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# If y is an integer such that y < -3, which of the following expression

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Manager
Joined: 13 May 2017
Posts: 107
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
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WE: Account Management (Entertainment and Sports)
If y is an integer such that y < -3, which of the following expression  [#permalink]

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27 Nov 2018, 12:04
1
2
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Difficulty:

75% (hard)

Question Stats:

47% (01:25) correct 53% (01:21) wrong based on 95 sessions

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If y is an integer such that y < -3, which of the following expressions must be correct?

I. y – $$y^2$$ + 12 < 0
II. $$y^2$$ – y – 12 > 0
III. $$2y^2$$ – 3y – 27 > 0

A. I only
B. II only
C. III only
D. I and II
E. I, II, and III
Intern
Joined: 26 Nov 2018
Posts: 6
Re: If y is an integer such that y < -3, which of the following expression  [#permalink]

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27 Nov 2018, 12:16
Its option C as 18+9 of the 1st two term will always be greater than positive 27 and let’s assume y= -3.00009 which will always be greater then when made positive after multiplication

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Manager
Joined: 13 May 2017
Posts: 107
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
GMAT 2: 570 Q36 V31
GPA: 3.14
WE: Account Management (Entertainment and Sports)
If y is an integer such that y < -3, which of the following expression  [#permalink]

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01 Dec 2018, 06:56
Given that y<-3, which inequality is correct?

$$I. y - y^2$$+12 < 0 -> modify inequality to be in standard form (standard form is when at $$ax^2$$+bx+c < 0, a is positive and on the right hand there is zero) -> multiply with (-1)
$$y^2$$ - y - 12 > 0 - inequality sign changes

Factorize: (y - 4)(y + 3) > 0 -> y=4, y=-3 -> these are the zero points (pls see 2nd pic) -> the inequality is > 0 when y< -3 or y>4

$$II. y^2$$ - y - 12 - this is the same as the first one after multiplying with (-1)

$$III. 2y^2$$- 3y - 27 >0

Factorize: (2y - 9)(y + 3) > 0 -> y=4.5 and y=-3 are the zero points (see first pic) -> when y<-3 or y>4.5 -> inequality > 0

Therefore, y<-3 fits with I. II. and III. as well -> E
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Intern
Joined: 18 Oct 2018
Posts: 16
Re: If y is an integer such that y < -3, which of the following expression  [#permalink]

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08 Dec 2018, 09:23
rencsee wrote:
If y is an integer such that y < -3, which of the following expressions must be correct?

I. y – $$y^2$$ + 12 < 0
II. $$y^2$$ – y – 12 > 0
III. $$2y^2$$ – 3y – 27 > 0

A. I only
B. II only
C. III only
D. I and II
E. I, II, and III

The fastest way of solving this is simply plugging in -4 and -5, respectively.
Re: If y is an integer such that y < -3, which of the following expression   [#permalink] 08 Dec 2018, 09:23
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