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

 It is currently 25 Mar 2019, 23:34

### 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

# If 20/5 = 1/2^m + 1/2^n what is nm ?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Jul 2018
Posts: 5
If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

Updated on: 20 Feb 2019, 02:21
5
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:02) correct 46% (02:32) wrong based on 78 sessions

### HideShow timer Statistics

If $$\frac{20}{2^{5}} = \frac{1}{2^{m}} + \frac{1}{2^{n}}$$ what is nm ?

a) 0
b) 3
c) 8
d) 16
e) 24

Originally posted by Pdirienzo on 19 Feb 2019, 11:05.
Last edited by Pdirienzo on 20 Feb 2019, 02:21, edited 1 time in total.
Intern
Joined: 07 Feb 2018
Posts: 12
Location: India
Concentration: Technology, General Management
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

19 Feb 2019, 14:03
Guys....anyone knows..how to solve this..appreciate responses
Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 206
Location: Malaysia
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

19 Feb 2019, 15:40
1
Pdirienzo wrote:
If $$\frac{20}{5} = \frac{1}{2^{m}} + \frac{1}{2^{n}}$$ what is nm ?
a) 0
b) 3
c) 8
d) 16
e) 24

I didn't get the algebraic key to solve it, but I had some thoughts.

when we think about the idea that the sum of two fractions is 4,
this means that at least m or n must be negative to convert the fraction to an integer.
Also we can conclude that if one of the variables (m or n) is negative, the other can't be positive because it will give a mixed number upon summation.
so the options of m and n are either (-ve,-ve) or (-ve,0).

by looking at the value of 4, it is an even number.
so (-ve,0) is excluded because it would result in an odd number (because 2^0 = 1, which is odd).

by thinking about the (-ve,-ve) option, I though of the pair (-1,-1), which would make mn = 1, but it is not in the answer choices
_________________
..Thanks for KUDOS
Manager
Joined: 20 Mar 2018
Posts: 57
Location: Ghana
Concentration: Finance, Real Estate
If 20/5 = 1/2^m + 1/2^n what is n?  [#permalink]

### Show Tags

Updated on: 20 Feb 2019, 02:47
20/(2^5)=1/2^m + 1/2^n
20/(2^5)=2^n+2^m/(2^m*2^n)
20(2^m*2^n)=(2^n+2^m)2^5
2^2*5(2^m*2^n)=(2^n+2^m)2^5
5(2^m*2^n)=(2^n+2^m)2^3
Now the only way the LHS will equate the RHS is when m=3 ,n=1 or when n=3 ,m=1
5(2^3*2^1)=(2^1+2^3)2^3
Now ,5*2=(2^1+2^3)
So m*n =3
Ans is B

Posted from my mobile device

Originally posted by Staphyk on 20 Feb 2019, 00:36.
Last edited by Staphyk on 20 Feb 2019, 02:47, edited 1 time in total.
Intern
Joined: 13 Jul 2018
Posts: 5
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

20 Feb 2019, 02:22
Sorry, there was a mistake in the question, already edited the original
Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 206
Location: Malaysia
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

20 Feb 2019, 02:47
Staphyk wrote:
(2^2*2^m*2^n)=2^n+2^m
2^2+m+n= 2(1^n+1^m)

Hi Staphyk
In General, taking 2 as a common factor is not a valid simplification step.
Think about it. $$2^3 + 2^2 \neq{2(1^3+1^2)}$$
_________________
..Thanks for KUDOS
Manager
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

20 Feb 2019, 03:14
2
Here are my two cents.

20/32 = 5/8

= (1+4)8 = 1/8 +4/8
= 1/8 + 1/2

= 1/2^3 + 1/2^1

SO by comparing both side

we get m=3 and n=1

so mn = 3

I could not write full soultion in this due to typing overhead.

Posted from my mobile device
_________________
Ankit
GMAT is tough so I am ...
Giving Kudos is the best way to encourage and appreciate people
Intern
Joined: 31 Dec 2018
Posts: 18
Location: India
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

20 Feb 2019, 03:34
20/2^5=2^m+2^n/2^mn
4*5/2^5=2^m+2^n/2^mn
5/2^3=2^m+2^n/2^mn
so all individual values of m and n, mn should always be 3 to satisfy the equation.

3 Kudos short.

Posted from my mobile device
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5443
Location: United States (CA)
Re: If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

21 Feb 2019, 18:19
1
Pdirienzo wrote:
If $$\frac{20}{2^{5}} = \frac{1}{2^{m}} + \frac{1}{2^{n}}$$ what is nm ?

a) 0
b) 3
c) 8
d) 16
e) 24

(Note: Here we are assuming that both m and n are integers.)

Simplifying, we have:

20/(2^5) = 1/(2^m) + 1/(2^n)

5/2^3 = 1/(2^m) + 1/(2^n)

5 = (2^3)/(2^m) + (2^3)/(2^n)

5 = 2^(3 - m) + 2^(3 - n)

The only way to express 5 as the sum of two integer powers of 2 is 5 = 4 + 1 = 2^2 + 2^0. So, either of (3 - m) or (3 - n) is equal to 2 and the other one is equal to 0. If 3 - m = 2 and 3 - n = 0, then m = 1 and n = 3. In this case, we get mn = 3. If 3 - m = 0 and 3 - n = 2, we get m = 3 and n = 1 and again, mn = 3.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Joined: 11 May 2018
Posts: 17
Location: India
If 20/5 = 1/2^m + 1/2^n what is nm ?  [#permalink]

### Show Tags

23 Feb 2019, 07:30
2
$$\frac{20}{2^5} = \frac{1}{2^m} + \frac{1}{2^n}$$

$$\frac{5}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}$$

$$\frac{(4 +1)}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}$$

$$\frac{(2^2+1)}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}$$

$$\frac{1}{2^1} + \frac{1}{2^3} = \frac{1}{2^m} + \frac{1}{2^n}$$

this implies m = 1 when n = 3 or m = 3 when n = 1

thus mn = 3
If 20/5 = 1/2^m + 1/2^n what is nm ?   [#permalink] 23 Feb 2019, 07:30
Display posts from previous: Sort by