GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 May 2020, 05:09

### 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 m and n are the positive integers whose sum is 64,

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 27 Oct 2017
Posts: 1783
WE: General Management (Education)
If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 18:20
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:13) correct 20% (02:27) wrong based on 35 sessions

### HideShow timer Statistics

GMATBusters’ Quant Quiz Question -5

If m and n are the positive integers whose sum is 64, then ratio of m to n cannot be:
A. 1/7
B. 1/3
C. 5/11
D. 1/2
E. 3/5

_________________
Retired Moderator
Joined: 27 Oct 2017
Posts: 1783
WE: General Management (Education)
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 18:20
Let the ratio of m/n = a/b
hence the number can be represented as ax, bx where x is a positive integer.
Sum = 64
So, ax+bx= 64
a+b = 64/x
hence the sum of numerator and denominator in ratio must be a factor of 64.
out of given options, 1:2, sum = 1+2= 3 which is not a factor of 64. hence it is the required answer.
_________________
Manager
Joined: 16 Sep 2011
Posts: 128
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 18:29
1
1
If m and n are the positive integers whose sum is 64, then ratio of m to n will be such that if we add Numerator and Denominator it will divide 64...
A. 1/7 , here x+ 7x= 8x can divide 64
B. 1/3, here x+ 3x = 4x can divide 64
C. 5/11, here 5x+11x= 16x can divide 64
D. 1/2, here x+2x= 3x cannot divide 64
E. 3/5, here 3x+5x=8x can divide 64

Director
Joined: 14 Dec 2019
Posts: 657
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 18:30
2
If m and n are the positive integers whose sum is 64, then ratio of m to n cannot be:
A. 1/7
B. 1/3
C. 5/11
D. 1/2
E. 3/5

$$m+n = 64$$

It can be $$16 + 48 = 64$$ => $$\frac{16}{48}$$ => $$\frac{1}{3}$$
Therefore if the addition of Numerator and Denominator is divisibile by 64 then that ratio is possible.

A. $$\frac{1}{7}$$ - 1+7 = 8 divisible by 64 => This ratio is possible
B. $$\frac{1}{3}$$ - 1+3= 4 divisible by 64 => This ratio is possible
C. $$\frac{5}{11}$$ - 5+11 = 16 divisible by 64 => This ratio is possible
D. $$\frac{1}{2}$$ - 1+2 = 3 not divisible by 64 => This ratio is not possible - Answer
E. $$\frac{3}{5}$$ - 3+5 = 8 divisible by 64 => This ratio is possible

Director
Joined: 22 Feb 2018
Posts: 737
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 18:38
1
Going back from solution,
A) 1/7, means m and n are 1 & 7, whose sum is 8 and 8 is factor of 64. So out
B) 1/3, means m and n are 1 & 3, whose sum is 4 and 4 is factor of 64. So out
C) 5/11, means m and n are 11 & 5, whose sum is 16 and 16 is factor of 64. So out,
D) 1/2, means m and n are 1 & 2, whose sum is 3 and 3 is not factor of 64. So correct.
E) 3/5, means m and n are 3 & 5, whose sum is 8 and 8 is factor of 64. So out,

So, D is correct.
Manager
Joined: 04 Jun 2019
Posts: 79
Location: United States
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 20:12
m+n=64 and n:m=xa:ya=x:y => (x+y)*a=m+n=64 => 64 must be divided by X+y
x:y is ratio of n to m
Now let's check
A. 1/7: 1+7=8 64:8=8 ok
B. 1/3: 1+3=4 64:4=16 ok
C. 5/11: 5+11=16 64:16=4 ok
D. 1/2: 1+2=3 64:3=21.333 RIGHT ANSWER
E. 3/5: 3+5=8 64:8=8 ok

Posted from my mobile device
Intern
Joined: 13 Nov 2019
Posts: 33
Location: India
GPA: 4
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 20:23
It is told that m,n > 0 and m,n are integers.
Attachments

New Doc 2020-02-16 08.09.13_5.jpg [ 771.24 KiB | Viewed 388 times ]

VP
Joined: 28 Jul 2016
Posts: 1019
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE: Project Management (Investment Banking)
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 20:40
if m and n are positive integers that mean
m+n = 64
now 64 is factor of 2 with no odd factor
thus the sum of m and n should be of the form 2^nk
looking a options
A. 1/7 = 7k + k = 64 = 8k = 64 (valid)
B. 1/3 = 3k+k = 4k = 64 (valid_
C. 5/11 = 16k = 64 (valid)
D. 1/2 = 3k = 64 (invalid)
E. 3/5 = 8k = 64 (valid)
_________________

Keep it simple. Keep it blank
Senior Manager
Joined: 31 May 2018
Posts: 432
Location: United States
Concentration: Finance, Marketing
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

15 Feb 2020, 22:38
If m and n are the positive integers whose sum is 64, then ratio of m to n cannot be:

A. $$\frac{1}{7}$$
m = t and n = 7t
m+n = 8t = 64 (possible)
m= 8 n = 56

B. $$\frac{1}{3}$$
m = t and n = 3t
m+n = 4t = 64 (possible)
m = 16 n = 48

C. $$\frac{5}{11}$$
m = 5t and n = 11t
m+n = 16t = 64 (possible)
m = 20 n = 44

D. $$\frac{1}{2}$$
m = t and n = 2t
m+n = 3t (this must be integer since m and n are integers)
64 is not divisible by 3 so this is not possible (correct)

E. $$\frac{3}{5}$$
m = 3t and n = 5t
m+n = 8t = 64
m = 24 n = 40 (possible)
Intern
Joined: 25 Mar 2013
Posts: 11
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

16 Feb 2020, 00:01
Solution:

Question 5: If m and n are the positive integers whose sum is 64, then ratio of m to n cannot be:

A. 1/7
B. 1/3
C. 5/11
D. 1/2
E. 3/5

In this question, the most important point to note is that we need to select the option that CANNOT be value of $$\frac{m}{n}$$.

According to the information in the question, both m and n are positive integers and $$m + n = 64$$.

Considering each of the options:

Option A: $$\frac{1}{7}$$ In this fraction, since denominator is much greater than numerator, we would think of values close to 64 that have 7 as one of the factors for the denominator. $$8*7 = 56$$ is closest to 64. Then, numerator is $$64 - 56 = 8$$. Thus, option A can be eliminated as $$\frac{1}{7}$$ can be written as $$\frac{8}{56}$$ and $$8 + 56 = 64$$. Thus, it can be the value of $$\frac{m}{n}$$ and hence it is not the right answer.

Option B: Similarly, $$\frac{1}{3}$$ can also be written as $$\frac{16}{48}$$. Thus, option B can also be eliminated.

Option C: In, $$\frac{5}{11 }$$ the numerator and denominator can be multiplied by same positive integer to find the equivalent fraction.$$\frac{(5*4)}{(11*4)}$$ = $$\frac{20}{44}$$ and $$44 + 20 = 64$$. Thus, option C is also eliminated.

Option D: $$\frac{1}{2}$$. Fraction closest to $$\frac{1}{2}$$ is $$\frac{21}{42 }$$ in which $$21 + 42 = 63$$. Thus, option D is the correct answer.

Option E: 3/5 can be written as $$\frac{(3*8) }{ (5*40)} = \frac{24}{40}$$ and $$24 + 40 = 64$$. Thus, option E is not the answer.

Option D $$\frac{1}{2}$$ is the correct answer.
Manager
Joined: 05 May 2016
Posts: 142
Location: India
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

### Show Tags

16 Feb 2020, 05:46
Solution:

Given: m+n=64

Now lets do it option wise:

A. 1/7 => m=x, n=7x => 8x, which is divisible by 64, so it can be the ratio.
B. 1/3 => m=x, n=3x => 4x, which is divisible by 64, so it can be the ratio.
C. 5/11 => m=5x, n=11x => 16x, which is divisible by 64, so it can be the ratio.
D. 1/2 => m=x, n=2x => 3x, which is not divisible by 64, so it cannot be the ratio.
E. 3/5 => m=3x, n=5x => 8x, which is divisible by 64, so it can be the ratio.

Re: If m and n are the positive integers whose sum is 64,   [#permalink] 16 Feb 2020, 05:46