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

Question

A bowl is filled with consecutively numbered tiles from 1 to x. Joe pulls out a tile and uses it to construct Sequence Q, which consists of 10 consecutive integers starting with the number drawn. If Joe then selects one number from Sequence Q, what is the probability that the selected number is a multiple of 3?

(1) The last number in Sequence Q is a prime number that is less than 20.
(2) x <= 10

(1) The last number in Sequence Q is a prime number that is less than 20.
(2) x <= 10

ian7777 · Accepted Answer

My answer is A.

We're looking for the number of multiples of three in a list of 10 consecutive numbers. If the list starts with a multiple of three, it will end with a multiple of three, and there will be 4 multiples in the list, making the probability 4/10. If it starts with any other number, the list will have exactly 3 multiples of 3, and the probability will be 3/10. Try a few and you'll see it.

So the question is just to figure out what it starts and ends with.

1) says that the last number is a prime number less than 20. That means it's not a multiple of 3, so there can't be 4 multiples, but there must be 3 multiples. --> sufficient.

2) says the first number is less than or equal to 10. Since that can be anything, multiple of 3 or not, we cannot know --> Insufficient.

mallelac · Answer

I think it is B.

(1)If Q is less than 20 and a prime number too, then Q can be 19,17,13,11 etc. This gives us different probabilities because of multiples of 3 vary depending on the last prime number.

(2) If x <= 10, then because the sequence consists of 10 integers, it should be between 1 and 10. It has 3,6,9 as multiples of 3. The probability is C(3,1) / C(10,1) = 3/10

What is OA?

mallelac · Answer

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?

crackgmat750 · Answer

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

ian7777 · Answer

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?

mallelac · Answer

Yes Ian, it makes sense now. 8-)

Shrivathsan · Answer

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

exc4libur · 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)

freyamehta · Answer

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

KarishmaB · Answer

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)

Sks0106 · Answer

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.

mSKR · Answer

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

IanStewart · Answer

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

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