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Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8

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Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 01:44
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 02:16
1
1) y=16 Therefore, x= 4 or -4. Insufficuient
2) 15x>12x+3, x>1, Insufficuient
Combining. x=4.
IMO C
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 02:38
1
(1) \(5^y > 25^8\) and \(y = x^2\)
--> \(5^y > 5^{16}\)
--> \(y > 16\)
--> \(x^2 > 16\)
--> \(x < -4\) or \(x > 4\) --> Insufficient

(2) \(2^{15x} > 8^{4x}∗8\)
-->\(2^{15x} > 2^{12x}∗2^3\)
-->\(2^{15x} > 2^{12x + 3}\)
--> \(15x > 12x + 3\)
--> \(3x > 3\)
--> \(x > 1 \)
--> Possible values of \(x = {1.5, 2, 3, 5, . . . }\) --> Insufficient

Combining (1) & (2),
Since \(x > 1\), \(x < -4\) or \(x > 4\)
--> \(x > 4\) only
--> \(x > 3\) always--> Sufficient
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Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post Updated on: 19 Nov 2019, 01:02
#1
5^y>25^8 and y=x^2
5^y>5^16 and y=x^2
y has to be atleast 17 and value can be +/-4
so x>3 sufficient
#2
2^15x>8^4x∗8
2^15x>2^12x+3
15x>12x+3
x>1
insufficient
from 1 &2
sufficient
IMO C

Is x>3?

(1) 5^y>25^8 and y=x^2
(2) 2^15x>8^4x∗8

Originally posted by Archit3110 on 18 Nov 2019, 02:39.
Last edited by Archit3110 on 19 Nov 2019, 01:02, edited 1 time in total.
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 04:33
1
Quote:
Is x>3?

(1) 5^y>25^8 and y=x^2
(2) 2^{15x}>8^4x∗8


(1) 5^y>25^8 and y=x^2 insufic

\(5^y>{25}^8…5^y>5^{16}…y>16\)
\(y=x^2:x^2>16…|x|>4…x>4,x<-4\)

(2) 2^{15x}>8^4x∗8 insufic
\(2^{15x}>8^{4x}∗8…2^{15x-3}>2^{12x}…15x-3>12x…3x>3…x>1\)

(1&2) sufic
\(x>1:|x|>4…x>4\)

Ans (C)
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 07:31
1
Is x>3?

(1) \(5^y>25^8 and y=x^2\)
\(5^{x^2}>(5^2)^8\)
\(x^2 > 16\)

Let \(x^2 = 25\)
=> x = +/- 5

INSUFFICIENT.

(2) \(2^{15x}>8^{4x}∗8\)
\(2^{15x}>8^{4x + 1}\)
\(2^{15x}>2^{3*(4x + 1)}\)
15x > 3*(4x + 1)
x > 1

INSUFFICIENT.

Together 1 and 2.
x = 5, 6, 7 ....
Hence x > 3 always

SUFFICIENT.

IMO Answer C.
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 07:47
1
IMO C

From 1 - x>+-4
From 2- x>1
Combining both, x>3..
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 10:09
1
(1)This gives y>16

Then x^2>16
x can be any value except -4 to 4
INSUFFICIENT

(2)this gives x>1....so INSUFFICIENT

combining both we can get.....x>4.


So SUFFICIENT

OA:C

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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 12:38
1
We are asked if x>3.

1. 5^y > 25^8 and y=x^2
5^y > (5^2)^8
5^y > 5^16
hence y>16. But y=x^2
hence x^2 > 16
(x-4)(x+4) > 0
x<-4 or x>4
This is insufficient because when x=-5, x<3, but when x=5, then x>3.

2. 2^15x > 8^4x * 8
2^15x > (8)^(4x+1)
2^15x > (2)^(3[4x+1])
This implies 15x>12x+3 hence x>1
This is insufficient because when x=2, then x<3. but when x=4, then x>3.

1+2
x<-4 or x>4 and x>1.
This means we are able to conclude that x>4 since that is the range that satisfies both statements.
Within the range of x>4, x>3. Hence both statements taken together is sufficient.

The answer is option C.
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 14:24
1
Is x>3?

(1) 5^y > 25^8 and y=x^2
(2) 2^(15x) > 8^(4x)*8

(1) 5^ y > 5^2^8 so, y > 16 . now, x^2 > 16. so, x > 4 or x < -4. Not sufficient.
(2) 15 x > 12x + 3 or, 3x > 3 or, x > 1 . not sufficient
Together, x is greater than 3. sufficient.
C is the answer.
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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8  [#permalink]

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New post 18 Nov 2019, 15:05
1
Is x >3?

(Statement1):
y >16 and \(y = x^{2}\)

(x —4)(x+4) >0
Clearly insufficient

(Statement2): 15x > 12x+ 3
3x > 3
x >1
—> if x=4, then Yes
—> If x=2, then No
Insufficient

Taken together 1&2,
x >1
(x—4)(x+ 4) >0

—> x >4
Sufficient
The answer is C

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Re: Is x > 3? (1) 5^y > 25^8 and y = x^2 (2) 2^(15x) > 8^(4x)*8   [#permalink] 18 Nov 2019, 15:05
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