If k and p represent non-zero digits within the integers

@Jamifahad:ok i got it .Sorry for that silly question there .OA is A .

looking at the question we know we are adding as units digit is 6(8+8), so 1 is carried over to next number
thus we know
9( 8 + 1 carried over) +K = p
9+k = 16
k = 7
hence P = 6= A

The question is quite straight forward. Look at the big picture first. Eight hundred something gets added to (the addition sign is missing here) another 3 digit number to give you sixteen hundred something.
This means the second number should be either seven hundred something or eight hundred something. So k is either 7 or 8.
If you put k = 7, you get 878 + 788 = 1666. So you get p = 6.
k cannot be 8 because 888 + 888 gives you seventeen hundred something.

8k8
+k88
-------
1,6p6
-------

If k and p represent non-zero digits within the integers above, what is p?

1. 6
2. 7
3. 8
4. 9
5. 17

What's the logic behind this to solve these problems? Can someone please explain? I struggle badly on these and they seem to appear on the real GMAT.

8k8
+k88
-------
1,6p6
-------

If k and p represent non-zero digits within the integers above, what is p?

1. 6
2. 7
3. 8
4. 9
5. 17

What's the logic behind this to solve these problems? Can someone please explain? I struggle badly on these and they seem to appear on the real GMAT.

Apologies as I have posted in the wrong forum before.

Well for this one, its just logic -

..8k8
+k88
-------
16p6

Now this means we have to add 2 numbers - one greater than 800 and the other unknown to get 1600. This second number should be near 800 by logic, infact a little less than 800 as the first number is a little more than 800, to get the sum to 1600.

you can even check by picking the bottom number to be 800 something or 900 something (by picking k as 8/9). It wont work as it will make the total way more than 1600 something.
e.g.
888+888=1776 => not the form of 16p6 => WRONG

lets try 7
878+788=1666 =>PERFECT k=7,p=6!


Ans: A

(Units digit of 9+k) = p

Also,
(Tens digit of 9+k) + 8 + k = 16
=> k = 8 - (Tens digit of 9+k)
=> k = 7

Therefore p = units digit of 16 = 6
The answer is (A)

Hi gsaxena26,

There are no hard and fast rules to tackle such questions.These questions can easily be handled with quick substitution techniques.

8k8
k88 +
------
16P6
------

Now we start working from right to left :

Step 1 :

8+8 =16 ;we already have six as unit digit(in answer),the 1 gets carried off .

Step 2:

We should now think of a number for k which should help us to arrive at 16 when added in the end(since we have 16 in answer)
so lets quickly check how this could be done :

Let k=4 ;then (k+8)+1= 4+8+1=13 => P=3 and 1 will be carried to next 8+1+k=9+4=13 => Wrong (we want total to be 16)

Let k=7 ; then k+8+1=16 =>P=6 1 will be carried to next 8+1+k=8+7+1=16 => correct (we want total to be 16) .

Henece, P = 6.

The steps might seem to be time consuming,but belive me once you start calculating yourself this would be a cake walk and will not
take much of your time.

Confused! Does anybody explain better.

Substitution technique means essntially trial and error here.
Out of 5 answer choices lets say P= 6 that is the answer choice A)
so the equation stabds as
8k8
k88
------
1666

now 8+8=16 so carry over is 1
now clearly k has to be 7 to make it 6 at the decimal place (7+8+1) =16
carry over is 1. so in the hudred place (8+ 7+1) = 16
which gives us the result 1666 which is correct
so p is 7
hope this clarifies