If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠1
(2) x + 2 is a multiple of y.
IMO: E
(1) y ≠1
(2) x + 2 is a multiple of y.
IMO: E
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Is y=2?
Source: Beat The GMAT — Data Sufficiency |
To prove: y =2
Stmt 1: y ≠1. y can take any value for different x for which x mod y = 0 will be satisfied. INSUFFICIENT.
Stmt 2: (x+2) mod y = 0.
x mod y + 2 mod y = 0
0 + 2 mod y = 0 (Given x mod y = 0)
2 mod y = 0
That means y can be either 1 or 2 for which 2 mod y = 0 will be satisfied. INSUFFICIENT.
Stmt 1 and Stmt 2 combined:
From Stmt 1, y ≠1
From Stmt 2, y = 1 or y = 2
Hence together, y = 2.
Ans: C.
What is the OA?
Stmt 1: y ≠1. y can take any value for different x for which x mod y = 0 will be satisfied. INSUFFICIENT.
Stmt 2: (x+2) mod y = 0.
x mod y + 2 mod y = 0
0 + 2 mod y = 0 (Given x mod y = 0)
2 mod y = 0
That means y can be either 1 or 2 for which 2 mod y = 0 will be satisfied. INSUFFICIENT.
Stmt 1 and Stmt 2 combined:
From Stmt 1, y ≠1
From Stmt 2, y = 1 or y = 2
Hence together, y = 2.
Ans: C.
What is the OA?
Swati
here the question is about factors and multiples and you ultimately need to know whether y always = 2.
first statement does nothing to clarify - x coud be 6 and y=3 or x could be 4 and y = 2
Insufficient
Second statement brings up the idea of factoring with addition. if x is a multiple of y then that means that y divides evenly into x. however if x + 2 is also divisible by y then that means that y is a factor of 2 because if x divides evenly and x+2 divides evenly then that means that 2 must be a multiple of y. HOwever this still doen't answer our quesiton because y could equal 1 or 2.
When you put both pieces of information together you find that y must be 1 or 2 and it can't be 1. Therefore y must equal 2. the answer is C. (This answer might be different if they didn't define y as an integer)
first statement does nothing to clarify - x coud be 6 and y=3 or x could be 4 and y = 2
Insufficient
Second statement brings up the idea of factoring with addition. if x is a multiple of y then that means that y divides evenly into x. however if x + 2 is also divisible by y then that means that y is a factor of 2 because if x divides evenly and x+2 divides evenly then that means that 2 must be a multiple of y. HOwever this still doen't answer our quesiton because y could equal 1 or 2.
When you put both pieces of information together you find that y must be 1 or 2 and it can't be 1. Therefore y must equal 2. the answer is C. (This answer might be different if they didn't define y as an integer)
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA
Answer should be C and Not E.GmatKiss wrote:If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠1
(2) x + 2 is a multiple of y.
IMO: E
Solution: --
stmt 1: Y NOT = 1 [ Not sufficient]
stmt 2: X+2 is a multiple of Y
now we already know that X is a multiple of y.
and from statment 2 we also know that x+2 is a multiple of y.
Let's put some values
Let Y =2,3,4,5... etc
for Y =2.. X can be anything from 2.... to infinity (all even)
Let X =2 then x+2= 4 which is also a multiple of y.
if x =4 then x+2 = 6 which is also a multiple of y.
This condition will not hold true if we choose any other value of y, say for example y =3
then X can be 3, 6, 9 ..
but then x+2 will no longer be a factor
LOGIC: -- x+2 means a difference of 2.. (table of 2 -- every consecutive number has a common difference of 2)
similarly: table of 3 every consecutive number has a common difference of 3
But for Y =1 this condition will always remain trueHence, stmt 2 is also Not sufficient.
Combine both the statments and we can eliminate Y =1
Therefore only one value of Y will remain and i.e. 2
OPTION C
