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

Question

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

GMATBusters · Answer

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.
Answer = D

pk123 · Answer

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

hence D is the answer

shameekv1989 · Answer

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

Answer - D

Raxit85 · Answer

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.

KhulanE · Answer

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

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ajaymahadev · Answer

It is told that m,n > 0 and m,n are integers.

globaldesi · Answer

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)
thus D answer

shridhar786 · Answer

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)

aditibarjatya · Answer

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.

bM22 · Answer

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.

So answer will be D.

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

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