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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (01:56) correct
46%
(02:23)
wrong
based on 189
sessions
History
Date
Time
Result
Not Attempted Yet
A house has \(x\) cakes and \(y\) people, with \(x\geq{2}\) and \(y\geq{1}\). How many values of \(y\) are there, such that all the cakes can be distributed among the people, with each receiving an equal number and none left over?
(1) \(x = a^2\)\(b^3\), where a and b are distinct primes.
(2) \(b = a+1\), where a and b are distinct primes.
(1) \(x = a^2\)\(b^3\), where a and b are distinct primes.
(2) \(b = a+1\), where a and b are distinct primes.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
01 May 2020, 22:42
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HI Cellchat
Are you sure that you have posted a complete question with correct OA?
Cause the question has not defined what are a and b and in absence of this information, the question can NOT have answer Option A
The question must mention that a and b are prime numbers for x to have unit number of factors (i.e. possible values of y)
Question: How many values of y exist such that y is a divisor of x i.e. y is a factor of x?
After combining the statements
e.g. If x = 2^2*3^3 then the total factors of x i.e. total possible values of y will be (2+1)*(3+1) = 12
BUT
e.g. If x = 4^2*5^3 = 2^4*5^3 then the total factors of x i.e. total possible values of y will be (4+1)*(3+1) = 20
So with the given input the answer of question should be Option E
02 May 2020, 11:40
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Given: A house has \(x\) cakes and \(y\) people, with \(x\geq{2}\) and \(y\geq{1}\).
Asked: How many values of \(y\) are there, such that all the cakes can be distributed among the people, with each receiving an equal number and none left over?
y must be a factor of x.
(1) \(x = a^2\)\(b^3\), where a and b are distinct primes.
Number of factors of x = 3*4 = 12
Number of values of y such that all the cakes can be distributed among the people, with each receiving an equal number and none left over = 12
SUFFICIENT
(2) \(b = a+1\), where a and b are distinct primes.
Since there is no relation provided between x & y
NOT SUFFICIENT
IMO A
