Challenge Ps (m21-14) : Retired Discussions [Locked]
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 03 Dec 2016, 16:18

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Challenge Ps (m21-14)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 408 [1] , given: 0

Challenge Ps (m21-14) [#permalink]

### Show Tags

29 Oct 2007, 18:04
1
KUDOS
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2

Source: GMAT Club Tests - hardest GMAT questions

[Reveal] Spoiler:
I set everything up correctly except one thing:

1/x=2.24x why do we use 3.24 instead of 2.24? Thx.

SOLUTION: challenge-ps-m21-54733.html#p1181186
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 408 [0], given: 0

### Show Tags

29 Oct 2007, 19:03
trivikram wrote:
GMATBLACKBELT wrote:
ywilfred wrote:
Don't get what you're saying...

nm i get this now. silly error.
3

can you share it with us

Thanks

Solution: x=(1/x)3.24 I made it x=(1/x)2.24
Intern
Joined: 12 Nov 2009
Posts: 46
Followers: 0

Kudos [?]: 17 [0], given: 2

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

30 Nov 2009, 18:19
Hi,

Why do we consider 3.24 and not 2.24?
Is it because

x= 1/x(1+2.24)?

Please let me know.

Thanks!
CIO
Joined: 02 Oct 2007
Posts: 1218
Followers: 94

Kudos [?]: 905 [1] , given: 334

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

01 Dec 2009, 01:54
1
KUDOS
Hi,

Consider an example. $$x$$ is 50% greater than 2. Find $$x$$. Now, in order to find $$x$$ we'll have multiply 2 by 50% and add 2:

$$x = 2*50% + 2 = 1 + 2 = 3$$

Now let's check if we did it right:

$$\frac{3-2}{2}*100% = 50%$$

If $$x$$ is 200% greater than 2, the process of finding $$x$$ remains the same:

$$x = 2*200% + 2 = 4 + 2 = 6$$

Check:

$$\frac{6-2}{2}*100% = 200%$$

I hope it helps .
Gmatter111 wrote:
Hi,

Why do we consider 3.24 and not 2.24?
Is it because

x= 1/x(1+2.24)?

Please let me know.

Thanks!

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 03 Feb 2010
Posts: 3
Followers: 0

Kudos [?]: 6 [6] , given: 0

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

03 Feb 2010, 07:08
6
KUDOS
The answer is D

I'd rather check all the answers quickly by comparing each fraction to it's reciprocal

A 8/10 = 10/8 which is 64=100 (36% smaller)
B 11/10 = 10/11 which is 121=100 (21% larger)
C 15/10 = 10/15 which is 225=100 (125% larger)
D 18/10 = 10/18 which is 324=100 <- correct 324 is 224% larger than 100
E 22/10 = 10/22 which is 484=100 (384% larger)

this shouldn't take more than 1:00 if you are comfortable with squares of numbers >10
Cheers
M
Intern
Joined: 15 Nov 2009
Posts: 31
Location: Moscow, Russia
Followers: 0

Kudos [?]: 12 [0], given: 0

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

03 Feb 2010, 11:22
You should see the difference between 'a is N% bigger than b' and 'a is N% of b'.
In the first case a - b = N%b, while in the second a = N%b.
That's why a^2=3.24, but not 2.24.
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 224

Kudos [?]: 1593 [0], given: 235

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

04 Feb 2010, 08:41
I just have a small doubt.

X is 224% greater than y

then why x = 224% *y + y

why noy

x= 224%*x + y

I m just confused with the wording, not the logic.

Do we always consider this 224% to be calculate for the number we comparing.
My doubt is there coz of this statement 224% greater than y..no where stated 224% of x or y.

Pls help.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Joined: 17 Dec 2009
Posts: 2
Location: Houston, TX
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

04 Feb 2010, 10:31
Ans (D)

224% more than means 3.24x

1.8
reciprocal =10/18=5/9

(5/9)*3.24=1.8
so, D
_________________

-Hail The gmatclub !

Intern
Joined: 14 Oct 2009
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

23 Mar 2010, 17:07
I set up the equation as follows:
Let x be the number

[x - (1/x)]
------------- = 2.24
(1/x)

working it out, you end up with

x^2 = 3.24
x=1.8
Intern
Joined: 21 Dec 2010
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

08 Feb 2011, 03:50
a= 1/a + 2.24 * [1/a]

a= 3.24 * [1/a]

a^2 = 3.24

a= 1.8
Intern
Joined: 30 Jul 2009
Posts: 20
Followers: 0

Kudos [?]: 4 [0], given: 3

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

08 Feb 2011, 07:38
X is 224% bigger then its reciprocal
X = (224/100 + 1 ) * 1/X
X^2=3.24
Now just solve for X
********
Tricks for faster way to solve the equation: (224/100 +1) = 3.24 and there is only 3 answer choices that can produce 4 in last digit when you square it. .8^2 doesn't come close to 3.24 and 2.2^2 is easy to guess not to be 324. That leaves only one choice left, 1.8!!!
Intern
Joined: 19 Aug 2010
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

08 Feb 2011, 08:26
I wasn't sure how to answer this at first, so I decided to try and estimate what numbers were close to twice the reciprocals. "A" was an obvious elimination since the reciprical increased instead of decreased and "E" was too big. I ended up going with "C", which is a trap answer if you forget to add 1 to 224%.
Manager
Joined: 10 Jan 2011
Posts: 244
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 53 [0], given: 25

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

08 Feb 2011, 10:41
The answer is D

as 1/x = (1+2.24)x
1/3.24 = x2
hence x= 1.8
_________________

-------Analyze why option A in SC wrong-------

Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 193
WE 1: SAP consultant-IT 2 years
WE 2: Entrepreneur-family business 2 years
Followers: 5

Kudos [?]: 13 [2] , given: 12

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

13 Jul 2011, 23:06
2
KUDOS
I'll go by the methodic official guide "type" approach:

z = 1/z (1+224/100)

z^2 = 324/100

z=1.8

this approach almost always works in % increase/decrease.
_________________

Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

Intern
Joined: 03 Feb 2012
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

11 Feb 2012, 01:21
I think that the option D is perfect because the one no. which is 224% greater than its reciprocal should be considered as:

x + 2.24x =3.24x
Intern
Joined: 25 Aug 2010
Posts: 46
Followers: 1

Kudos [?]: 12 [0], given: 3

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

11 Feb 2012, 01:55
GMATBLACKBELT wrote:
What positive number is 224% bigger than its reciprocal?

(A) 0.8
(B) 1.1
(C) 1.5
(D) 1.8
(E) 2.2

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

I set everything up correctly except one thing:

1/x=2.24x [highlight]why do we use 3.24 instead of 2.24?[/highlight] Thx.

the positive number bigger than the reciprocal by 224% means the following:

$$\frac{(positive number - reciprocal)}{reciprocal}= \frac{positive number}{reciprocal} - \frac{reciprocal}{reciprocal} = \frac{positive number}{reciprocal} - 1 = 224%$$
thus
$$\frac{positive number}{reciprocal} = 324%$$
Manager
Joined: 02 Feb 2012
Posts: 195
Location: United States
GPA: 3.08
Followers: 1

Kudos [?]: 5 [0], given: 104

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

11 Feb 2012, 17:08
Testing the numbers for me was the fastest solution as well.
Math Expert
Joined: 02 Sep 2009
Posts: 35843
Followers: 6830

Kudos [?]: 89754 [2] , given: 10381

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

12 Feb 2013, 05:07
2
KUDOS
Expert's post
What positive number is 224 percent greater than its reciprocal?

A. 0.8
B. 1.1
C. 1.5
D. 1.8
E. 2.2

We should find such $$x$$ that satisfy the following equation: $$x=\frac{1}{x}+\frac{1}{x}*\frac{224}{100}$$;

$$x=\frac{1}{x}*3.24$$;

$$x^2=3.24$$;

$$x=1.8$$ (since give that $$x$$ is a positive number).

_________________
Senior Manager
Joined: 15 Sep 2009
Posts: 271
GMAT 1: 750 Q V
Followers: 10

Kudos [?]: 68 [0], given: 6

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

12 Feb 2013, 05:34
One of those questions in which algebra works fastest because of the occurrence of perfect squares in the numbers.

==> x=224%(1/x) + 1/x
x=224%(1/x) + 100%(1/x)
x=324%(1/x)
x=3.24(1/x)
x^2=3.24=324/100
x=18/10=1.8

D is the correct answer.

It is a good idea to know the squares of integers between 1 and 20. Not compulsory to know, but still helpful if one does.

Another method (back-solving):

Alternatively, we could test the given options, find out which options is 3.24 times its reciprocal. It is also helpful to know the reciprocals of the first dozen positive integers, i.e. 1/1;1/2;1/3....1/12. Again, you don't have to know this, but it can help you convert into decimals easily.
Let us test the option.
A) 0.8 aka 4/5, whose reciprocal is 5/4 aka 1.25. ELIMINATE because the reciprocal is actually greater than the number, but we want the reciprocal to be (approximately) a third (or 1/3.24) of the number.
B) 1.1 aka 11/10, whose reciprocal is 10/11 aka is 0.909. ELIMINATE because the reciprocal is not approx a third of the number.
C) 1.5 aka 3/2, whose reciprocal is 2/3 aka 0.666. ELIMINATE because the reciprocal is not approx a third of the number.
D) 1.8 aka 18/10 aka 9/5, whose reciprocal is 5/9 aka 0.555. KEEP because the reciprocal is approx a third of the number. CORRECT ANSWER.
E) 2.2 aka 11/5, whose reciprocal is 5/11 aka 0.4545. ELIMINATE because the reciprocal is not approx a third of the number.

Both solutions yield D as the answer.

Personally, I find the method testing numbers easier faster to use, IN GENERAL, but for this particular question, algebra was far quicker. The testmakers design the questions with a specific "easier" solution in mind. It is important for the student to be flexible in order to use the "better" method to solve a PARTICULAR question. Hope you find this useful.

Cheers,
Der alte Fritz.
_________________

+1 Kudos me - I'm half Irish, half Prussian.

Manager
Joined: 20 Oct 2013
Posts: 78
Location: United States
Concentration: General Management, Real Estate
Followers: 0

Kudos [?]: 7 [1] , given: 15

Re: Challenge Ps (m21-14) [#permalink]

### Show Tags

21 Apr 2014, 04:17
1
KUDOS
Bigger than 224% the reciprocal -> x=(1+224%)1/x=3.241/x -> x^2=3.24->x=1.8
Re: Challenge Ps (m21-14)   [#permalink] 21 Apr 2014, 04:17
Similar topics Replies Last post
Similar
Topics:
2 PS 4 05 Jun 2012, 21:51
4 Challenges 1, Q10 4 25 May 2011, 00:59
3 ps 2 27 Mar 2011, 19:26
1 NOT ABLE TO ACCESS the challenges 12 30 Aug 2008, 10:24
7 How good are the Verbal Challenges? 7 06 Jun 2008, 17:27
Display posts from previous: Sort by

# Challenge Ps (m21-14)

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

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.