It is currently 19 Nov 2017, 05:38

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# is there a quick way to solve this

Author Message
TAGS:

### Hide Tags

Intern
Joined: 30 May 2008
Posts: 4

Kudos [?]: 4 [0], given: 0

is there a quick way to solve this [#permalink]

### Show Tags

11 Dec 2010, 16:35
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!

Kudos [?]: 4 [0], given: 0

Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 146

Kudos [?]: 225 [0], given: 0

Location: Toronto
Re: is there a quick way to solve this [#permalink]

### Show Tags

11 Dec 2010, 18:20
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!

Hi!

Do you have answer choices? Almost certainly the quickest way to get the right answer is to backsolve.

You could also work it out intiutively - we know that 480/x is 5 more than 480/(x+16). So, what factor pairs of 480 have one number that's 5 apart and another that's 16 apart?

1 480
2 240
3 160
4 120
5 96
6 80
8 60
10 48
12 40
15 32
16 30
20 24

the only pairs that match are 10*48 and 15*32 (x=32, x+16=48; 480/32 = 15 which is 5 more than 480/48 = 10).

So, x=32.

Kudos [?]: 225 [0], given: 0

Manager
Joined: 24 Nov 2010
Posts: 203

Kudos [?]: 94 [0], given: 7

Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Re: is there a quick way to solve this [#permalink]

### Show Tags

11 Dec 2010, 19:47
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!

480/x = 480/(x+16) + 5
=> 96/x = 96/(x+16) +1 (div. entire eqn by 5)
=> 96x+96*16 = 96x +x2 +16x
=> x2 + 16x - 96*16 = 0 (Also, 96*16 = 48*2*16 = 48*32, And 48-32=16)
=> x2 + 48x - 32x - 48*32 =0
=> x= (-48, 32)

note: x2 = "x squared"

i think it can be done in 2 mins since we don't have to complete the multiplication of any big numbers.

Kudos [?]: 94 [0], given: 7

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17791 [0], given: 235

Location: Pune, India
Re: is there a quick way to solve this [#permalink]

### Show Tags

12 Dec 2010, 19:36
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!

$$\frac{480}{x} = \frac{480}{{x+16}} + 5$$
$$\frac{96}{x} = \frac{96}{{x+16}} + 1$$

If there are no options to help out at this stage, consider that numbers in GMAT problems almost always fall beautifully in place.
I will first try x = 16 because I know 16*6 = 96
I get $$\frac{96}{16} = \frac{96}{{16+16}} + 1$$
6=4 (x is not 16)
Since I need to reduce the left hand side, I will try a bigger value of x, 24 because 96/24 = 4 but 24+16 = 40 which doesn't divide 96 completely.
Next number I will try will be 32 since 96/32 = 3. Also 96/(32 + 16) = 2. This satisfies the equation.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17791 [0], given: 235

Re: is there a quick way to solve this   [#permalink] 12 Dec 2010, 19:36
Display posts from previous: Sort by