If x and y are positive integers, is 2x a multiple of y? (1) x is a mu

Question

If x and y are positive integers, is 2x a multiple of y?

(1) x is a multiple of y.
(2) y is a multiple of x.

Jackal · Answer

I will go with (A) not confident though

Let K be an integer
we have 2x=Ky

1. Let M be an integer. 
We have x=My
Multiplying both sides by 2
2x=(2M)y

2. Let L be an integer
We have y=Lx
multiplying both sides by 2
2Lx=2y
2x=(2/L)y
We do not know whether 2/L leaves a zero remainder or not. So could be an integer but not sure.

Please provide original solution. Thank you.

intheend14 · Answer

Just try some numbers--I feel that's the quickest way to solve this.

Statement 1 says that x is a multiple of y--since they're both positive integers, than any multiple of x must be a multiple of y. Sufficient.
Statement 2 says that y is a multiple of x--however, if y/x>2, then no, if y/x<=2, then maybe. For example y=6 and x=2, 2x/y = 4/6, not an integer. But if y = 10 and x = 5, then 2x/y = 1. Insufficient.
Answer is A

vietnammba · Answer

A but Is it some sort of tricky question otherwise its too easy?

kinghyts · Answer

Given, x and y are positive integers

1. x is a multiple of y.
x = n*y

Since x/y = n, thus 2*x/y = 2*n = Integer and therefore 2*x is a multiple of y. Sufficient

2. y is a multiple of x.

y = n * x  
x/y = 1/n and 2*x/y = 2/n

Therefore, 2*x is a multiple of y, only when n = 1 or 2. For other cases, it is not a multiple. Insufficient

A) should be the answer

sanket1991 · Answer

Statement 1) If Y = a*b*c
X = a*b*c*z
hence z can be any integer value 
hence 1 is sufficient

Statement 2
Let X = a*b*c
so Y = a*b*c*z

Z can be any value (2,3,4) and hence statement II is insufficient

Ans. A

amitshri15 · Answer

(1) x is a multiple of y. x= Ky => x/y = k (integer) and 2x/y = 2*integer. hence Sufficient
(2) y is a multiple of x. y = mx => y/x = m (integer) but x/y = 1/m which not necessarily integer. Insufficient.

Answer is A.

82vkgmat · Answer

Answer = A IMO.
1) x is multiple of y --> 2x is multiple of y. SUFFICIENT.
2) y is multiple of x. Simple case y = x, then 2x is multiple of y. y=3x, 2x is NOT multiple of y. NOT SUFFICIENT.

Answer = A.

Give kudos if you like explanation.

Bunuel · Answer

The correct answer is A. Similar question to practice: if-x-and-y-are-positive-integers-is-2x-a-multiple-of-y-25135.html

bumpbot · Answer

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If x and y are positive integers, is 2x a multiple of y? (1) x is a mu

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If x and y are positive integers, is 2x a multiple of y? (1) x is a mu

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