If x and y are positive integers and 18 is a multiple of x*y^2, what

Question

If x and y are positive integers and 18 is a multiple of x*y^2, what is the value of y?

(1) x is a factor of 54 and is less than half of 54.
(2) y is a multiple of 3

GMATinsight · Answer

Question : what is the value of y?

Given:  18=2*3^2  is a multiple of  x*y^2 
i.e. Case1: x may be 2 and y may be 3 OR
Case2: x may be 18 and y may be 1

Statement 1 : x is a factor of 54 and is less than half of 54. 
i.e. x ≤27 and factor of 54
but as per cases mentioned above x may be 2 or 18 hence y may be 3 or 1 hence
NOT SUFFICIENT

Statement 2 : y is a multiple of 3 
i.e. y must be 3 (as per case 2)
SUFFICIENT

Answer: Option B

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • x and y are positive integers.
 o So,  y^2  must be a perfect square. 
• 18 is a multiple of  x*y^2 
 o  18 = k*x*y^2  where k is a positive integer. 
• Now, positive factors of 18 = 1, 2, 3, 6, 9 and 18
 o Perfect squares which are factors of 18 = 1 and 9
  So,  y^2  can be either 1 or 9
  Or, y can be either 1 or 3   
• We need to find the value of y and we can figure out the value of y in either of the following two ways:
 o if we can directly find out whether y is 1 or 3.
o Or, if we can determine  k*x

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:   x is a factor of 54 and is less than half of 54. 
• x is a factor of 54 and x < 54/2 or x < 27
  o So, there are more than one values possible for x. For example:
  x can be 1, in that case k could be 2 and hence  y = 3 
 x can also be 2, in that case k could be 9 and hence  y = 1 
 Also, x can be 9, in that case k could be 2 and hence  y = 1    
Since multiple possibilities exists for the value of  k*x  where y can either be 1 or 3, so we won't be able to determine the exact value of y from this statement.
Hence, statement 1 is not sufficient and we can eliminate answer options A and D
 Statement 2:   y is a multiple of 3 
 • Out of 1 and 3 only 3 is a multiple of 3.
 o Hence, y is 3  
Thus, the correct answer is  Option B.

If x and y are positive integers and 18 is a multiple of x*y^2, what

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GMAT Data Sufficiency (DS) Questions

If x and y are positive integers and 18 is a multiple of x*y^2, what

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