highly intellectual query!

Question

hey guys,

having trouble with a pretty complicated non-GMAT question here, but i figured trying to resolve it will be quite beneficial to the GMAT-preppers as well.

basically here's the situation: we have a standard playing deck of cards (52 total). Uncle Sam randomly picks out 2 cards from this deck, and we need to guess which ones they are. In order to make this guess, we're allowed to ask Uncle Sam two (and only two) questions, which can be pretty open-ended (except, of coz, for "which cards did u pick?").

now, which 2 questions can you come up with, having answers for which will allow you to guess the two missing cards?

let the intellectual flares begin!

kzslacker · Answer

from my side methinks we should start by assigning each card in the deck a standard numerical value (i.e. A=1, then all numbers 2 thru 10, J=11, Q=12, K=13). then we can ask Uncle Sam smth along the lines of what is the mathematical product of the two missing cards?
if the answer is smth like "1" thru "14", "18", "22", "26", "30", etc, you can make out the values of the two missing cards right away, you just need to figure out the suits now.
if the answer is smth like "24", "36", "48", etc, you're a lil more screwed - there are more number variations here.

am i on the right track here? there's gotta be a way to figure out the suits/number sets out of here with just one more question...

bagrettin · Answer

Is the answer for the question could be only "yes" and "no"?
Following your logic, we could just ask what is the sum and the difference of the numerical values of the two missing cards and then we could solve the system
x+y=a
x-y=b

May be you should specify the question more precisely.

gmatprep12 · Answer

Well, if I had to ask, 1) Whats the Suite? like Spade,heart 2) Whats the remainder when you divide by 13

bholakc · Answer

.....Guys Whats an official answer?

KarishmaB · Answer

Kudos for your second question.

viks4gmat · Answer

i'll hand you a kudos for that cheeky question :-)

, which by the way mathematically does make a lot of sense in identifying the card

soods26 · Answer

if you ask the remainder when divided by 13, you are asking for both the numbers. The same is the case with the colour, so basically you are asking 4 questions.

RuslanMRF · Answer

Can't understand why does it make sense to divide exactly by 13?

KarishmaB · Answer

There are 13 distinct number cards from 1 to 13 (A - 1, 2, 3 ... J - 11, Q - 12 and K - 13)
You divide by 13 because each one of these numbers will give a different remainder when divided by 13.
1/13 gives remainder 1.
2/13 gives remainder 2.
.
.
.
13/13 gives remainder 0.

RuslanMRF · Answer

VeritasPrepKarishma Thanks

highly intellectual query!

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