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23 May 2019, 02:10
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A
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Difficulty:
35%
(medium)
Question Stats:
69% (01:29) correct
31%
(01:23)
wrong
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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
M37-49
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
M37-49
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26 Nov 2021, 02:47
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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
General Discussion
23 May 2019, 02:24
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Bunuel
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
