GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Aug 2018, 18:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Tough PS 2

Author Message
Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

Updated on: 03 Jun 2009, 18:28
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

If $$2401^{2XY} = 49*343^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$

(2) $$\frac{1}{3}$$

(3) $$\frac{1}{2}$$

(4) $$1$$

(5) $$2$$

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Originally posted by Hades on 03 Jun 2009, 17:10.
Last edited by Hades on 03 Jun 2009, 18:28, edited 1 time in total.
SVP
Joined: 29 Aug 2007
Posts: 2420

### Show Tags

03 Jun 2009, 18:23
If $$2401^{2XY} = 49*243^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$
(2) $$\frac{1}{3}$$
(3) $$\frac{1}{2}$$
(4) $$1$$
(5) $$2$$

$$2401^({2XY}) = 49*243^({\frac{2}{3}X})$$
$$7^({4*2X*3x}) = 7^{2} * 3^({\frac{5*2}{3}X})$$
$$7^({24X^{2} - 2}) = 3^({\frac{10}{3}X})$$

What next ????????
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

03 Jun 2009, 18:27
omfg It should be 343, sorry
_________________

Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

03 Jun 2009, 18:30
Also

$$2401^{2XY}$$
$$=49^{4XY}$$
$$=7^{8XY}$$
_________________

SVP
Joined: 29 Aug 2007
Posts: 2420

### Show Tags

03 Jun 2009, 18:39
If $$2401^{2XY} = 49*343^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$
(2) $$\frac{1}{3}$$
(3) $$\frac{1}{2}$$
(4) $$1$$
(5) $$2$$

$$2401^{2XY} = 49*343^{\frac{2}{3}X}$$
$$7^{4*2X*3x} = 7^{2} * 7^{\frac{3*2}{3}X}$$
$$7^{24X^{2}} = 7^{{4X}$$
$$24X^{2} = 4X$$
$$6X^{2} - X = 0$$
$$x (6X-1) = 0$$
$$X = 0 or \frac{1}{6}$$
$$So X = 0$$
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

03 Jun 2009, 19:22
1
GMAT TIGER, check your exponent algebra...

$$2401^{2XY} = 49*343^{\frac{2}{3}X}$$

$$49^{4XY} = 7^{2}(7^{3})^{\frac{2}{3}X}$$

$$7^{8XY} = 7^{2}7^{\frac{3*2}{3}X}$$

$$7^{8XY} = 7^{2}7^{2X}$$

$$7^{8XY} = 7^{2+2X}$$

$$\longrightarrow 8XY=2+2X$$

Substitute in $$Y=3X$$

$$8X(3X)=2+2X$$

$$24X^{2}=2+2X$$

$$12X^{2}=1+X$$

$$12X^{2}=1+X$$

You can either factor:

$$12X^{2} - X - 1=0$$

$$X^{2} - \frac{1}{12X} - \frac{1}{12} = 0$$

$$X^{2} + \frac{1}{4X} - \frac{1}{3X} - \frac{1}{12} = 0$$

$$X(X + \frac{1}{4}) - \frac{1}{3}(X + \frac{1}{4}) = 0$$

$$(X - \frac{1}{3})(X + \frac{1}{4}) = 0$$

$$\longrightarrow X=\frac{1}{3}$$ OR $$X=-\frac{1}{4}$$

Or substitute:
(1) $$X=0 \longrightarrow 0 = 1$$

(2) $$X=\frac{1}{3} \longrightarrow 4/3 = 4/3$$

(3) $$X=\frac{1}{2} \longrightarrow 3 = 3/2$$

(4) $$X=1 \longrightarrow 12 = 2$$

(5) $$X=2 \longrightarrow 48 = 3$$

Final Answer, 2: $$X= \frac{1}{3}$$.
_________________

SVP
Joined: 29 Aug 2007
Posts: 2420

### Show Tags

03 Jun 2009, 23:47
If $$2401^{2XY} = 49*343^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$
(2) $$\frac{1}{3}$$
(3) $$\frac{1}{2}$$
(4) $$1$$
(5) $$2$$

$$2401^{2XY} = 49*343^{\frac{2}{3}X}$$
$$7^{4*2X*3x} = 7^{2} * 7^{\frac{3*2}{3}X}$$
$$7^{24X^{2}} = 7^{2X+2}$$
$$24X^{2} = 2x+2$$
$$12X^{2} - x - 1 = 0$$
$$(x-3) (x+4) = 0$$
$$X = {-4} or \frac{1}{3}$$
$$So X = \frac{1}{3}$$

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

04 Jun 2009, 00:06
GMAT TIGER wrote:
If $$2401^{2XY} = 49*343^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$
(2) $$\frac{1}{3}$$
(3) $$\frac{1}{2}$$
(4) $$1$$
(5) $$2$$

$$2401^{2XY} = 49*343^{\frac{2}{3}X}$$
$$7^{4*2X*3x} = 7^{2} * 7^{\frac{3*2}{3}X}$$
$$7^{24X^{2}} = 7^{2X+2}$$
$$24X^{2} = 2x+2$$
$$12X^{2} - x - 1 = 0$$
$$(x-3) (x+4) = 0$$
$$X = \frac{-1}{4} or \frac{1}{3}$$
$$So X = \frac{1}{3}$$

$$(x-3) (x+4) = 0$$
$$\longrightarrow x=3$$ OR $$x=-4$$....

unless you meant 1 over
_________________

SVP
Joined: 29 Aug 2007
Posts: 2420

### Show Tags

04 Jun 2009, 07:07
GMAT TIGER wrote:
If $$2401^{2XY} = 49*343^{\frac{2}{3}X}$$ and $$Y=3X$$

What is the value of X?

(1) $$0$$
(2) $$\frac{1}{3}$$
(3) $$\frac{1}{2}$$
(4) $$1$$
(5) $$2$$

$$2401^{2XY} = 49*343^{\frac{2}{3}X}$$
$$7^{4*2X*3x} = 7^{2} * 7^{\frac{3*2}{3}X}$$
$$7^{24X^{2}} = 7^{2X+2}$$
$$24X^{2} = 2x+2$$
$$12X^{2} - x - 1 = 0$$
$$(x-3) (x+4) = 0$$
$$X = {-4} or \frac{1}{3}$$
$$So X = \frac{1}{3}$$

$$(x-3) (x+4) = 0$$
$$\longrightarrow x=3$$ OR $$x=-4$$....

unless you meant 1 over

Obviously not.
Don't worry. Thats typo.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Senior Manager
Joined: 16 Jan 2009
Posts: 339
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)

### Show Tags

04 Jun 2009, 11:47
2401^(2xy) = 49*343^(2/3x)
2401^(2xy) = 49*49^x
2401^(2xy) = 2401^x
(2xy)=x
y=1/2

y=3x
x=1/6
_________________

Lahoosaher

Manager
Joined: 14 May 2009
Posts: 187

### Show Tags

04 Jun 2009, 12:59
amolsk11 wrote:
2401^(2xy) = 49*343^(2/3x)
2401^(2xy) = 49*49^x
2401^(2xy) = 2401^x
(2xy)=x
y=1/2

y=3x
x=1/6

$$49(49^{x}) \neq 2401^x$$
...
$$49(49^{x}) = 49^{x+1}$$
_________________

Manager
Joined: 05 Aug 2008
Posts: 88
Schools: McCombs Class of 2012

### Show Tags

24 Jun 2009, 11:50
I think what GMAT TIGER meant was

12x^2 -x - 1 = 0
(3x -1)(4x +1) = 0
x = 1/3 or -1/4

I think this is a bit easier to deal with than deal with the denominator. Great question overall though.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Tough PS 2 &nbs [#permalink] 24 Jun 2009, 11:50
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.