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

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

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New post 27 Nov 2018, 11:04
1
2
00:00
A
B
C
D
E

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
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Re: If y is an integer such that y < -3, which of the following expression  [#permalink]

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New post 27 Nov 2018, 11:16
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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WE: Account Management (Entertainment and Sports)
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If y is an integer such that y < -3, which of the following expression  [#permalink]

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New post 01 Dec 2018, 05:56
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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Re: If y is an integer such that y < -3, which of the following expression  [#permalink]

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New post 08 Dec 2018, 08:23
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.
GMAT Club Bot
Re: If y is an integer such that y < -3, which of the following expression &nbs [#permalink] 08 Dec 2018, 08:23
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If y is an integer such that y < -3, which of the following expression

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