Set 2: # 20 --> A collection of 36 cards

[apoorva.srivastva]

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.


Could not comprehend the statements>>>Please help!!

[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

[scoobydooby]

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

[apoorva.srivastva]

[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

[mike22629]

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?