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 = 42.
(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 = 42 .
  
ab
 
 -cd 
 
42
  
If there is no borrowed 10 from the tens digit of  m , so if for example, we have:
  
54
 
 -12 
 
42
  
Then,  a - c=4 .
 
But if there IS borrowed 10 from the tens digit of  m , so if for example, we have:
  
61
 
 -19 
 
42
  
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) Examples, we considered for the first statement ( 54 - 12  and  61 - 19 ) also satisfy the second statement, so even taken together the statements are not sufficient.

Answer: E

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 E

Aakash0811 · Answer

The two numbers m and n lie between 10-99 as per the question.

Analyzing Statement 1 :-
m-n=42
infers m is bigger than n.
now if we assume m = 52; then only lowest value of n = 10 will arrive, since 52-10=42
this puts the difference between 5(tens digit of m) and 1(tens digit of n) = 4;
Now, if we assume m = 62; then n = 20, again difference between ten's digits of m and n is 4.
Hence, a constant difference of 4 is arriving for any value of m and n when Statement 1 stands.
So Statement 1 is sufficient.

Analyzing Statement 2:-
Suppose m=15 and n = 11, hence the difference between their units digits are 5-1 = 4 not a multiple of 3(statement 2 satisfied), hence difference between tens digits is determined to be 1-1 = 0;
Now suppose m 26 and n =11, hence hence the difference between their units digits are 6-1 = 5 not a multiple of 3(statement 2 satisfied), hence difference between tens digits is determined to be 2-1 = 1;
Since the difference between tens digits is not fixed and depends upon values of m and n, 
Statement 2 is insufficient.

Thus the answer is A.

Please correct me if i am wrong in my process.

SamzayWarrior · Answer

Let m be- 10a+b
and n be- 10c+d

From statement 1, 10a+b - 10c-d= 42
---> 10(a-c) + b-d = 42
Not sufficient

From statement 2, b-d=1,2,4,5,7,8
Not sufficient

Now combining both statements, the only value that fits b-d would 2 such that 10(a-c) + (2) = 42, so 10(a-c) = 40 
---> a-c = 4
Therefore C

Can someone tell me what's wrong with this approach?  gmatophobia   chetan2u   KarishmaB   Bunuel   GMATPill

chetan2u · Answer

You have taken cases where b>d, that is 62-20 or 75-33 etc. But what happens when b 10(a-1-c)+2=42 a-1-c = 4 or a-c = 5 Hope it helps

bumpbot · Answer

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

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