a_{n-2}\), for \(n>2\).

But you are not right about the first two terms for the following statements:


(2) The fourth term in S is negative --> \(a_4=negative=a_3*a_2\) --> second and third term must have opposite signs, so third term is either positive or negative. Now, case 1: if third term is positive then first and second terms must be both negative (for first and second it's not possible to be both positive as in this case fourth term would be positive too and we know that it's negative) and case 2: if third term is negative then first and second terms must have opposite signs. So there are only 2 cases possible:

--+--+--+...
OR
-+--+--+-...

In both cases there is a repeated pattern of three terms in which 2 are negative and 1 positive (--+ or -+-) so in both cases out of 24 terms 2/3 will be negative, so there will be 16 negative terms. Sufficient.

Answer: B.
User avatar
utfan2424
Joined: 05 Nov 2009
Last visit: 28 Jan 2012
Posts: 22
Own Kudos:
Given Kudos: 3
Posts: 22
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I also get B. You can establish a pattern at 4 and each combination to get negative (- * + or + * -) gets to the same number of negative numbers. I must admist that I did this the long way, without a formula - prorbably took a little over 2 minutes.
User avatar
mbafall2011
Joined: 21 Mar 2010
Last visit: 03 Aug 2012
Posts: 240
Own Kudos:
87
 [1]
Given Kudos: 33
Posts: 240
Kudos: 87
 [1]
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rajeshaaidu
No clue! It's really tough one. Please give official explanation. A) and D) I have eliminated but I was confused between B) and C) because I was not able to explain stmt-B.

If you write out the options resulting from b

T3 below will be T1T2
T1 ---------- T2--------- T3--------------T4
-ve -ve +ve -ve
-ve +ve -ve -ve

For both these cases expand out the first 8 terms and you will see the ratio of 2:1 for negative to positive!
User avatar
fluke
User avatar
Retired Moderator
Joined: 20 Dec 2010
Last visit: 24 Oct 2013
Posts: 1,099
Own Kudos:
Given Kudos: 376
Posts: 1,099
Kudos: 5,095
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I classify these types of questions as torturous; because we need to count them out to be sure.

1. We can easily rule this out because the 3rd term is +ve; first two can either be -ve or all can be positive. Not sufficient.

2. This statement is little hairy.

X-------\(|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|\). 16 -ves

Y-------\(|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|-|-|+|\). 16 -ves

Sufficient.

Well after some thought; you may recognize the pattern that there are two negatives after every +ve; but I would rather write them all out and count them.

As you see for X; first position is -ve and the 2nd +ve. 3rd and 4th are negative and 5th +ve and the pattern continues. You may now count -ves. Likewise for Y.


Ans: "B"
User avatar
gmat1220
Joined: 03 Feb 2011
Last visit: 17 Feb 2020
Posts: 466
Own Kudos:
Given Kudos: 123
Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Products:
Posts: 466
Kudos: 987
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel you are awesome ! If I had seen this question on test day I would have marked C and move on ! But then I took numbers and yes it answered. So - its imperative to find the first negative term. That is the key for the pattern ? Right?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
User avatar
ziko
Joined: 28 Feb 2012
Last visit: 29 Jan 2014
Posts: 91
Own Kudos:
217
 [3]
Given Kudos: 17
Concentration: Strategy, International Business
GPA: 3.9
WE:Marketing (Other)
Posts: 91
Kudos: 217
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive
(2) The fourth term in S is negative


One important thing to understand is that in GMAT sequence questions there is almost always a pattern. So there is no real need to calculate all 24 integers' signs.
The most difficult part in this question is: If each term in S after the second is the product of the previous two terms .

It is the same as saying that:
x; y; xy; x(y^2); (x^2)(y^3); (x^3)(y^5); (x^5)(y^8); ...

1 st.) xy is positive. In this case both x and y are negative or they both positive. If both positive all the terms will be positive: (+) (+) (+) (+) (+) (+)... In case both are negative we have: (-) (-) (+) (-) (-) (-) (+).... Two different answers - statement is not sufficient

2 st.) x(y^2) is negative. There are two possible options: x is negative and y is positive, or x is negative and y is negative.
In the 1st option we have the following pattern: (-) (+) (-) (-) (+) (-) (-) (+)...
In the 2nd option we have the follwing pattern: (-) (-) (+) (-) (-) (+) (-) (-)... It starts slightly different but the pattern is the same, so we can conclude that the number of positives and negatives within 24 integers will be the same rerdless of the options. So the answer is B.
User avatar
ygdrasil24
Joined: 07 Apr 2012
Last visit: 15 Jan 2014
Posts: 70
Own Kudos:
Given Kudos: 45
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE:Operations (Manufacturing)
Schools: ISB '15
GMAT 1: 590 Q48 V23
Posts: 70
Kudos: 29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Even though OA is B and is right, # of negative terms is 17 and not 16. The first term has to be negative in both the scenarios of B.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ygdrasil24
Even though OA is B and is right, # of negative terms is 17 and not 16. The first term has to be negative in both the scenarios of B.

There are 24 numbers and 2/3 are negative, thus 16 numbers are negative not 17.
User avatar
ygdrasil24
Joined: 07 Apr 2012
Last visit: 15 Jan 2014
Posts: 70
Own Kudos:
Given Kudos: 45
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE:Operations (Manufacturing)
Schools: ISB '15
GMAT 1: 590 Q48 V23
Posts: 70
Kudos: 29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
ygdrasil24
Even though OA is B and is right, # of negative terms is 17 and not 16. The first term has to be negative in both the scenarios of B.

There are 24 numbers and 2/3 are negative, thus 16 numbers are negative not 17.

Yes 16, I over worked on the final answer :(
User avatar
gmatonline
Joined: 13 Apr 2014
Last visit: 03 Nov 2015
Posts: 8
Own Kudos:
Given Kudos: 1
Posts: 8
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive --> either all terms are positive, so zero negatives or +--... and not all terms are positive, so more than zero negatives. Not sufficient.

(2) The fourth term in S is negative --> again two cases:

--+--+--+...
OR
-+--+--+-...

The same here: in both cases there is a repeated pattern of three terms in which 2 are negative and 1 positive (--+ or -+-) so in both cases out of 24 terms 2/3 will be negative, so there will be 16 negative terms. Sufficient.

Answer: B.
tnx for this
avatar
ravishankar1788
Joined: 08 Jan 2014
Last visit: 19 May 2014
Posts: 15
Own Kudos:
Given Kudos: 4
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE:Analyst (Consulting)
Posts: 15
Kudos: 23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1st term x
2nd term y
S={x,y,xy,xy^2.........}

since 4th term is -ve , xY^2 is -ve i.e. x is -ve since y^2 cannot be -ve.
Now since 1st term is -ve there can be 2 different pattern for the sequence assuming 2nd term to be either +ve or -ve.

S={-,-,+,-,-,+,......}
or
S={-,+,-,-,+,-,......}

So its clear that either 2nd term is +ve or -Ve the # of -ve terms is equal for 24 terms(since # of terms is a product of 3).
avatar
sagnik2422
Joined: 20 May 2014
Last visit: 20 Jan 2015
Posts: 27
Own Kudos:
20
 [1]
Given Kudos: 1
Posts: 27
Kudos: 20
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ziko
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive
(2) The fourth term in S is negative


One important thing to understand is that in GMAT sequence questions there is almost always a pattern. So there is no real need to calculate all 24 integers' signs.
The most difficult part in this question is: If each term in S after the second is the product of the previous two terms .

It is the same as saying that:
x; y; xy; x(y^2); (x^2)(y^3); (x^3)(y^5); (x^5)(y^8); ...

1 st.) xy is positive. In this case both x and y are negative or they both positive. If both positive all the terms will be positive: (+) (+) (+) (+) (+) (+)... In case both are negative we have: (-) (-) (+) (-) (-) (-) (+).... Two different answers - statement is not sufficient

2 st.) x(y^2) is negative. There are two possible options: x is negative and y is positive, or x is negative and y is negative.
In the 1st option we have the following pattern: (-) (+) (-) (-) (+) (-) (-) (+)...
In the 2nd option we have the follwing pattern: (-) (-) (+) (-) (-) (+) (-) (-)... It starts slightly different but the pattern is the same, so we can conclude that the number of positives and negatives within 24 integers will be the same rerdless of the options. So the answer is B.

Why isn't fourth term x^2y^2
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
Given Kudos: 99,977
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sagnik2422
ziko
Sequence S consists of 24 nonzero integers. If each term in S after the second is the product of the previous two terms, how many terms in S are negative?

(1) The third term in S is positive
(2) The fourth term in S is negative


One important thing to understand is that in GMAT sequence questions there is almost always a pattern. So there is no real need to calculate all 24 integers' signs.
The most difficult part in this question is: If each term in S after the second is the product of the previous two terms .

It is the same as saying that:
x; y; xy; x(y^2); (x^2)(y^3); (x^3)(y^5); (x^5)(y^8); ...

1 st.) xy is positive. In this case both x and y are negative or they both positive. If both positive all the terms will be positive: (+) (+) (+) (+) (+) (+)... In case both are negative we have: (-) (-) (+) (-) (-) (-) (+).... Two different answers - statement is not sufficient

2 st.) x(y^2) is negative. There are two possible options: x is negative and y is positive, or x is negative and y is negative.
In the 1st option we have the following pattern: (-) (+) (-) (-) (+) (-) (-) (+)...
In the 2nd option we have the follwing pattern: (-) (-) (+) (-) (-) (+) (-) (-)... It starts slightly different but the pattern is the same, so we can conclude that the number of positives and negatives within 24 integers will be the same rerdless of the options. So the answer is B.

Why isn't fourth term x^2y^2

Each term in S after the second is the product of the previous two terms.
x
y
xy
y*xy = xy^2
xy*xy^2 = x^2y^3
...

Hope it's clear now.
 1   2   
Moderators:
Math Expert
105390 posts
496 posts