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Challenge Ps (m21-14)

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Challenge Ps (m21-14) [#permalink] New post 29 Oct 2007, 18:04
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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

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[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
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 [#permalink] New post 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



Answer is 1.8

Solution: x=(1/x)3.24 I made it x=(1/x)2.24
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Re: Challenge Ps (m21-14) [#permalink] New post 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!
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Re: Challenge Ps (m21-14) [#permalink] New post 01 Dec 2009, 01:54
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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!

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Re: Challenge Ps (m21-14) [#permalink] New post 03 Feb 2010, 07:08
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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
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Re: Challenge Ps (m21-14) [#permalink] New post 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.
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Re: Challenge Ps (m21-14) [#permalink] New post 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.
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Re: Challenge Ps (m21-14) [#permalink] New post 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
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Re: Challenge Ps (m21-14) [#permalink] New post 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
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Re: Challenge Ps (m21-14) [#permalink] New post 08 Feb 2011, 03:50
a= 1/a + 2.24 * [1/a]

a= 3.24 * [1/a]

a^2 = 3.24

a= 1.8
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Re: Challenge Ps (m21-14) [#permalink] New post 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!!!
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Re: Challenge Ps (m21-14) [#permalink] New post 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%.
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Re: Challenge Ps (m21-14) [#permalink] New post 08 Feb 2011, 10:41
The answer is D

as 1/x = (1+2.24)x
1/3.24 = x2
hence x= 1.8
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Re: Challenge Ps (m21-14) [#permalink] New post 13 Jul 2011, 23:06
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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.
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Re: Challenge Ps (m21-14) [#permalink] New post 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
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Re: Challenge Ps (m21-14) [#permalink] New post 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

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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%
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Re: Challenge Ps (m21-14) [#permalink] New post 11 Feb 2012, 17:08
Testing the numbers for me was the fastest solution as well.
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Re: Challenge Ps (m21-14) [#permalink] New post 12 Feb 2013, 05:07
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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).

Answer: D.
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Re: Challenge Ps (m21-14) [#permalink] New post 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.

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Re: Challenge Ps (m21-14) [#permalink] New post 21 Apr 2014, 04:17
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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
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