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, 20:45

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76% (01:52) correct

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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

[Reveal] Spoiler: OA

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

23 Aug 2012, 20:54

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, 01:39

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]

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]

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]

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]

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] 13 Feb 2013, 12:41

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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?

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