|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 30 May 2014
Posts: 3
|
If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
 Updated on: 04 Jul 2017, 20:35
Question Stats:
55% (02:35) correct 45% (02:37) wrong based on 150 sessions
HideShow timer Statistics
If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be the value of: \(\frac{a^{3}*b + b^{3}*a}{a^{3}*b^{3}}\) A. 0.02 B. 0.05 C. 775 D. 1,525 E. 5,725 After ~10+ minutes I got to the answer, but I can clearly not afford to spend that much in a problem. How do you solve this problem under 2.5 minutes? What is the trick?
Thanks! (PS, Algebra, Inequality, 49-51) Source: MathRevolution
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by ekniv on 04 Jul 2017, 14:17.
Last edited by Bunuel on 04 Jul 2017, 20:35, edited 2 times in total.
Renamed the topic and edited the question.
|
|
|
|
|
|
|
|
Math Expert
Joined: 02 Aug 2009
Posts: 8792
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
04 Jul 2017, 17:13
ekniv wrote: (PS, Algebra, Inequality, 49-51) Source: MathRevolution
If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be the value of:
\(\frac{a^{3}*b + b^{3}*a}{a^{3}*b^{3}}\)
A. 0.02
B. 0.05
C. 775
D. 1,525
E. 5,725
After ~10+ minutes I got to the answer, but I can clearly not afford to spend that much in a problem. How do you solve this problem under 2.5 minutes? What is the trick?
Thanks! Hi, Firstly please give the topic name as first few words of the Q.. Now for the Q... Simplify and find RANGE.. \(\frac{a^{3}*b + b^{3}*a}{a^{3}*b^{3}}\)=\(\frac{ab(a^{2} + b^{2}}{ab(a^{2}*b^{2}}\)=\(\frac{a^{2} + b^{3}}{a^{2}*b^{2}}\).. 1) You can work from here Now the NUMERATOR will be just b^2 but denominator would reduce drastically.. 2) further simplify.. \(\frac{a^2+b^2}{a^2*b^2}\).. a^2 will be very small as compared to b^2 so neglect in the numerator.. \(\frac{b^2}{a^2b^2}=\frac{1}{a^2}\).. Now let's find the range of this.. \(\frac{1}{(0.02)^2}=\frac{1}{0.0004}=\frac{10000}{4}=2500\).. \(\frac{1}{(0.01)^2}=\frac{1}{0.0001}=\frac{10000}{1}=10000\).. Range is 2500 to 10000.. Only E remains. E
_________________
|
|
|
|
|
|
|
|
Intern
Joined: 03 Jun 2017
Posts: 7
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
04 Jul 2017, 17:19
The way I solved this problem was by picking a smart number for b (100) and a (0.01) and then I used logic.
Step 1) You know that 0.01x0.01x0.01 will have 6 decimal places so a3∗b= some decimal.
Step 2) b3∗a = 1,000,000 * 0.01 = 10,000, which is your numerator
Step 3) a3∗b3 = something with 6 decimal places * 1,000,000 = 1, which will be your denominator
Here I looked at the answer choices and immediately crossed A and B. From here I realized that by increasing b, the value will be only decreasing so I picked the first number closest to 10,000.
Hope this helped.
|
|
|
|
|
|
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3248
Location: India
GPA: 3.12
|
If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
05 Jul 2017, 12:14
The given expression is as follows : \(\frac{a^{3}*b + b^{3}*a}{a^{3}*b^{3}}\) It can be further simplified as \(\frac{ab(a^{2} + b^{2})}{ab(a^{2}*b^{2})}\) = \(\frac{a^{2} + b^{2}}{a^{2}*b^{2}}\) Now coming to values that a and b can take : a will be of form \(x * 10^{-2}\) and b will be of form \(y * 10^2\) Substituting these values, \(\frac{a^{2} + b^{2}}{a^{2}*b^{2}}\) = \(\frac{(x^2 * 10^{-4}) + (y^2 * 10^{4})}{(x^2 * 10^{-4}) * (y^2 * 10^{4})}\) = \(\frac{(x^2 * 10^{-4}) + (y^2 * 10^{4})}{(x^2 * 10^{-4}) * (y^2 * 10^{4})}\) This equation can be approximated to (since x and y are extremely small) \(\frac{(10^{-4}) + (10^{4})}{(10^{-4}) * (10^{4})}\) = \(\frac{(10^{-4}) + (10^{4})}{(10^{-4 + 4})}\) (because \(a^m*a^n = a^{m+n}\)) = \(\frac{(10^{-4}) + (10^{4})}{(10^{0})}\) = \(10^4 = 10000\) which is the largest value possible for the expression The value closest to this will be Option E.
_________________
You've got what it takes, but it will take everything you've got
|
|
|
|
|
|
Senior Manager
Joined: 29 Jun 2017
Posts: 411
GPA: 4
WE: Engineering (Transportation)
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
06 Sep 2017, 00:51
ekniv wrote: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be the value of: \(\frac{a^{3}*b + b^{3}*a}{a^{3}*b^{3}}\) A. 0.02 B. 0.05 C. 775 D. 1,525 E. 5,725 After ~10+ minutes I got to the answer, but I can clearly not afford to spend that much in a problem. How do you solve this problem under 2.5 minutes? What is the trick?
Thanks! (PS, Algebra, Inequality, 49-51) Source: MathRevolution Equation can be written as 1/a^2 + 1/b^2 I HAVE THE WAY WHICH YOU ARE LOOKING FOR-
a belongs (0.01,0.02) 1/a belongs ( 50,100) 1/a^2 belongs ( 2500, 100 00 ) b belongs (100,200) 1/b^2 belongs (0.25x 10^-4 , 10^-4 ) Lets find min value of given equation. 2500 + 0.25x10^-4 = 2500.0 something >2500 which is E
|
|
|
|
|
|
Non-Human User
Joined: 09 Sep 2013
Posts: 15594
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
Show Tags
20 Jun 2020, 01:22
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
|
|
|
|
|
|
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
20 Jun 2020, 01:22
|
|
|
|
|
|
|
close
