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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
If x and y are positive numbers, is x/y an integer?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:27) correct 27% (01:23) wrong based on 55 sessions

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GMATBusters’ Quant Quiz Question -6

If x and y are positive numbers, is x/y an integer?
1) 2x is divisible by y
2) x is divisible by 2y

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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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1) if x = 3, y =2. 2x is divisible by y but x/y is not an integer.
if x = 6, y =2. 2x is divisible by y but x/y is an integer.
Hence NOT SUFFICIENT

2) x/2y = Integer, Hence x/y = 2*Integer = integer
SUFFICIENT

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Senior Manager  P
Joined: 31 May 2017
Posts: 412
Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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If x and y are positive numbers, is x/y an integer?
1) 2x is divisible by y
2) x is divisible by 2y

A) 2x is divisible by y
1)If X=0.1 and Y=0.2, then X/Y is integer.
2)If X=9, Y=2, then X/Y = 4.5 which is not an integer.

B) X is divisible by 2y.
If X is divisible by 2y, then X/Y is always integer. Option B is sufficient.

Ans B
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Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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1) if x=2 and y=4, then 2x/y=1, which is an integer. However, x/y=1/2 is not an integer.
if x=4 and y=4, then 2x/y=2, which is an integer. Likewise, x/y=1 is an integer.
Clearly this statement is not sufficient.
2) x/(2y)=k, where k is a positive integer. It follows that x/y=2k which is also an integer as k is an integer.
Clearly this statement is sufficient.
Intern  B
Joined: 20 Sep 2015
Posts: 27
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Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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Qs: is x/y an integer?

given : x and y are positive numbers.

1) 2x is divisible by y

2x/y = integer i.e. 2x = y * integer= integer as x, y are positive integer.

consider cases, if x =3, y =2 then 2x/y= 2*3/2= 3= integer but x/y = 3/2 is not integer. not satisfying the condition
if x= 6, y= 2, then 2x/y = 2*6/2 = integer and x/y = 6/2 = integer. satisfying the condition.
as there are two case possible in this condition, it is not sufficient to answer the question.

2) x is divisible by 2y
x/2y= integer i.e x/y= 2*integer= Integer'
It is given that x is a multiple of y, So always the x/y will be the integer. hence sufficient condition.

Manager  S
Joined: 05 May 2016
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Location: India
Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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Statement 1: 2x is divisible by y

lets x=4, y =2,in this case yes, x/y is an integer, but what if, x=3, y=2, 2x is still divisible by y but x/y is not an integer. So Statement 1 is Insufficient.

Statement 2: x is divisible by 2y

In this case, x has to be a multiple of 2 and y both otherwise the statement will not hold true, so x/y will always be an integer either +ve or -ve.
So Sufficient.

GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6333
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: If x and y are positive numbers, is x/y an integer?  [#permalink]

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1
#1
2x is divisible by y
we can have ; x= 1 and y = 2 ; so NO
and x= 4 and y = 4 ; so yes ; insufficient
#2
x is divisible by 2y

x has to be factor of 2 *y ; and x has to be even always
x=2 , y = 1 ; yes
x=4 , y = 2 ;yes
x = 6 , y = 3 , yes
sufficient
IMO B

If x and y are positive numbers, is x/y an integer?
1) 2x is divisible by y
2) x is divisible by 2y Re: If x and y are positive numbers, is x/y an integer?   [#permalink] 02 Feb 2020, 01:04

# If x and y are positive numbers, is x/y an integer?  