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# As j increases from 135 to 136

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As j increases from 135 to 136 [#permalink]  08 Aug 2012, 08:23
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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]  08 Aug 2012, 10:23
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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
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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]  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

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Re: As j increases from 135 to 136 [#permalink]  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

The values of j are defined: 135 and 136!
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Re: As j increases from 135 to 136 [#permalink]  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]  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]  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]  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.

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As j increases from 135 to 136, which of following must [#permalink]  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]  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]  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]  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 [#permalink]  29 Apr 2015, 16:23
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Re: As j increases from 135 to 136   [#permalink] 29 Apr 2015, 16:23
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