BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

prepfortests1

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Tue Oct 14, 2008 1:05 pm

prepfortests1

by simba12123 » Wed Oct 29, 2008 8:37 am
What is the sum of the 20th and 21st terms in the sequence 1, 3, 9, 27... where each term is 3 times the preceding term?

1. 4×3^19
2. 10×3^19
3. 4×3^20
4. 10×3^20
5. 3^39


qa is1

i counted out and got to the point of 3^19+3^20 and fell for trap of qa is 5. what did i do wrong?
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2134
Joined: Mon Oct 20, 2008 11:26 pm
Thanked: 237 times
Followed by:25 members
GMAT Score:730

Re: prepfortests1

by logitech » Wed Oct 29, 2008 8:54 am
simba12123 wrote:What is the sum of the 20th and 21st terms in the sequence 1, 3, 9, 27... where each term is 3 times the preceding term?

1. 4×3^19
2. 10×3^19
3. 4×3^20
4. 10×3^20
5. 3^39


qa is1

i counted out and got to the point of 3^19+3^20 and fell for trap of qa is 5. what did i do wrong?
Simba,

First of all, counting will take some time, especially if you face a question that asks to find 5326th term. So it is always a good idea to look for a rule

1st term is 3^0=1
2nd term is 3^1=3
.....
......
20th term is 3^(20-1) = 3^19
21st term is 3^(21-1) = 3^20


So --> 3^19+3^20 = 3^19 ( 1 + 3 ) = 4 x 3^19

Hence, A
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
Top
Legendary Member
Posts: 621
Joined: Wed Apr 09, 2008 7:13 pm
Thanked: 33 times
Followed by:4 members

by vittalgmat » Wed Oct 29, 2008 8:55 am
U almost got to the last step!!!

3^19 + 3^20 = 3^19 + 3^19 *3.

Taking the common factor 3^19,

3^19(1+3)

= 4* 3^19

HtHelps

-V
Top
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Sun Oct 19, 2008 12:09 am
Location: Faisalabad, Pakistan

by tkhalid » Wed Oct 29, 2008 9:05 am
I just want to add a simple formula

Tn = a * r^(n-1)

Where, Tn= nth term
a= first term
r= common ratio (in this case it was 3)

I hope this will help in future to determine geometric terms
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

Re: prepfortests1

by Stuart@KaplanGMAT » Wed Oct 29, 2008 11:23 am
simba12123 wrote:What is the sum of the 20th and 21st terms in the sequence 1, 3, 9, 27... where each term is 3 times the preceding term?

1. 4×3^19
2. 10×3^19
3. 4×3^20
4. 10×3^20
5. 3^39

i counted out and got to the point of 3^19+3^20 and fell for trap of qa is 5. what did i do wrong?
There's no simple way to add exponents unless they have the same base AND the same power. For example, if we have:

x^4 + x^7,

there's no easy way to add them together.

However,

3(x^4) + 4(x^4) = 7(x^4).

You applied the "multiplication of exponents" rule:

(x^a) * (x^b) = x^(a+b)

For addition, we need to do what vittalgmat did so well - get a common denominator to equalize the powers.

To do so, we almost always factor out from the bigger power to reduce it to the lower power.

Using the multiplication of exponents rule noted above, we can rewrite 3^20 as:

3^1 * 3^19 = 3(3^19)

Once we substitute that into your sum, we get:

3^19 + 3^20 = 1(3^19) + 3(3^19) = 4(3^19)
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 52
Joined: Thu Jul 31, 2008 12:30 pm
Thanked: 5 times

by dhanda.arun » Wed Oct 29, 2008 5:15 pm
Hi,
This is simply a Geometric Progeression where a= 1 and r = 3.
So Tn = a.r^(n-1)
T20 = 3^19
T21 = 3^20
Adding ->
3^19(1+3)
= 4.3^19
Top
Senior | Next Rank: 100 Posts
Posts: 42
Joined: Thu Oct 30, 2008 1:21 am

by mbaapplicant2008 » Thu Oct 30, 2008 1:50 am
Great, it is choice A: 4×3^19
Top
Legendary Member
Posts: 833
Joined: Mon Aug 04, 2008 1:56 am
Thanked: 13 times

by vivek.kapoor83 » Thu Oct 30, 2008 2:52 am
it has to be A only.
Top
Senior | Next Rank: 100 Posts
Posts: 94
Joined: Tue Oct 14, 2008 1:05 pm

geomteric progression

by simba12123 » Sat Nov 01, 2008 9:43 am
This is a final weakspot for me. I am struggling to understand Stuart Kovinsky. However, I have one last question about this. By following the logical steps, doesn't this all boil down to ---

3^20 + 3^21 as 3^20 as best factor to pull out of? Hence I see no real reason to go to 3^19.

second question : a.) 3(3^19)= 3^20
b.) (3^2)(3^19) = 3^21

Unforutunately, I am lost on this one!
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

Re: geomteric progression

by Stuart@KaplanGMAT » Wed Nov 05, 2008 1:19 pm
simba12123 wrote:This is a final weakspot for me. I am struggling to understand Stuart Kovinsky. However, I have one last question about this. By following the logical steps, doesn't this all boil down to ---

3^20 + 3^21 as 3^20 as best factor to pull out of? Hence I see no real reason to go to 3^19.
We're asked to add the 20th and 21st terms in the sequence. Since the first term is 1 = 3^0, the 20th and 21st terms are actually 3^19 and 3^20.

In other words, the nth term in the sequence is 3^(n-1), NOT 3^n.
second question : a.) 3(3^19)= 3^20
b.) (3^2)(3^19) = 3^21

Unforutunately, I am lost on this one!
a) 3(3^19) = (3^1)(3^19) = 3^(1+19) = 3^20
b) (3^2)(3^19) = 3^(2+19) = 3^21

Both rely on the multiplication rule for exponents: when you mutliply two terms with the same base, you ADD the exponents, i.e.:

(x^a)(x^b) = x^(a+b)
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Post new topic Post Reply
• Page 1 of 1