GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Aug 2020, 04:53

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
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

New post Updated on: 04 Jul 2017, 20:35
1
18
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

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

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.
Most Helpful Expert Reply
Math Expert
avatar
V
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

New post 04 Jul 2017, 17:13
7
5
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
_________________
General Discussion
Intern
Intern
avatar
B
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

New post 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
User avatar
V
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

New post 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
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 411
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be  [#permalink]

Show Tags

New post 06 Sep 2017, 00:51
2
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





ekniv
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
User avatar
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

New post 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.
_________________
GMAT Club Bot
Re: If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be   [#permalink] 20 Jun 2020, 01:22

If 0.01 < a < 0.02, and 100 < b < 200, which of the following can be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne