Hi Srivatsva,

I think the answer is D.)

The sum of numbers from 1 to 9 = 9 * 10/2 = 45 --- (1)

#1 Sum of remaining numbers units digit = 6
so, we'll have 45*3 = 135 for 3 sets of cards from which we hadn't remove any card. We are actually removing it from 4th set of 9 cards.

Hence, 135 + xx=xx6 for the units digit to be 6 we need to add a number that will return units digit of 6. That number xx must definitely end with 1. So assuming that if you remove 1 from the numbers 1 to 9 you'll have the sum of the rest 8 numbers to be 44. So 135 + 44 <>6 so the number has to be other than 1..Just plugging value would give you the number to be 4.

If you remove 4 the sum of the rest of the numbers will be 41 and hence 135 + 41 = xx6

Hence A is sufficient.

#2 The sum of the remaining 35 cards is 45*3=135 (for 3 sets of cards) + 4th set = 176.

135 + xx=176 so xx=41 and hence the number has to be 4

Hence B is sufficient.

So answer is D.)

-Deepak

yes D

1) sum of the digits of all 36 cards; 4*(1+2+....9)=4*9*10/2=180
let x be the number removed
sum of the digits of the remaining 35 cards has 6 as the units digit
this can happen only if 4 was removed (180-x=ab6)
sufficient


2) sum of digits of 36 cards: 180
sum of digits of 35 cards: 176
=> card removed: 180-176=4
sufficient

hence, D

[quote="DeepakR"]Hi Srivatsva,

I think the answer is D.)

The sum of numbers from 1 to 9 = 9 * 10/2 = 45 --- (1)

#1 Sum of remaining numbers units digit = 6
so, we'll have 45*3 = 135 for 3 sets of cards from which we hadn't remove any card. We are actually removing it from 4th set of 9 cards.

Hence, 135 + xx=xx6 for the units digit to be 6 we need to add a number that will return units digit of 6. That number xx must definitely end with 1. So assuming that if you remove 1 from the numbers 1 to 9 you'll have the sum of the rest 8 numbers to be 44. So 135 + 44 <>6 so the number has to be other than 1..Just plugging value would give you the number to be 4.

If you remove 4 the sum of the rest of the numbers will be 41 and hence 135 + 41 = xx6

Hence A is sufficient.

#2 The sum of the remaining 35 cards is 45*3=135 (for 3 sets of cards) + 4th set = 176.

135 + xx=176 so xx=41 and hence the number has to be 4

Hence B is sufficient.

So answer is D.)

-Deepak[/quote]

Thanks Bro..OA is D

I could be wrong, but logic alone is sufficient to answer this question.

1st Statement) When you subtract any number between 0 and 9 from another digit between 0 and 9, you know it will always be a distinct integer. For example lets say that the units digit of the remaining numbers is 8. The sum of the numbers has a certain unit digit, lets say 9. Subtracting 1 is the only way to get the units digit to 8. Any other digit will produce a different units digits.

Same logic can be applied to second statement.

I probably did not explain this well, but im quite sure that this problem does not require actually figuring out the answer.

Opinions?