Manhattan Quant Guides

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 184
Joined: Thu Nov 25, 2010 9:57 pm
Thanked: 1 times
Followed by:5 members
GMAT Score:700

Manhattan Quant Guides

by chaitanya.mehrotra » Mon Jul 18, 2011 11:01 pm
A quantity increases in a manner such that the ratio of its values in any two
consecutive years is constant. If the quantity doubles every 6 years, by what
factor does it increase in two years?

Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Mon Jul 18, 2011 11:45 pm
Hi,
Let's say the quantities are t1,t2,t3,...
Given that t2/t1 =t3/t2 =t4/t3 =.... = r.
So, t1,t2,t3.. are in a geometric series.
Given that t7/t1 = 2
So, r^6 = 2
We need to find t3/t1 = r^2.
So, r^2 = 2^(1/3)
Cheers!

Things are not what they appear to be... nor are they otherwise

User avatar
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Mon Nov 18, 2013 2:03 pm
Followed by:1 members

by ozlemmetje » Sat Apr 18, 2015 12:39 pm
Frankenstein wrote:Hi,
Let's say the quantities are t1,t2,t3,...
Given that t2/t1 =t3/t2 =t4/t3 =.... = r.
So, t1,t2,t3.. are in a geometric series.
Given that t7/t1 = 2
So, r^6 = 2
We need to find t3/t1 = r^2.
So, r^2 = 2^(1/3)
Hi!

could you pls explain what "t7/t1 = 2" means? and why "r^2 = 2^(1/3)" ?? Can somebody explain how to solve this problem in other words?

Thanks in advance!

User avatar
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Mon Nov 18, 2013 2:03 pm
Followed by:1 members

by ozlemmetje » Sat Apr 18, 2015 12:39 pm
Frankenstein wrote:Hi,
Let's say the quantities are t1,t2,t3,...
Given that t2/t1 =t3/t2 =t4/t3 =.... = r.
So, t1,t2,t3.. are in a geometric series.
Given that t7/t1 = 2
So, r^6 = 2
We need to find t3/t1 = r^2.
So, r^2 = 2^(1/3)
Hi!

could you pls explain what "t7/t1 = 2" means? and why "r^2 = 2^(1/3)" ?? Can somebody explain how to solve this problem in other words?

Thanks in advance!

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Apr 18, 2015 3:29 pm
A quantity increases in a manner such that the ratio of its values in any two consecutive years is constant. If the quantity doubles every 6 years, by what factor does it increase in two years?

Can someone provide a simple solution?
Here is a formula for exponential growth:

Final amount = original amount * multiplier^(number of changes).

Into the formula above, plug in the following values:
Original amount = 1.
Final amount = 2. (Since the original amount doubles every 6 years.)
2-year multiplier = x. (The factor by which the original amount increases in 2 years.)
Number of changes = 3. (Since over 6 years the original amount will be multiplied by x three times.)

2 = 1 * x^3
x = 2^(1/3).

Alternate approach:

Since the GMAT would provide answer choices, we could PLUG IN THE ANSWERS.
The answer choices would represent by what factor the original amount increases in 2 years.
Answer choices:
2^(1/6)
2^(1/4)
2^(1/3)
2^(1/2)
2^(2/3).

Let the original amount = 1.
When the correct answer choice is plugged in, the original amount will double to 2 in 6 years.

Answer choice D: 2^(1/2)
Amount after 2 years = 1 * 2^(1/2) = 2^(1/2)
Amount after 4 years = 2^(1/2) * 2^(1/2) = 2.
Since the amount is increasing TOO QUICKLY, the correct multiplier must be SMALLER.
Eliminate D and E.

Answer choice B: 2^(1/4)
Amount after 2 years = 1 * 2^(1/4) = 2^(1/4)
Amount after 4 years = 2^(1/4) * 2^(1/4) = 2^(1/2)
Amount after 6 years = 2^(1/2) * (2^1/4) = 2^(3/4).
Since the amount is increasing TOO SLOWLY, the correct multiplier must be GREATER.
Eliminate A and B.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Sun Apr 19, 2015 11:12 pm
We could also say that if it is multiplied by a factor of x each year, that

x� = 2

Taking the sixth root of each side, we find that x = �√2, so it goes up by the sixth root of 2 each year. Our question wants two years, so we'd just square this and be done.