If m and n are positive two-digit integers, what is the value of the

Question

If m and n are positive two-digit integers, what is the value of the tens digit of m minus the tens digit of n ?

(1) m - n = 43.
(2) The units digit of m minus the units digit of n is not a multiple of 3.

gmatophobia · Answer

Assume

m =  x_{1} y_{1}

n =  x_{2} y_{2}

m - n =  10x_{1}+y_{1} - 10x_{2}-y_{2}

Once we have figured out, we can evaluate individual statements. The working is shown in the attached image.

IMO C

G-Man · Answer

Given both m and n are two-digit numbers

Statement1:
Given m-n = 43

lets assume m>53 and n>10

let us take m = 80 then n = 37, then the difference of 10s digit numbers is 5
but when m = 88 then n = 29 and the difference is 6
Not Sufficient

Statement2:
Given the difference in 10s digits is not a multiple of 3.
m and n could be any set of numbers
Not Sufficient

Combining:
Difference is 5
Hence C

Bunuel · Answer

Official Solution:

If  m  and  n  are positive two-digit integers, what is the value of the tens digit of  m  minus the tens digit of  n  ? 
 
Let  m  be  ab , where  a  is the tens digit and  b  is the units digit, and  n  be  cd , where  c  is the tens digit and  d  is the units digit. The question asks to find the value of  a - c .
 
(1)  m - n = 43 .
  
ab
 
 -cd 
 
43
  
 CASE 1:  If there is no borrowed 10 from the tens digit of  m , so if for example, we have:
  
55
 
 -12 
 
43
  
Then,  a - c=4 .
 
 CASE 2:  If there IS borrowed 10 from the tens digit of  m , so if for example, we have:
  
62
 
 -19 
 
43
  
Then,  a - c=5 .
 
Not sufficient.
 
(2) The units digit of  m  minus the units digit of  n  is not a multiple of 3. 
 
This one is clearly insufficient.
 
(1)+(2) We cannot have CASE 1 from (1) because if it were the case then the units digit of  m  minus the units digit of  n  ( b-d ) would simply be 3, which IS a multiple of 3, so we must have CASE 2, which means that  a - c=5 . Sufficient.

Answer: C

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If m and n are positive two-digit integers, what is the value of the

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