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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]  23 Aug 2012, 19:45
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15% (low)

Question Stats:

76% (02:13) correct 24% (01:18) wrong based on 397 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Aug 2012, 00:27, edited 2 times in total.
Renamed the topic and edited answer choices.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]  23 Aug 2012, 19:54
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Please, write well your question. It seems that choices C and E are the same.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]  24 Aug 2012, 00:39
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Expert's post
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.

Hope it's clear.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]  13 Feb 2013, 10:58
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]  13 Feb 2013, 11:31
Expert's post
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]  13 Feb 2013, 11:41
Expert's post
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]  05 Jul 2013, 12:01
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.

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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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]  05 Jul 2013, 12:10
Expert's post
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.

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 $$10y-4>7$$ --> $$y>11/10$$.
When $$y\leq{\frac{4}{10}}$$), then we have $$-(10y-4)>7$$ --> $$y<-3/10$$.

Hope it's clear.
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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]  09 Jul 2013, 15:14
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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I am going through the Algebra work book (MGMAT) and I am trying to figure out why the answer to question 5, in the Chapter 7 problem set is -.8.

Here is the question
If l10y-4l>7 & Y,1, which one of the following could be y?

a.-.8
b. -.1
c. .1
d. 0
e. 1

I know how to solve the problem, I am just not sure how the answer is -.8 when the solution are:

Y>11/10 or 1.1 & Y<-3/10 or -.3

I tried to combine the inequality but it didnt make sense, once I changed the signs to go in the same direction.
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Kudos [?]: 40929 [0], given: 5576

Expert's post
Nai222 wrote:
I am going through the Algebra work book (MGMAT) and I am trying to figure out why the answer to question 5, in the Chapter 7 problem set is -.8.

Here is the question
If l10y-4l>7 & Y,1, which one of the following could be y?

a.-.8
b. -.1
c. .1
d. 0
e. 1

I know how to solve the problem, I am just not sure how the answer is -.8 when the solution are:

Y>11/10 or 1.1 & Y<-3/10 or -.3

I tried to combine the inequality but it didnt make sense, once I changed the signs to go in the same direction.

Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: members/member-73391.html Pay attention to the rule 3 and 5. Thank you.
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