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# If |10y-4| > 7 and y < 1, which of the following could be y?

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If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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Updated on: 24 Aug 2012, 01:27
3
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Question Stats:

77% (01:28) correct 23% (01:55) wrong based on 604 sessions

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If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

Originally posted by feellikequitting on 23 Aug 2012, 20:45.
Last edited by Bunuel on 24 Aug 2012, 01:27, edited 2 times in total.
Renamed the topic and edited answer choices.
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Joined: 02 Sep 2009
Posts: 54371
Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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24 Aug 2012, 01:39
7
3
laythesmack23 wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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13 Feb 2013, 11:58
why cant we get an answer by simply substituting values in the equation |10y - 4| > 7
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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13 Feb 2013, 12:31
mehasingh wrote:
why cant we get an answer by simply substituting values in the equation |10y - 4| > 7

In my opinion applying rules in modulus is much more easier than checking for multiple values.

The rules are simple.

1) !x! < a -------> -a < x < a
so if !x-a! < r then -r < x-a < r -------> a-r < x < a+r

2) !x! > a ------> either x > a or x < -a
so if !X-a! > r then either x-a > r ------> x > a+r
or x-a < -r -----> -x+a > r --------> x < a-r

Regards,

Abhijit
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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13 Feb 2013, 12:41
mehasingh wrote:
why cant we get an answer by simply substituting values in the equation |10y - 4| > 7

Actually we can, this would also be a correct approach.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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05 Jul 2013, 13:01
Bunuel wrote:
laythesmack23 wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.

If I am not mistaken you have a typo in your explanation: 10y-4>7 shall be y>11/10 not y>4/10.
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If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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05 Jul 2013, 13:10
rhallik wrote:
Bunuel wrote:
laythesmack23 wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.

If I am not mistaken you have typos in your explanation: 10y-4>7 shall be y>11/10 not y>4/10. The same applies to -(10y-4)...

No typo there.

When $$y>\frac{4}{10}$$, then we have $$10y-4>7$$ --> $$y>\frac{11}{10}$$.

When $$y\leq{\frac{4}{10}}$$), then we have $$-(10y-4)>7$$ --> $$y<-\frac{3}{10}$$.

Hope it's clear.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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09 Jul 2013, 16:14
If |10y - 4| > 7 and y < 1, which of the following could be y?

|10y - 4| > 7
|10(-.8) - 4| > 7
|-8-4| > 7
|-12| > 7
|12| > 7
12 > 7

(A)
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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18 Jun 2017, 02:43
rhallik wrote:
Bunuel wrote:
laythesmack23 wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.

If I am not mistaken you have a typo in your explanation: 10y-4>7 shall be y>11/10 not y>4/10.

Bunuel how are you getting the y > 4/10?
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Posts: 54371
Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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18 Jun 2017, 02:56
Nunuboy1994 wrote:
rhallik wrote:
Bunuel wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.

If I am not mistaken you have a typo in your explanation: 10y-4>7 shall be y>11/10 not y>4/10.

Bunuel how are you getting the y > 4/10?

4/10 is a transition point for 10y-4 (transition point is a value of a variable for which expression in absolute value changes its sign).

When $$y>\frac{4}{10}$$, then 10y - 4 > 0, so |10y - 4| = 10y - 4.

When $$y\leq{\frac{4}{10}}$$, then 10y - 4 <= 0, so |10y - 4| = -(10y - 4).
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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01 Jul 2017, 05:21
Bunuel wrote:
laythesmack23 wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

We can simply plug answer choices less than 1 and see which one satisfies given inequality, or do the following:

$$|10y - 4| > 7$$ means that either $$10y-4>7$$ (when $$y>\frac{4}{10}$$) or $$-(10y-4)>7$$ (when $$y\leq{\frac{4}{10}}$$).

Solve both inequalities:
$$10y-4>7$$ --> $$y>1.1$$. Since we are told that $$y<1$$, then discard this solution.

$$-(10y-4)>7$$ --> $$y<-0.3$$. Only answer choice which is less than -0.3 is -0.8.

Answer: A.

Hope it's clear.[/quo

How can u assume that the answer is -0.8 when get the solved answered as -0.3??

please explain @bunnel
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Posts: 54371
If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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01 Jul 2017, 05:29
shinrai15 wrote:

How can u assume that the answer is -0.8 when get the solved answered as -0.3??

please explain @bunnel

We did not get that y = -0.3. We got that y < -0.3 (y is LESS than 0.3). -0.8 IS LESS than -0.3, so y could be -0.8
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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01 Jul 2017, 07:44
Bunuel wrote:
shinrai15 wrote:

How can u assume that the answer is -0.8 when get the solved answered as -0.3??

please explain @bunnel

We did not get that y = -0.3. We got that y < -0.3 (y is LESS than 0.3). -0.8 IS LESS than -0.3, so y could be -0.8

Thank you @bunnel for clarifying..
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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01 Jul 2017, 08:08
Solve the equation by taking out the modulus so we get 10y - 4 > 7 or 10y - 4 < -7.

On solving the equations as per the condition that y <0 we get that y < -3/10 I.e. y < -0.3; thus the only option that fits is -0.8, hence option A

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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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02 Jul 2017, 01:20
feellikequitting wrote:
If |10y - 4| > 7 and y < 1, which of the following could be y?

A. -0.8
B. -0.1
C. 0.1
D. 0
E. 1

Plug-in answer choices into inequality

Let y = -0.8...........|10* -0.8 - 4| > 7.............|-12| > 7.......12 > 7

Answer: A
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Re: If |10y-4| > 7 and y < 1, which of the following could be y?  [#permalink]

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Re: If |10y-4| > 7 and y < 1, which of the following could be y?   [#permalink] 16 Apr 2019, 17:22
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