AP ratio

Expert replies

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun May 10, 2009 6:54 am

The sum of n terms of two arithmetic progressions are in the ratio
(3n + 8) : (7n + 15). Find the ratio of their 12th terms.

7/16
9/16
11/23
16/9
16/7

Charged up again to beat the beast

Like this post

Source: Beat The GMAT — Problem Solving | Sun May 10, 2009 6:54 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Sun May 10, 2009 11:07 am

ratio of the sum of the nth term of the two APs:

=n/2[2a1+(n-1)d1]/n/2[2a2+(n-1)d2]

=>[2a1+(n-1)d1]/[2a2+(n-1)d2]=(3n+8)/(7n+15)............1

we want a1+11d1/a2+11d2
so we manipulate the LHS of 1 to get the ratio in the above form by putting n-1=22 or n=23

2(a1+11d1)/2(2a2+11d2)=3*23+8/7*23+15
=(a1+11d1)/(a2+11d2)=69+8/151+15
=>ratio of the 12th terms=77/176=7/16

hence, A

Last edited by scoobydooby on Thu May 14, 2009 8:07 am, edited 1 time in total.

Like this post

kanha81: Master | Next Rank: 500 Posts; Posts: 431; Joined: Sat Jan 10, 2009 9:32 amFollowed by: 1 member; Thanked: 16 times

by kanha81 » Thu May 14, 2009 7:07 am

scoobydooby wrote:ratio of the sum of the nth term of the two APs:

=n/2[2a1+(n-1)d1]/n/2[2a2+(n-1)d2]

=>[2a1+(n-1)d1]/[2a2+(n-1)d2]=(3n+8)/(7n+15)............1

we want a1+11d1/a2+11d2
so we manipulate the LHS of 1 to get the ratio in the above form by putting n-1=22 or n=23

2(a1+11d1)/2(2a2+11d2)=3*23+8/7*23+15
=(a1+11d1)/(a2=11d2)=69+8/151+15
=>ratio of the 12th terms=77/176=7/16

hence, A

I am quite confused!

How did you manipulate and came to know that n-1=22?
From what I understand, we need to find the ratio for the 12th term.

So then, shouldn't the equation form be-

(3n+5) / (7n+15) = [2a1+(n-1)d1] / [2a2+(n-1)d2]
where n=12, so rhs becomes- (2a1+11d1) / (2a2+11d2)

Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT

Like this post

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Thu May 14, 2009 8:06 am

we have (3n+5) / (7n+15) = [2a1+(n-1)d1] / [2a2+(n-1)d2]
=>(3n+5) / (7n+15) =[a1+(n-1)d1/2]/[a2+(n-1)d2/2]

(divding numerator and the denominator of the RHS by 2)

for the ratio of the 12th terms we need: (a1+11d1) / (a2+11d2)

by observing the RHS, we can obtain this by putting (n-1)/2=11
=>n=22+1=23

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review