 It is currently 15 Jun 2019, 21:25 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

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. For all counting numbers X,  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Founder  Joined: 18 Apr 2015
Posts: 6866
Followers: 114

Kudos [?]: 1326  , given: 6284

For all counting numbers X, [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 70% (00:39) correct 29% (01:09) wrong based on 17 sessions

For all counting number x, $$x^* = \frac{2}{x}$$

 Quantity A Quantity B $$x$$ $$(x^*)^*$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for the right solution and explanation
[Reveal] Spoiler: OA

_________________ Manager  Joined: 15 Jan 2018
Posts: 147
GMAT 1: Q V
Followers: 3

Kudos [?]: 185  , given: 0

Re: For all counting numbers X, [#permalink]
1
KUDOS
This problem is a disguised function problem. The testmakers want you to see that asterisk and freak out because you've never studied anything with an asterisk in it before and clearly can't be expected to do this one. But here's the trick: don't freak out. Nobody else has studied this asterisk thing either, because the testmakers just made it up! But they will always give you instructions. You just need to follow the instructions. Let's try this one.

What they're telling us is that when you see the asterisk, take the thing under it and divide 2 by it. Fair enough. If you look under Quantity B, we see (x*)*. It's nested! Just follow PEMDAS and do the function inside the parenthesis first. So for x*, we've been shown that it's 2/x. Great. But now we have (2/x)*. This just means do it again. Take the 2/x and divide 2 by it. What we get is 2/2/x, which doesn't look great when typed that way, but you know what I mean.

How to simplify a three-level fraction? Back up. We have 2 divided by 2/x. We can pretend the first 2 is also a fraction and call it 2/1. So now we have 2/1|2/x. Now we have a four-level fraction! We made it worse! Not really though.

If you have a four-level fraction, just flip the bottom fraction and then multiply it by the top fraction, so 2/1|2/x should become 2/1 times x/2. This is easier to write on a whiteboard than in a text editor, but you should see that the 2s cancel out and we're left with just x. So the answer is C.
_________________

-
-
-
-
-

Need help with GRE math? Check out our ground-breaking books and app. Director Joined: 20 Apr 2016
Posts: 900
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 666  , given: 147

Re: For all counting numbers X, [#permalink]
1
KUDOS
Carcass wrote:

For all counting number x, $$x^* = \frac{2}{x}$$

 Quantity A Quantity B $$x$$ $$(x^*)^*$$

Here QTY A = x and we can leave it as it is.

Now for QTY B = $$(x^*)^*$$ = $$(\frac{2}{x})^*$$ (since it is given, $$x^* = \frac{2}{x}$$)

= $$(\frac{2}{2}) * x$$
= x

Hence QTY A = QTY B. i.e option C
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html Director  Joined: 07 Jan 2018
Posts: 644
Followers: 7

Kudos [?]: 601  , given: 88

Re: For all counting numbers X, [#permalink]
1
KUDOS
I am a bit confused on this.

Let us take $$x = 1$$
For $$X*$$ we get, $$\frac{2}{1}$$$$= 2$$
Again we repeat the operation for 2 and end up with 1

However, Let us take a larger number than 2 for eg. 10
we have $$x = 10$$
For$$X*$$ we get, $$\frac{2}{10}=$$$$\frac{1}{5}$$
At this point I think we cannot perform the 2nd operation because the function is defined for counting numbers only and we now have a fraction
I think the ans should be (D)
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern Joined: 07 Feb 2018
Posts: 13
Followers: 0

Kudos [?]: 2 , given: 0

Re: For all counting numbers X, [#permalink]
Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 79 , given: 99

Re: For all counting numbers X, [#permalink]
When ever I encounter such a question where there is some unknown operator then I really can not comprehend what to do..

as Here I am flabbergasted to discern the function of * and what does it mean in mathematical term (x^*)^*.?? Re: For all counting numbers X,   [#permalink] 17 May 2018, 23:50
Display posts from previous: Sort by

For all counting numbers X,  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.