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Is (4^x)^{(5-3x)}=1 ? [#permalink ]
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)

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 ]
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 ]
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 ]
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=0 or

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 ]
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 ]
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=0 or

x=\frac{5}{3} .

So basically the question asks is

x=0 or

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 ]
04 Dec 2013, 08:08
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=0 or

x=\frac{5}{3} .

So basically the question asks is

x=0 or

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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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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

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Re: DS- solve for x [#permalink ]
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=0 or

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 ]
26 Apr 2014, 08:58
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=0 or

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.

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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. What are GMAT Club Tests ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

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