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25 Jun 2019, 09:41
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A
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Difficulty:
75%
(hard)
Question Stats:
37% (01:38) correct
63%
(02:34)
wrong
based on 54
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At a particular moment, a restaurant has x biscuits and y patron(s), with x≥2 and y≥1. How many values of y are there, such that all the biscuits can be distributed among the patrons, with each patron receiving an equal number of whole biscuits and with no biscuits left over?
(1) x=a^2b^3, where a and b are different prime numbers
(2) b=a+1
(1) x=a^2b^3, where a and b are different prime numbers
(2) b=a+1
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25 Jun 2019, 10:27
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Statement 1- We can find the number of factors of x. Number of values y can take is equal to number of factors of x.
Sufficient
Statement 2- we have no clue about a and b.
Insufficient
Posted from my mobile device
Sufficient
Statement 2- we have no clue about a and b.
Insufficient
Posted from my mobile device
25 Jun 2019, 10:32
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In general, it makes no logical sense to ask a DS question in this way. If a DS question tells you "there are y patrons", then y represents a single (unknown) value. They can't ask how many values of y are possible, because the answer is automatically "one". It's easy to see why this question format is illogical with a simpler example question:
If y is a positive integer, how many values of y are possible?
1. 3 < y < 10
2. y < 6
There is no "right answer" to this question, because the question setup makes no sense.
So logically, the answer to the original question should be D no matter what the statements say: as the question tells us, there is one value for y, we just don't know what it is. They mean for the question to say something different: How many positive divisors does the positive integer x have? If that's the question, Statement 1 is sufficient, because Statement 1 gives us the prime factorization of x. From any prime factorization, you can count a number's divisors (add 1 to each exponent, and multiply what you get, so in this question x would have 3*4 = 12 divisors). Statement 2 clearly is not sufficient, so the answer is A.
If y is a positive integer, how many values of y are possible?
1. 3 < y < 10
2. y < 6
There is no "right answer" to this question, because the question setup makes no sense.
So logically, the answer to the original question should be D no matter what the statements say: as the question tells us, there is one value for y, we just don't know what it is. They mean for the question to say something different: How many positive divisors does the positive integer x have? If that's the question, Statement 1 is sufficient, because Statement 1 gives us the prime factorization of x. From any prime factorization, you can count a number's divisors (add 1 to each exponent, and multiply what you get, so in this question x would have 3*4 = 12 divisors). Statement 2 clearly is not sufficient, so the answer is A.
