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26 Jun 2018, 05:51
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
68% (01:08) correct
32%
(01:25)
wrong
based on 192
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If x is a positive integer, is \(\frac{x}{21}\) an integer?
(1) \(\frac{4x}{21}\) is an integer.
(2) \(\frac{12x}{21}\) is an integer.
(1) \(\frac{4x}{21}\) is an integer.
(2) \(\frac{12x}{21}\) is an integer.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
26 Jun 2018, 06:12
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Bunuel
Factorize 21, we get 3 * 7. So the numerator x should have at-least one 3 and one 7 then\(\frac{x}{21}\)will be an integer.
Option 1 :
\(\frac{4x}{21}\) --> 4 = \(2^2.\)
For \(\frac{4x}{21}\)to be an integer, x should have at-least one 3 and one 7.
So, \(\frac{x}{21}\) is an integer. Option 1 satisfies.
Possible answer: A or D
Option 2:
\(\frac{12x}{21}\) ------> 12 = \(2^2 * 3\).
Here we already have 3, so \(x = 7\) will make \(\frac{12x}{21}\) a integer.
But x=7, doesn't make \frac{x}{21} a integer. So definite NO.
We need to prove definite YES.
\(\frac{12x}{21}\)------> \(x = 21\) , will make \(\frac{12x}{21}\)an integer
So, x/21 is also an integer for x=21. So definite YES.
Only answer is A.
26 Jun 2018, 07:21
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Solution
Given:
- • x is a positive integer
To find:
- • is \(\frac{x}{21}\) an integer
Analysing Statement 1
- • As per the information given in statement 1, \(\frac{4x}{21}\) is an integer
• As 4 and 21 are co-prime to each other, x must be divisible by 21
- o Therefore, \(\frac{x}{21}\) must be an integer
Hence, statement 1 is sufficient to answer
Analysing Statement 2
- • As per the information given in statement 2, \(\frac{12x}{21}\) is an integer
• The numbers 12 and 21 are not co-prime to each other, hence, we can’t say whether x is divisible by 21 or not
Hence, statement 2 is not sufficient to answer
Hence, the correct answer is option A.
Answer: A
