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Is (4^x)^{(5-3x)}=1 ?

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Is (4^x)^{(5-3x)}=1 ? [#permalink] New post 12 Nov 2009, 11:03
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Is (4^x)^{(5-3x)}=1?

(1) x is an integer.
(2) The product of x and positive integer y is not x.

NOTE: the expression is 4 raised to xi.e 4^x and this is again raised to (5-3x)
[Reveal] Spoiler: OA

Last edited by kp1811 on 12 Nov 2009, 11:40, edited 1 time in total.
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Re: DS- solve for x [#permalink] New post 12 Nov 2009, 11:33
kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


For (4^x)^{(5-3x)}=1, 5x-3x^2=0 i.e x^2=5/3. If "x" is an integer this is not possible. So statement 1 is sufficient.

Statement 2 says that x is not= 0. This is not sufficient.

Hence "A" should be the answer.
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Re: DS- solve for x [#permalink] New post 12 Nov 2009, 11:44
have edited my original post for expression (in case its confusing)
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Re: DS- solve for x [#permalink] New post 12 Nov 2009, 11:45
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kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


First of all (4^x)^{(5-3x)}=4^{x*(5-3x)}

This expression to be equal to 1, x*(5-3x) must be equal to 0.

x*(5-3x)=0, x=0or x=\frac{5}{3}.

So basically the question asks is x=0 or x=\frac{5}{3}.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) xy\neq{x}, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence (4^x)^{(5-3x)} does not equal to 1.

Answer: C.

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Re: DS- solve for x [#permalink] New post 15 Nov 2009, 01:11
Thats right 'C' it is.. The language in the stat2 gives a hint..
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Re: DS- solve for x [#permalink] New post 04 Dec 2013, 07:57
Bunuel wrote:
kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


First of all (4^x)^{(5-3x)}=4^{x*(5-3x)}

This expression to be equal to 1, x*(5-3x) must be equal to 0.

x*(5-3x)=0, x=0or x=\frac{5}{3}.

So basically the question asks is x=0or x=\frac{5}{3}.

(1) x is not an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) xy\neq{x}, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence (4^x)^{(5-3x)} does not equal to 1.


Typo on Statement 1: Should read x IS an integer

Great question!
Cheers

J :)
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Re: DS- solve for x [#permalink] New post 04 Dec 2013, 08:08
Expert's post
jlgdr wrote:
Bunuel wrote:
kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


First of all (4^x)^{(5-3x)}=4^{x*(5-3x)}

This expression to be equal to 1, x*(5-3x) must be equal to 0.

x*(5-3x)=0, x=0or x=\frac{5}{3}.

So basically the question asks is x=0or x=\frac{5}{3}.

(1) x is not an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) xy\neq{x}, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence (4^x)^{(5-3x)} does not equal to 1.


Typo on Statement 1: Should read x IS an integer

Great question!
Cheers

J :)


Typo edited. Thank you.

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Re: DS- solve for x [#permalink] New post 26 Apr 2014, 00:07
Bunuel wrote:
kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


First of all (4^x)^{(5-3x)}=4^{x*(5-3x)}

This expression to be equal to 1, x*(5-3x) must be equal to 0.

x*(5-3x)=0, x=0or x=\frac{5}{3}.

So basically the question asks is x=0 or x=\frac{5}{3}.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) xy\neq{x}, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence (4^x)^{(5-3x)} does not equal to 1.

Answer: C.




Hi Bunuel,
Is it not possible that the expression can be equal to 1 also because 1^1=1.

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Re: DS- solve for x [#permalink] New post 26 Apr 2014, 08:58
Expert's post
seabhi wrote:
Bunuel wrote:
kp1811 wrote:
Is (4^x)^{(5-3x)}=1?
(1) x is an integer.
(2) The product of x and positive integer y is not x.


First of all (4^x)^{(5-3x)}=4^{x*(5-3x)}

This expression to be equal to 1, x*(5-3x) must be equal to 0.

x*(5-3x)=0, x=0or x=\frac{5}{3}.

So basically the question asks is x=0 or x=\frac{5}{3}.

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) xy\neq{x}, hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence (4^x)^{(5-3x)} does not equal to 1.

Answer: C.




Hi Bunuel,
Is it not possible that the expression can be equal to 1 also because 1^1=1.


We have 4^{x*(5-3x)}=1. The left-hand side is 4 in some power, not 1^1.

_________________

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: DS- solve for x   [#permalink] 26 Apr 2014, 08:58
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