A bowl is filled with consecutively numbered tiles from 1 to x. Joe

Ian,

Is not D in that case?

(1)What you say is correct as for 1.

(2)If x <= 10 and the sequence consists of 10 tiles, then x = 10 because if x <10, the sequence of 10 tiles cannot be constructed. It means the probability is certain again with 3/10.

Thus both individually suffice to get the answer. Is it not D then?

Exactly..that's what I feel and think answer should be D. But the answer given is A.

No, it's A. You're reading the question wrong. x is the last number is the bowl that this dude is pulling his numbers out of. But once he pulls out the first number, Q is built by finding the next 9 consecutive numbers.

So if guy pulls out a 3, then Q will be 3,4,5,6,7,8,9,10,11,12. If he pulls out a 5, Q will be 5,6,7,8,9,10,11,12,13,14.

So x doesn't have to do with the number of numbers in Q, nor is it the last number in Q. It's actually the highest limit of what the first number of Q could be.

Does that make sense?

Yes Ian, it makes sense now.

Actually for the second statement ...
(2) x <= 10

consider x =10 and i pick up 3 - 3,4,5,6,7,8,9,10,11,12 - i have 4 multiples of 3 (3,6,9,12) -prob - 4/10
Consider i pick 4 - 4,5,6,7,8,9,10,11,12,13 - i have 3 multiples of 3(6,9,12)- prob -3/10

since there are 2 results ..A is the answer

numbered tiles: {1,2,3,4,…x}
sequence Q: {a,a+1,a+2…a+9}

(1) The last number in Sequence Q is a prime number that is less than 20: sufic.
a+9=prime<20={19,17,13,11}; and a={10,8,4,2};
there are only 3 multiples of THREE between each sequence of Q from {10-19}{8-17}{4-13}{2-11};

(2) x≤10: insufic.
if sequence Q is {10…19} it has 3 multiples of THREE {12,15,18}
if sequence Q is {3…12} it has 4 multiples of THREE {3,6,9,12}

Answer (A)

Can one of the experts explain this hard problem?
VeritasKarishma
Bunuel

Note that there are two lists here:


List 1: 1, 2, 3, ... x

List Q - 10 consecutive integers starting with a number picked from list 1

Q has 10 consecutive numbers. How many of these will be multiples of 3? It depends on which number you start Q with. If you start with a multiple of 3 such as say 6, you will take another 9 numbers in which there will be exactly 3 more multiples of 3.
6, 7, 8, 9, 10, 11, 12, 13, 14, 15
So in all 4 multiples. You start and end with a multiple of 3.

If you instead start with a non multiple of 3 (such as 7 or 8), then you will get 3 multiples of 3 in the next 9 numbers so in all 3 multiples. Neither the start nor the end will be a multiple of 3.

So the point is whether the number you pick from list 1 to make Q is a multiple of 3 or not.

(1) The last number in Sequence Q is a prime number that is less than 20.
If the last number of Q is a prime number, it cannot be a multiple of 3 so the number you picked from list 1 was also not a multiple of 3. Hence Q will have exactly 3 multiples of 3.
Hence probability that a number picked up from Q is a multiple of 3 is 3/10.
Sufficient.

(2) x <= 10
Doesn't tell us anything about whether the first number picked for Q is a multiple of 3 or not.
Not sufficient.

Answer (A)

agree with explanation for option A.
However for option B, the question says 'Joe pulls out a tile and uses it to construct Sequence Q, which consists of 10 consecutive integers starting with the number drawn' that means the first number should be 1 and last number should be 10 else the sequence cannot be 10 elements.
On that basis, i think answer should be D.
Happy to take other's views.

Q is less than x
sequene is q,q+1,q+2 ,,,,
but for B we have no information about q.Hence not sufficient
sequqnce can be : 4,5,6,7,8 ( if x= 8 and q=4) ; probability = 1/5
if sequene = 3,4,5,6,7,8,9 ( if x= 9 and q=3 ) ;probability = 3/7
not sufficient

I think the question means that Joe is pulling out a tile, which has some number on it between 1 and x, and then whatever number is on the tile becomes the smallest number in the sequence Q. So if x is 8, say, then Joe could pull out a tile with any whole number on it between 1 and 8, and the sequence would start there -- it doesn't need to start from 1.

That said, the question is improperly framed, and you could never see something quite like it on the GMAT, because it's not clear what probability the question is even asking about. Joe is doing two things that are potentially random: picking a tile to start the sequence, then picking a number from the sequence. So what probability are we even measuring? The probability before he even picks a tile, or the probability once he has settled on his sequence? From Statement 1, we can deduce the intention: it's the probability once he has decided on the sequence. But we need to know what question we're answering from the question stem, not from one of the two statements. So it's not a good question.

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