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As j increases from 135 to 136

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As j increases from 135 to 136 [#permalink] New post 08 Aug 2012, 08:23
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A
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C
D
E

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Question Stats:

77% (01:57) correct 23% (01:09) wrong based on 74 sessions
As j increases from 135 to 136, which of the following must decrease?
I. 1 - j^2

II. j - j^2

III. \frac{1}{j^2}

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: As j increases from 135 to 136 [#permalink] New post 08 Aug 2012, 10:23
Since as per Qs J is a positive no. We can try a pretty small no and check all options.
Let say j=2 and it increase to 3
i) decrease from -3 to -8
ii) decrease from -2 to -4
iii) decrease from 1/4 to 1/9
Answer: E

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Last edited by SOURH7WK on 08 Aug 2012, 11:13, edited 1 time in total.
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Re: As j increases from 135 to 136 [#permalink] New post 08 Aug 2012, 10:52
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metallicafan wrote:
As j increases from 135 to 136, which of the following must decrease?
I. 1 - j^2

II. j - j^2

III. \frac{1}{j^2}

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

Source: http://www.gmathacks.com


I y = 1 - x^2 is the equation of a downward parabola, intercepting the x axis at -1 and 1. So, far away from the roots, the values of the function are decreasing as x increases. YES

II y=x-x^2 is also the equation of a downward parabola, roots 0 and 1. Again, far away from the roots, the values of the function are decreasing as x increases. YES

III Definitely decreases, the larger the denominator, the smaller the value of the fraction. YES

Answer E

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Re: As j increases from 135 to 136 [#permalink] New post 08 Aug 2012, 10:53
SOURH7WK wrote:
Since as per Qs J is a positive no. We can try a pretty small no and check all options.
Let say j=2 and it increase to 3
i) decrease from -3 to -8
ii) decrease from -2 to -4
iii) decrease from 1/4 to 1/9
Answer: C



The values of j are defined: 135 and 136!

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Re: As j increases from 135 to 136 [#permalink] New post 08 Aug 2012, 14:05
Ouch! I didn't notice it was a function. :(

Thank you!

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Re: As j increases from 135 to 136 [#permalink] New post 27 Aug 2012, 08:13
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take a smaller number like 2 and 3 and solve. We get the ans to be E

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Re: As j increases from 135 to 136 [#permalink] New post 29 Aug 2012, 07:04
It can be solved using values

(1) 1- j^2 : Obviously if j increases, value of J^2 will increase. This will in turn decrease the value of 1- j^2

(2) J-J^2 = J*(1-J)

when J=135, we get -135*134
when J=136, we get -136*135
Therefore, from the values we can easily see it is decreasing.

(3) 1/J^2 : as the denominator decrease, so the result will decrease.

As in all three cases, values decrease the answer is E

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Re: As j increases from 135 to 136 [#permalink] New post 10 Dec 2012, 00:31
I. 1-j^2 Of course, a larger portion is taken from 1. Definitely the value will decrease.
II. j - j^2 I thought of smaller positive consecutive numbers such as 2 and 3. -2 vs. -6 shows a decrease.
\frac{1}{j^2} The larger the denominater, the smaller the fraction.

Answer: I,II, III or (E)

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As j increases from 135 to 136, which of following must [#permalink] New post 02 Mar 2013, 21:41
As j increases from 135 to 136, which of the following must decrease?

I. 1 - j^2

II. j - j^2

III. \frac{1}{j^2}

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

Source: Gmat Hacks 1800

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Re: As j increases from 135 to 136, which of following must [#permalink] New post 02 Mar 2013, 23:04
I. As j increases, j^2 will increase too. Therefore 1-j^2 will decrease.
II. j-j^2 = j(1-j). As j increases, 1-j will decrease and be negative. Multiplied by the increased j, this gives us a more negative figure. Therefore j-j^2 will decrease too.
III. Simple reciprocal. As j increases from 135 to 136, 1/j^2 is bound to decrease

E it is.

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Re: As j increases from 135 to 136, which of following must [#permalink] New post 03 Mar 2013, 00:03
megafan wrote:
As j increases from 135 to 136, which of the following must decrease?

I. 1 - j^2

II. j - j^2

III. \frac{1}{j^2}

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

Source: Gmat Hacks 1800




Assume j increases from 2 to 4
I. 1 - j^2
1- 2^2 = 1-4 = -3
1- 3^2 = 1-9 = -8
So this is true

II. j - j^2
2- 2^2 = 2-4 = -2
3- 3^2 = 3-9 = -6
So this is true

III. \frac{1}{j^2}
\frac{1}{2^2} = 0.25
\frac{1}{4^2} = 0.0XX
So this is true

Therefor , E :)

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Re: As j increases from 135 to 136, which of following must [#permalink] New post 03 Mar 2013, 02:07
Expert's post
megafan wrote:
As j increases from 135 to 136, which of the following must decrease?

I. 1 - j^2

II. j - j^2

III. \frac{1}{j^2}

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III

Source: Gmat Hacks 1800


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Re: As j increases from 135 to 136, which of following must   [#permalink] 03 Mar 2013, 02:07
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