GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Jul 2020, 09:51

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

Math Revolution and GMAT Club Contest! There is a sequence An when n

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 10 Sep 2012
Posts: 22
GMAT 1: 700 Q49 V35
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 07 Dec 2015, 06:36
1
Given A 1 =a , A 2 =b , and A n+2 =A n+1 ∗A n

Sequence can be written as - a, b, ab, ab2, a2b3,a3b5... the 6th term i.e A 6 = a3b5
We need to find out whether A 6 <0

Now analyzing statement 1
a < 0
a is negative so a3 is negative, however we don't know the sign of b, so statement 1 is not sufficient.

Analyzing statement 2
ab < 0
either a or b is negative (but not both)
if a is - and b is +, then a3b5 is -
if a is + and b is -, then a3b5 is -
Hence in both cases, a3b5 is negative, which means we can state for sure that A 6 is less than 0. Sufficient.

Answer - B
Manager
Manager
User avatar
B
Status: In the realms of Chaos & Night
Joined: 13 Sep 2015
Posts: 136
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 07 Dec 2015, 08:23
1
A1 = a; A2= b & An+2 = An+1 x An
=> A3 = A2 x A1 = b x a = ab
=> A4 = A3 x A2 = ab x b = a x b^2
=> A5 = A4 x A3 = axb^2 x ab = a^2xb^3
=> A6 = A5 x A4 = a^2xb^3 x axb^2 = a^3xb^5

Case 1 : a<0 => A6 has odd power for for a -ve 'a'. Sufficient
Case 2 : ab<0 => Either a or b is -ve. Both have odd powers hence A6 will always be -ve.

--------------------------------------------------------------------------------------------------------------
Share a Kudo, if this helped. Generosity will be reciprocated.
Intern
Intern
User avatar
B
Joined: 29 Aug 2013
Posts: 35
Location: Bangladesh
GPA: 3.76
WE: Supply Chain Management (Transportation)
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 07 Dec 2015, 10:29
1
QUESTION #5:

There is a sequence An when n is a positive integer such that A1=a, A2=b, and An+2=An+1∗An. Is A6<0?
(1) a < 0
(2) ab < 0

Solution:
A6=A5XA4=a^2 X b^3 X ab^2=a^3b^5
A5=A4XA3=ab^2 X ab=a^2 b^3
A4=A3XA2=ab X b=ab^2
A3=A2XA1=ab

A6=a^3b^5

we have to prove whether A6<0 ?
statement 1) a<0: : If a<0, (means: -a) then for the value of +b, value of A6 will be less than zero, but for the value of -b, A6 will be greater than zero . so hereby data is insufficient.
Statement (2) ab < 0: If ab is less than zero then one value between a and b must be negative. if a is negative and b is positive then the value of A6 is less than zero. If a is positive and b is negative, then the value of A6 will be less than zero.So hereby, data is sufficient.

Answer: (B)
Senior Manager
Senior Manager
avatar
B
Joined: 23 Sep 2015
Posts: 361
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Reviews Badge
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 08 Dec 2015, 02:31
1
A1=a, A2=b, and An+2=An+1∗An. Is A6<0?

\(A3 = ab\)
\(A4 = ab^2\)
\(A5 = a^2b^3\)
\(A6 = a^3b^5\)

Since both exponents are odd, we need to know the signs of both a and b to determine A6

1) Insufficient, if b is positive the answer is YES but NO if b is negative
2)Sufficient, only 1 of the two can be negative so the answer is YES

Answer B
_________________
Intern
Intern
avatar
Joined: 17 Aug 2014
Posts: 10
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 08 Dec 2015, 04:29
Answer is A

Statement1:a<0

An+2=An+1*An
A6=A5*A4
A3=a*b
A4=a*b^2
A5=a^2*b^3
A6=a^3*b^4

When a<0, a^3 is -ve, b^4 is always +ve irrespective of b is +ve or -ve , therefore A6 =a^3*b^4 is <0. Statement 1 is sufficient

Statement 2:
A6 can be written as (ab)^3*b.
When ab is <0, then
1)a is -ve and b is +ve --> A6=-ve
2) b is -ve and a is +ve. -->A6=+ve
Not sufficient
Intern
Intern
User avatar
S
Status: Current Student
Joined: 26 Mar 2014
Posts: 26
Location: Bangladesh
Concentration: Entrepreneurship, Finance
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 08 Dec 2015, 10:25
The sequence is: n is positive, so,
A3=A2*A1=ab [when n=1]
A4=A3*A2=ab^2 [when n=2]
A5=A4*A3=a^2*b^3 [when n=3]
A6=A5*A4=a^3*b^4 [when n=4]
Statement 1: it says a is negative. If a is negative, then A6 must be negative since b is always positive. Sufficient.
Statement 2: Either a or b is negative. We don't know which one. Insufficient.
Answer is A.
Intern
Intern
User avatar
Joined: 16 Nov 2015
Posts: 5
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 08 Dec 2015, 10:47
1
B. Statement (2) alone is sufficient.

Given,
\(A_1\)=a, \(A_2\)=b
\(A_{n+2}\) = \(A_n\)(\(A_{n+1}\))

Now,
\(A_3\) = \(A_{1+2}\) = \(A_1\)(\(A_2\)) = ab
\(A_4\) = \(A_{2+2}\) = \(A_2\)(\(A_3\)) = (ab) * b = a\(b^{2}\)
\(A_5\) = \(A_{3+2}\) = \(A_3\)(\(A_4\)) = (a\(b^{2}\)) * ab = \(a^{2}\)\(b^{3}\)
\(A_6\) = \(A_{4+2}\) = \(A_4\)(\(A_5\)) = (\(a^{2}\)\(b^{3}\)) * (a\(b^{2}\)) = \(a^{3}\)\(b^{5}\)

We get, \(A_6\) = \(a^{3}\)\(b^{5}\)

(1) a is negative; b could either be positive or negative and therefore we cannot conclude \(a^{3}\)\(b^{5}\) is negative. Insufficient!
(2) ab is negative; Since we know only one of them is negative, we know that \(a^{3}\)\(b^{5}\) will always be negative. Sufficient!
_________________
The harder the battle, the sweeter the victory!
Intern
Intern
User avatar
Joined: 01 Nov 2015
Posts: 29
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 09 Dec 2015, 05:17
1
Consider A1 and A2 to be +ve => A6 is also positive
If A1 and A2 both are -ve
A3 = -ve * -ve = +ve
A4 = +ve * -ve = -ve
A5 = -ve - +ve = -ve
A6 = -ve * -ve = +ve => A6 is positive


Now to Statement 1
a = A1 < 0 => a is -ve
Since we have evaluated b as -ve, let evaluate b as +ve now
A1 = -ve
A2 = +ve
A3 = +ve * -ve = -ve
A4 = -ve * +ve = +ve
A5 = +ve * -ve = -ve
A6 = -ve * +ve = -ve => A6 is negative

Therefore Not sufficient

Statement 2
ab <0 => a < 0 or b < 0
if a < and b > 0, => A6 is negative (by above)

if a is +ve and b is -ve
A1 = +ve
A2 = -ve
A3 = -ve * +ve = -ve
A4 = -ve * -ve = +ve
A5 = +ve * -ve = -ve
A6 = -ve * +ve = -ve => A6 is negative

Therefore ab < 0 is sufficient

Answer is B
Intern
Intern
avatar
B
Joined: 21 Jan 2013
Posts: 36
Concentration: General Management, Leadership
Schools: LBS
GPA: 3.82
WE: Engineering (Computer Software)
GMAT ToolKit User Reviews Badge
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 09 Dec 2015, 08:52
1
A3 = A2*A1 = (ab)
A4 = A3*A2 = (ab)b
A5 = A4*A3 = (ab)b(ab) = (b) * (ab)^2
A6 = A5*A4 = (b) * ((ab)^2) * (ab)(b) = (b^2) * ((ab)^3)

Is A6 < 0 can be rewritten as : is (b^2) * ((ab)^3) < 0 ?

Since b^2 is always non negative ; rephrased question will be is ab < 0?

Option B answers the rephrased question directly.

Answer : B
Intern
Intern
User avatar
Joined: 04 Sep 2015
Posts: 3
Location: Singapore
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 09 Dec 2015, 09:18
1
There is a sequence An when n is a positive integer such that A1=a, A2=b, and An+2=An+1∗An. Is A6<0?

(1) a < 0
(2) ab < 0

Answer - B ,

A- statement 1 a<0, doesn't tell us type of sequence INSUFFICIENT
B- statement ab<0, atleast one is +ve and other is -ve.
consider terms to solve
a = -1, b= 1; sequence becomes -1, 1, -1, -1, 1, -1
a = 1, b= -1; sequence becomes 1, -1, -1, 1, -1, -1,
a6 is -ve in both of the cases. Hence statement 2 is sufficient
Intern
Intern
avatar
Joined: 15 Aug 2015
Posts: 3
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 10 Dec 2015, 11:57
1
So this is the first time posting on this site, so I apologize in advance if it doesn't look as polished as some of the other posts from more experienced members.

The answer I came up with is B.

The method I took was to work out what A6 is by plugging in what we already know.

A3 = A2*A1
A4 = A3*A2
A5 = A4*A3
A6 = A5*A4

This ends up giving you B^5 * A^3. Since we know that a base to an odd power is going to be the same sign as the base, i.e. positive base remains positive, negative base remains negative, then we know that A6 will be negative if and only if one of these bases, A or B, is negative and the other is positive.

Answer choice A only tells us about one of the bases, so it is wrong. B, on the other hand, does tell us about both. The product of two numbers will be less than zero if, and only if, one of the numbers if positive and the other is negative.

B.
Intern
Intern
avatar
Joined: 10 Dec 2015
Posts: 3
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 11 Dec 2015, 03:59
1
IMO Answer is B

A6 is a^3*b^5. Therefore, we need to know the power of both a and b. a<0 does not give us any information regarding the value of b. Hence, not sufficient. For ab<0, A6 can be written as (a^3*b^3)*b^2. Now ab<0 implies a^3*b^3 is <0. and b^2 would always be >0. Hence A6<0 and therefore sufficient.

Let me know if my logic is correct. Cheers
Intern
Intern
avatar
B
Joined: 05 Jun 2013
Posts: 25
Reviews Badge
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 11 Dec 2015, 09:55
2
A1=a, A2=b, and An+2=An+1∗An.
Is A6<0?

From equation, An+2=An+1∗An
A6=A5*A4
A5=A4*A3
A4=A3*A2
A3=A2*A1

Therefore A6= (A2)^5 * (A1)^3
Now lets take the choices

(1) a < 0
a<0 and b>0, Then A6<0 Yes
But if a<0 ,b<0 Then A6 >0 No

Choice 1 is insufficient.


(2) ab < 0
Means that a and b are of opposite signs . Therefore A6 which is equal to (A2)^5 * (A1)^3 will always be negative and A6<0.

Therefore B is sufficient.

Hence choice B is answer.
Intern
Intern
User avatar
Joined: 22 Dec 2014
Posts: 30
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 13 Dec 2015, 00:32
1
QUESTION #5:

There is a sequence An when n is a positive integer such that A1=a, A2=b, and An+2=An+1∗An. Is A6<0?

(1) a < 0
(2) ab < 0

\(A_1=a, A_2=b\)
--> \(A_3=b*a\)
--> \(A_4=(b*a)*b=b^2*a\)
--> \(A_5=(b^2*a)*(b*a)=b^3*a^2\)
--> \(A_6=(b^3*a^2)*(b^2*a)=b^5*a^3\) --> The powers of a and b are odd --> \(A_6\) has the same sign as \((a*b)\) does

(1) \(a< 0\) --> cannot define the sign of \(a*b\) --> insufficient
(2) \(a*b< 0\) --> \(A_6 < 0\) --> sufficient

Asnwer: B
Intern
Intern
avatar
B
Joined: 02 Feb 2015
Posts: 1
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 13 Dec 2015, 02:10
Answer B

Using the criteria given, A6=a^3*b^5

Condition 1:-
if a<0 then b can either be >0 or <0
if b>0 then A6<0
if b<0 then A6>0
Hence Insufficient

Condition 2:-
ab<0
Alright let's see,
I can write A6 as (ab)^3*b^2
So basically the sign of A6 will be dependent on sign of (ab) because b^2 will always be positive.
Hence Sufficient.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64949
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 14 Dec 2015, 08:06
Bunuel wrote:

Math Revolution and GMAT Club Contest Starts!



QUESTION #5:

There is a sequence \(A_n\) when n is a positive integer such that \(A_1=a\), \(A_2=b\), and \(A_{n+2}=A_{n+1}*A_n\). Is \(A_6<0\)?

(1) a < 0
(2) ab < 0

Check conditions below:



Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum


We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:

PS + DS course with 502 videos that is worth $299!



All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.


NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!



MATH REVOLUTION OFFICIAL SOLUTION:

If we alter the original condition and question: \(A_3=A_2×A_1=ab\), \(A_4=A_3×A_2=(ab)b=a(b^2)\), \(A_5=A_4×A_3=(ab^2)(ab)=a^2b^3\) and \(A_6=A_5×A_4=(a^2b^3)(ab^2)=a^3b^5\). The result is \(A_6=a^3b^5<0\)? → ab<0?. (A square of every number is a positive number. Even if we divide both sides by \(a^2b^4\) the direction of the inequality does not change.)

So, when we look at 2), ab<0, which means “yes” to question. This is sufficient. Therefore, the correct answer is B.
_________________
Manager
Manager
User avatar
B
Joined: 17 Jun 2015
Posts: 182
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT ToolKit User CAT Tests
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n  [#permalink]

Show Tags

New post 24 Dec 2015, 06:25
Sixth term is equal to a^3 * b^5

Statement 1, although suggests that a is negative and odd power of negative is negative, it does not tell us anything about b. hence insufficient

Statment 2 can be interpreted as

ab<0

that implies (a < 0 and b > 0 ) or (a>0 and b<0) i.e in either cases the polarity of a and b are opposite to each other. Since both are odd powers in the sixth term, Yes the sixth term is less than zero.

Hence B
_________________
Fais de ta vie un rêve et d'un rêve une réalité
GMAT Club Bot
Re: Math Revolution and GMAT Club Contest! There is a sequence An when n   [#permalink] 24 Dec 2015, 06:25

Go to page   Previous    1   2   [ 37 posts ] 

Math Revolution and GMAT Club Contest! There is a sequence An when n

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne