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Is y > -4?

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Is y > -4? [#permalink] New post 05 Mar 2012, 05:46
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 [#permalink] New post 05 Mar 2012, 05:57
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Is y > -4?

(1) (1/7)^(4y) > (1/7)^(8y + 14) --> \frac{1}{7^{4y}}>\frac{1}{7^{8y+14}} --> 7^{8y+14}>7^{4y} --> 8y+14>4y --> y>-3.5, hence y>-4. Sufficient.

(2) 4y^2 + 12 y < 0 --> reduce by 4 and factor out y: y(y+3)<0 --> roots are -3 and 0, "<" sign indicates that the solution lies between the roots: -3<y<0, hence y>-4. Sufficient.

Answer: D.

Solving inequalities (to understand the reasoning for second statement):
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________

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: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 [#permalink] New post 05 Mar 2012, 06:22
Expert's post
Bunuel wrote:
Is y > -4?

(1) (1/7)^(4y) > (1/7)^(8y + 14) --> \frac{1}{7^{4y}}>\frac{1}{7^{8y+14}} --> 7^{8y+14}>7^{4y} --> 8y+14>4y --> y>-3.5, hence y>-4. Sufficient.

(2) 4y^2 + 12 y < 0 --> reduce by 4 and factor out y: y(y+3)<0 --> roots are -3 and 0, "<" sign indicates that the solution lies between the roots: -3<y<0, hence y>-4. Sufficient.

Answer: D.

Solving inequalities (to understand the reasoning for second statement):
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.


For 1) is the same (of course is subjective) to do: 7^-4y > 7^-8y+14.......in the end: y>7/2 ?????

For 2) divide by 4 we have : y(y+3)<0 the sign is LESS so, as consequence the value of x is between (not at the extreme as in case of sign > ) -3<x<0. In this case of course our variable is y but is the same, is only one unknown.

Thanks for links, I have already read; very useful .

By the way OA is D but I have never seen a post from you wrong. Precious work.
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 [#permalink] New post 05 Mar 2012, 06:28
Expert's post
carcass wrote:
Bunuel wrote:
Is y > -4?

(1) (1/7)^(4y) > (1/7)^(8y + 14) --> \frac{1}{7^{4y}}>\frac{1}{7^{8y+14}} --> 7^{8y+14}>7^{4y} --> 8y+14>4y --> y>-3.5, hence y>-4. Sufficient.

(2) 4y^2 + 12 y < 0 --> reduce by 4 and factor out y: y(y+3)<0 --> roots are -3 and 0, "<" sign indicates that the solution lies between the roots: -3<y<0, hence y>-4. Sufficient.

Answer: D.

Solving inequalities (to understand the reasoning for second statement):
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.


For 1) is the same (of course is subjective) to do: 7^-4y > 7^-8y+14.......in the end: y>7/2 ?????

For 2) divide by 4 we have : y(y+3)<0 the sign is LESS so, as consequence the value of x is between (not at the extreme as in case of sign > ) -3<x<0. In this case of course our variable is y but is the same, is only one unknown.

Thanks for links, I have already read; very useful .

By the way OA is D but I have never seen a post from you wrong. Precious work.


The red part should be 7^(-4y) > 7^(-8y-14). Else is correct.
_________________

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.


What are GMAT Club Tests?
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Re: Is y > -4? [#permalink] New post 17 Jun 2013, 04:03
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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: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 [#permalink] New post 28 Oct 2013, 23:15
Bunuel wrote:
Is y > -4?
(1) (1/7)^(4y) > (1/7)^(8y + 14) --> \frac{1}{7^{4y}}>\frac{1}{7^{8y+14}} --> 7^{8y+14}>7^{4y} --> 8y+14>4y --> y>-3.5, hence y>-4. Sufficient.


Hi Bunuel! I have read the theory for solving inequalities, but still I am not very comfortable with the subject. Could you please explain why while solving statement 1 we do not consider the sign for y? Generally while solving inequality for a variable we consider the cases when y>0 and y<0. Then in this particular case why the sign of y is not necessary? TIA.
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 [#permalink] New post 29 Oct 2013, 01:36
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vjns wrote:
Bunuel wrote:
Is y > -4?
(1) (1/7)^(4y) > (1/7)^(8y + 14) --> \frac{1}{7^{4y}}>\frac{1}{7^{8y+14}} --> 7^{8y+14}>7^{4y} --> 8y+14>4y --> y>-3.5, hence y>-4. Sufficient.


Hi Bunuel! I have read the theory for solving inequalities, but still I am not very comfortable with the subject. Could you please explain why while solving statement 1 we do not consider the sign for y? Generally while solving inequality for a variable we consider the cases when y>0 and y<0. Then in this particular case why the sign of y is not necessary? TIA.


The sign of y has nothing to do when solving 7^{8y+14}>7^{4y}.

Consider another way. Since 7^{4y} is positive irrespective of value of y, then we can safely reduce both sides by it and write: \frac{7^{8y+14}}{7^{4y}}>1 --> 7^{8y+14-4y}>1.

7^{8y+14-4y}>1 to hold true the exponent must be positive: 8y+14-4y>0 --> y>-3.5.

Hope this helps.
_________________

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.


What are GMAT Club Tests?
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12   [#permalink] 29 Oct 2013, 01:36
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