Is the integer y a multiple of 4?
(1) 3(y^2) is a multiple of 18.
(2) y = p/q, where p is a multiple of 12 and q is a multiple of 3.
I. DVY NO SINFO (Acronym I use for Data Sufficiency. DVY NO = Determine Value, Yes/No. S = Simplify. Info = What information is needed?)
II. Solve for Statements 1 and Statements 2.
I. Yes/No. Simplify: Is y/4 an integer? Info: y value.
II.
- St. 1: 3(y^2) is a multiple of 18.
y^2 = multiple of 6.
if y^2 = 6, then y = 6^(1/2) ---> y/4 is not an integer.
if y^2 = 12, then y = 12^(1/2)---> y/4 is not an integer.
if y^2 = 18, then y = 18^(1/2)---> y/4 is not an integer.
Last step: Use multiples of both 6 & 4 and work backwards.
if y = 12, then y^2 = 144 ---> y^2 is a multiple of 6 and y/4 is an integer.
if y = 24, then y^2 = 576 ---> y^2 is a multiple of 6 and y/4 is an integer.
St. 1: Insufficient. Choices A & D are eliminated. Options B, C, and E remain.
- St. 2: y = p/q, where p is a multiple of 12 and q is a multiple of 3.
B = any integer
p = B * 3 * 4 ---> p is a multiple of 12
C = any integer
q = C * 3 ---> q is a multiple of 3
Let's say B = 2, C = 1:
y = (2 * 3 * 4)/(1 * 3 ) = 2 * 4. Divisible by 4.
Let's say B = 2, C = 3:
y = (2 * 3 * 4)/(3 * 3 ) = (2 * 4)/3. Not divisible by 4.
St. 2: Insufficient. B is eliminated. Options C & E remain.
- St. 1 & St. 2 Together:
Here I was going with the guess that the answer is E because both statements have numbers that are and are not divisible by 4. Is this a correct assumption? Is this assumption valid for other Yes/No Data Sufficiency problems as well (i.e., if St. 1 has yes & no answers and if St. 2 has yes & no answers, I can assume that St. 1 & St. 2 together will also have yes & no answers therefore the answer is E.)?
Also, is there a faster way to solve this problem than plugging in numbers?
I appreciate any help provided.
(1) 3(y^2) is a multiple of 18.
(2) y = p/q, where p is a multiple of 12 and q is a multiple of 3.
I. DVY NO SINFO (Acronym I use for Data Sufficiency. DVY NO = Determine Value, Yes/No. S = Simplify. Info = What information is needed?)
II. Solve for Statements 1 and Statements 2.
I. Yes/No. Simplify: Is y/4 an integer? Info: y value.
II.
- St. 1: 3(y^2) is a multiple of 18.
y^2 = multiple of 6.
if y^2 = 6, then y = 6^(1/2) ---> y/4 is not an integer.
if y^2 = 12, then y = 12^(1/2)---> y/4 is not an integer.
if y^2 = 18, then y = 18^(1/2)---> y/4 is not an integer.
Last step: Use multiples of both 6 & 4 and work backwards.
if y = 12, then y^2 = 144 ---> y^2 is a multiple of 6 and y/4 is an integer.
if y = 24, then y^2 = 576 ---> y^2 is a multiple of 6 and y/4 is an integer.
St. 1: Insufficient. Choices A & D are eliminated. Options B, C, and E remain.
- St. 2: y = p/q, where p is a multiple of 12 and q is a multiple of 3.
B = any integer
p = B * 3 * 4 ---> p is a multiple of 12
C = any integer
q = C * 3 ---> q is a multiple of 3
Let's say B = 2, C = 1:
y = (2 * 3 * 4)/(1 * 3 ) = 2 * 4. Divisible by 4.
Let's say B = 2, C = 3:
y = (2 * 3 * 4)/(3 * 3 ) = (2 * 4)/3. Not divisible by 4.
St. 2: Insufficient. B is eliminated. Options C & E remain.
- St. 1 & St. 2 Together:
Here I was going with the guess that the answer is E because both statements have numbers that are and are not divisible by 4. Is this a correct assumption? Is this assumption valid for other Yes/No Data Sufficiency problems as well (i.e., if St. 1 has yes & no answers and if St. 2 has yes & no answers, I can assume that St. 1 & St. 2 together will also have yes & no answers therefore the answer is E.)?
Also, is there a faster way to solve this problem than plugging in numbers?
I appreciate any help provided.
