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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] New post 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
[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] New post 24 Aug 2012, 00:39
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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] New post 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] New post 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] New post 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] New post 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] New post 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] New post 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.

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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] New post 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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Help Please [#permalink] New post 29 Oct 2013, 10:51
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] New post 29 Oct 2013, 10:57
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.

Also, please read carefully and follow: members/member-73391.html Pay attention to the rule 3 and 5. Thank you.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: Help Please   [#permalink] 29 Oct 2013, 10:57
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