Suppose that x and y are positive three-digit integers and that the

Question

Suppose that x and y are positive three-digit integers and that the sum of their tens digits is t. Which of the following cannot be the tens digit of x+y ?

A. t - 10
B. t - 9
C. t - 1
D. t 
E. t + 1

namanqqkm · Answer

lets say x= abc and y = def then acc to Q b + e = t 
lets say t= 2 then x+ y can give t+1 if c + f> 10 and t if c= f<10 
lets say t =12 then assume numbers x= 161 and y= 161 adding them in tens digit we get 2 which is 12-10 or t- 10 
same way scenario two consider x= 166 and y = 166 and adding them in tens digit we get 3 which is 12-9 or t-9

hence ans is c

Dereno · Answer

Let the three digit number be abc = x , def =y.

Sum of digits = x+y = abc + def

We are given that tens digit of the sum = t

Case 1:

CARRY - with respect to units digit addition  .

If we get a carry, the max digits for c and f is 9+9=18. With 1 as carry.

So, the tens digit can be either t ( without any carry ) or (t+1) from carry.

So options D and E are out.

Case 2:

Can the sum of tens digits give us a carry or not  ??

8+9 in the tens digit gives us 17 = t , with 7 being tens place and 1 moves out, which is 10 going out.

17 -10 = 7

That’s t-10, which is possible.

Case 3:

Carry from units digit and a carry going out to hundreds  .

Carry from units can lead to t+1.

While a carry moving out of tens is t-10.

So, cumulative we get (t-10+1) = (t-9).

So, options A and B possible.

So, answer is  Option C

Kinshook · Answer

Suppose that x and y are positive three-digit integers and that the sum of their tens digits is t.

Which of the following cannot be the tens digit of x+y ?

Let x be abc and y be def

x+y: -

abc
def
-----
(a+d)(b+e)(c+f)

Sum of their tens digit = b + e = t

Tens digit of x+y = b + e = t ; if c+f <= 9 and b+e<=9
Tens digit of x+y = b + e + 1= t + 1; if c+f > 9 and b+e+1<=9
Tens digit of x+y = b + e - 10 = t - 10; if c+f <= 9 and b+e>9
Tens digit of x+y = b + e + 1 - 10= t - 9; if c+f > 9 and b+e+1>9

IMO C

Suppose that x and y are positive three-digit integers and that the

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