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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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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]

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New post 23 Aug 2012, 20:54
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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]

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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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New post 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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New post 13 Feb 2013, 12:31
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]

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New post 13 Feb 2013, 12:41
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Re: If |10y-4| > 7 and y < 1, which of the following could be y? [#permalink]

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

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New post 05 Jul 2013, 13:10
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.

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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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Help Please [#permalink]

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New post 29 Oct 2013, 11:51
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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Re: Help Please [#permalink]

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New post 29 Oct 2013, 11:57
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.

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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] 06 Apr 2016, 03:54
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