M37-43

Question

If  \frac{m}{n} = \frac{3}{8}  then which of the following cannot be the value of  n - m  ?
 
I.  -25 
 
II.  0 
 
III.  12

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

Bunuel · Answer

Official Solution:

If  \frac{m}{n} = \frac{3}{8}  then which of the following cannot be the value of  n - m  ?
 
I.  -25 
 
II.  0 
 
III.  12

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

First of all, notice that we are NOT told that  m  and  n  are integers.
 
 \frac{m}{n} = \frac{3}{8} , and  n - m=-25  has a solution:  m = -15 , and  n = -40 .
 
 \frac{m}{n} = \frac{3}{8} , and  n - m=12  has a solution:  m =\frac{36}{5} , and  n =\frac{96}{5} 
 
 \frac{m}{n} = \frac{3}{8} , and  n - m=0  does NOT have a solution because  n - m=0  means that  n = m  but  \frac{m}{n} = \frac{3}{8}  means that  n 
eq m  .

Answer: B

Kamlendu · Answer

Thankyou for the great question

Bunuel · Answer

I'm glad to know you appreciated it. Thanks for the praise!

Vidds0214 · Answer

Is there an alternate solution to solve this?

Bunuel · Answer

Check  here .

adarsh2209 · Answer

I like the solution - it’s helpful.

himssss29 · Answer

m=3k, n=8k (k=0, any real number, not necessary an integer)

n−m=5k

checking validity-

I) Value= −25k 
 k Needed= −5 ✅ Possible

II) Value= 0
 k Needed = 0 (not allowed — makes m/n = 0/0, undefined) ❌ Not possible

III) Value= 12
 k Needed= 2.4 (perfectly fine — k just needs to be non-zero, not an integer) ✅ Possible

Only II  cannot be the value of n − m, since it's the sole case that forces k = 0, which breaks the original condition m/n = 3/8 (division by zero).

M37-43

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