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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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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

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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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
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

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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.

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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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink ]
05 Jul 2013, 12:10
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 \(10y-4>7\) --> \(y>11/10\).

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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