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Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0

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carcass
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Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   05 Mar 2012, 06:46
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Is y > -4?

(1) (1/7)^(4y) > (1/7)^(8y + 14)

(2) 4y^2 + 12 y < 0
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D
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Bunuel
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Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   05 Mar 2012, 06:57
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Is y > -4?

(1) (1/7)^(4y) > (1/7)^(8y + 14)

    \(\frac{1}{7}^{4y} > \frac{1}{7}^{8y+14}\);

    \(7^{8y+14}>7^{4y}\);

    \(8y+14>4y\);

    \(y>-3.5\)

Since \(y>-3.5\), then y must also be greater than -4. Sufficient.

(2) 4y^2 + 12 y < 0

Reduce by 4 and factor out \(y\): \(y(y+3)<0\)

The 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):
https://gmatclub.com/forum/x2-4x-94661.html#p731476 (check this one first)
https://gmatclub.com/forum/inequalities ... 91482.html
https://gmatclub.com/forum/data-suff-in ... 09078.html
https://gmatclub.com/forum/range-for-va ... me#p873535
https://gmatclub.com/forum/everything-i ... me#p868863

Hope it helps.
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carcass
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   05 Mar 2012, 07:22
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 y < 0 [#permalink] New post   05 Mar 2012, 07:28
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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.
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   17 Jun 2013, 05:03
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184
All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189

700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   29 Oct 2013, 00:15
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 y < 0 [#permalink] New post   29 Oct 2013, 02:36
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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.
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   24 Jul 2017, 10:03
Good question. Just need some careful calculations.

S1:

(1/7)^4y >(1/7)^(8y+14)

Now this can not be directly equated. You will need to write it like this.

(7)^-4y>(7)^-(8y+14)

or

-4y>-(8y+14)

hence y>-3.5

Sufficient

S2:

4y^2 +12y <0

This will give you -3<y<0

hence y >-4

Sufficient

Answer is D
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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink] New post   13 Nov 2022, 14:39
Hello from the GMAT Club BumpBot!

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Re: Is y > -4? (1) (1/7)^(4y) > (1/7)^(8y + 14) (2) 4y^2 + 12 y < 0 [#permalink]
13 Nov 2022, 14:39
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