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26 Nov 2021, 02:46
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If positive integer \(x\) is divisible by 330, \(x\) must be divisible by which of the following?
I. \(\frac{x}{330}\)
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
I. \(\frac{x}{330}\)
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
26 Nov 2021, 02:46
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Official Solution:
If positive integer \(x\) is divisible by 330, \(x\) must be divisible by which of the following?
I. \(\frac{x}{330}\)
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
Given: \(\frac{x}{330}=integer\)
Check the options:
I. \(\frac{x}{330}\). In this case \(\frac{x}{(\frac{x}{330})}=330=integer\). So, \(x\) must be divisible by \(\frac{x}{330}\).
II. \(330 - x\). In this case \(\frac{x}{330-x}\) is not necessarily an integer. For example, consider \(x=330\). We'd get \(\frac{x}{330-x}=\frac{330}{0}\), which is undefined.
III. \(330 + x\). In this case \(\frac{x}{330+x}\neq integer\) because the denominator is greater than the numerator (\(0 < \frac{x}{330+x} < 1\) ).
Answer: A
If positive integer \(x\) is divisible by 330, \(x\) must be divisible by which of the following?
I. \(\frac{x}{330}\)
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
Given: \(\frac{x}{330}=integer\)
Check the options:
I. \(\frac{x}{330}\). In this case \(\frac{x}{(\frac{x}{330})}=330=integer\). So, \(x\) must be divisible by \(\frac{x}{330}\).
II. \(330 - x\). In this case \(\frac{x}{330-x}\) is not necessarily an integer. For example, consider \(x=330\). We'd get \(\frac{x}{330-x}=\frac{330}{0}\), which is undefined.
III. \(330 + x\). In this case \(\frac{x}{330+x}\neq integer\) because the denominator is greater than the numerator (\(0 < \frac{x}{330+x} < 1\) ).
Answer: A
Iserhard
Joined: 07 Mar 2021
Last visit: 01 Jul 2025
Posts: 8
Given Kudos: 2
Location: Brazil
Schools: IESE '27 (A) Judge '26 (A) IMD'26 (II)
GMAT Focus 1: 605 Q79 V82 DI79 
GPA: 8.4
09 Jan 2025, 00:43
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I did not quite understand the solution. Hello,
I understand that x is an integer, but why the options must be integers also? I chose D.
Example: x = 660. So, 660/(330+660) = 2/3. It's divisible, just not an integer.
Thanks
I understand that x is an integer, but why the options must be integers also? I chose D.
Example: x = 660. So, 660/(330+660) = 2/3. It's divisible, just not an integer.
Thanks
