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.

Bunuel · Accepted 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

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards