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

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Difficulty:   25% (medium)

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

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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

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

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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.
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Manager  S
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Posts: 128
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

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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  P
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Re: If m and n are the positive integers whose sum is 64,  [#permalink]

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

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

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

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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  V
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Re: If m and n are the positive integers whose sum is 64,  [#permalink]

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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)
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Senior Manager  P
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]

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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  B
Joined: 25 Mar 2013
Posts: 11
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

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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  S
Joined: 05 May 2016
Posts: 142
Location: India
Re: If m and n are the positive integers whose sum is 64,  [#permalink]

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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

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