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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1786
WE: General Management (Education)
If y/x = 3, Is x a factor of y?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 44% (01:38) correct 56% (01:11) wrong based on 27 sessions

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GMATBusters’ Quant Quiz Question -4

If y/x = 3, Is x a factor of y?
1) x is even
2) x > 0

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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1786
WE: General Management (Education)
Re: If y/x = 3, Is x a factor of y?  [#permalink]

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The Official Solution is as follows: Attachment: WhatsApp Image 2020-02-03 at 6.49.55 PM (3).jpeg [ 60.88 KiB | Viewed 247 times ]

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Re: If y/x = 3, Is x a factor of y?  [#permalink]

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If y/x = 3, Is x a factor of y?

1) x is even
2) x > 0

Given: y/x = 3 , y=3x

A) X is even
If x is 2 , then y=3x , substitute x in the equation and we get y = 3(2) , y = 6. This give x is a factor of y.
If x is 0.4, then y=3(0.4), y = 1.2 , This also gives X (0.4) is a factor of Y (1.2)

Option A is sufficient.

B) x > 0
This says X is a non negative number. We have already considered an even number x=2 in option A. Even if we consider X as negative number, X is a factor of Y.

Option B is sufficient.

Ans: D
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Re: If y/x = 3, Is x a factor of y?  [#permalink]

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Qs : Is x a factor of y?

given :
as y/x= 3 i.e. y= 3x,
y could be = 3, 6, 9, 12, 15, 18....

1) x is even

as x is even so
x = 2, 4, 6,
and y= 6, 12, 18,...
we see that x is always a factor of y , y/x = integer. hence sufficient to answer.

2) x > 0
in statement, no information is given whether x is integer or fraction. if it is integer then above case may be valid but in case of fraction it may not be the case.
consider x= 1/3, so y= 3 x 1/3= 1
but 1/3 is not a factor of 1 hence it not always true. not sufficient condition.

Intern  B
Joined: 17 Aug 2019
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If y/x = 3, Is x a factor of y?  [#permalink]

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All wee need to know to answer this question is whether x is a non-zero integer. From y/x we know that x is different from 0, so all there is to know is whether x is an integer. .
1) It says that x is even, and; therefore, an integer.
Clearly, this statement is sufficient.
2) Here x is a non-zero number but it does not specify whether x is an integer or not.
Clearly, this statement is insufficient.

Originally posted by AndreV on 01 Feb 2020, 20:08.
Last edited by AndreV on 03 Feb 2020, 12:47, edited 2 times in total.
VP  V
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GMAT 1: 600 Q46 V27 Re: If y/x = 3, Is x a factor of y?  [#permalink]

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Given : y/x=3

Is x a factor of y? Y/N

Let's consider cases before going for statements.
y=6 x=2 Obvious case.
y=3 x=1
y=-3 x=-1
y=1 x=1/3
y=12 x=4
y=-6 x=-2

Statement 1) x is even
Sufficient. From all the examples above. Fractions cannot be even. So that cannot be the case.

Statement 2) x > 0

y=1 x=1/3 - No
y=12 x=4 - Yes

Sufficient.

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Manager  S
Joined: 05 May 2016
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Location: India
Re: If y/x = 3, Is x a factor of y?  [#permalink]

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Statement 1: x is even

Since x is an integer and for y/x to be x has to be an factor y. 24/8 or 12/4. Either +ve or -ve, x will be a factor of y.

Sufficient.

Statement 2: x > 0.

If x is 1/2 the 2y = 3, so x doesn't necessarily be a a factor of y for x/y to be = to 3. and also any of the cases above, so Insufficient.

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Re: If y/x = 3, Is x a factor of y?  [#permalink]

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If y/x = 3, Is x a factor of y?
1) x is even
2) x > 0

#1
x is even ; so value of y would have to be a factor of x ; eg 6/2 ; 18/6 ; 12/4 ; sufficient
#2
x>0
not necessarily sufficient
as y =1 and x = 1/3 ; or any integer value of x & y
insufficient
IMO A
Senior Manager  P
Joined: 09 Jan 2017
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Re: If y/x = 3, Is x a factor of y?  [#permalink]

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IMO Option D.
Rewriting the statement:-

If y/x = 3, Is x a factor of y?
1) x is even
2) x > 0

y=3x
1>X even - X is a factor of Y - Sufficient
2> X>0 - X even or odd - X is a factor of Y - Sufficeint Re: If y/x = 3, Is x a factor of y?   [#permalink] 02 Feb 2020, 05:55

# If y/x = 3, Is x a factor of y?  