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Math Expert V
Joined: 02 Sep 2009
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If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 67% (01:25) correct 33% (01:19) wrong based on 91 sessions

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FRESH GMAT CLUB TESTS QUESTION

If positive integer x is divisible by 330, x must be divisible by which of the following?

I. x/330
II. 330 - x
III. 330 + x

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

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Re: If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

If positive integer x is divisible by 330, x must be divisible by which of the following?

I. x/330
II. 330 - x
III. 330 + x

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

X=330Q

II 330-x= 330-330Q= 330(1-Q). Not sure is it can perfectly divide X
III 330+x=330 + 330Q= 330(1+Q). Not sure is it can perfectly divide X

I x/(x/330) = 330. X is perfectly divisible by the given expression. Only I
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Director  P
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Posts: 502
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Re: If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Question asks if x/(I, II or III) = integer and given x=330a where a is any positive integer

$$\frac{x}{x/330}$$ is always 330

I is always true

II is true if a>1, not true if a=1

In case of III, numerator<denominator and so not divisible

Therefore only I is true

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Re: If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

If positive integer x is divisible by 330, x must be divisible by which of the following?

I. x/330
II. 330 - x
III. 330 + x

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

we can simply take some value and check for options
upon doing calculation only option A stands valid..
Director  P
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Location: United States
Re: If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

If positive integer x is divisible by 330, x must be divisible by which of the following?

I. x/330
II. 330 - x
III. 330 + x

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

x=m330

I. x/330: x/(x/330)…x330/x=330

II. 330 - x: x/330-x…m330/(330-m330)…330m/(330(1-m))=m/(1-m)

III. 330 + x: x/330+x…m330/(330+m330)…330m/(330(1+m))=m/(1+m)

Ans A
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Re: If positive integer x is divisible by 330, x must be divisible by whic  [#permalink]

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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

If positive integer x is divisible by 330, x must be divisible by which of the following?

I. x/330
II. 330 - x
III. 330 + x

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Asked: If positive integer x is divisible by 330, x must be divisible by which of the following?

x=330k where k is an integer

I. x/330
x/330 = k; x=330k is divisible byk
MUST BE TRUE
II. 330 - x
330 - x = 330 - 330k = 330(1-k); x may not be divisible by (1-k)
COULD BE TRUE
III. 330 + x
330 + x = 330 + 330k = 330(1+k); x may not be divisible by (k+1)
COULD BE TRUE

IMO A
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E-mail : kinshook.chaturvedi@gmail.com Re: If positive integer x is divisible by 330, x must be divisible by whic   [#permalink] 08 Nov 2019, 09:12
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