|
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, 21:35
10
This post was
BOOKMARKED
D
E
Question Stats:
52% (02:21) correct 48% (02:25) wrong based on 119 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, 15:17.
Last edited by Bunuel on 04 Jul 2017, 21:35, edited 2 times in total.
Renamed the topic and edited the question.
|
|
|
|
|
|
Math Expert
Joined: 02 Aug 2009
Posts: 5784
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be [#permalink]
Show Tags
04 Jul 2017, 18:13
4
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
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
_________________
Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor
|
|
|
|
|
|
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, 18:19
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.
|
|
|
|
|
|
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2582
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, 13:14
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
|
|
|
|
|
|
Director
Joined: 29 Jun 2017
Posts: 504
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, 01:51
1
This post was
BOOKMARKED
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
_________________
Give Kudos for correct answer and/or if you like the solution.
|
|
|
|
|
|
|
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be
[#permalink]
06 Sep 2017, 01:51
|
|
|
|
|
|
|
|
|
|
|
close
