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03 Feb 2020, 05:01
Kudos
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E
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:
70% (01:01) correct
30%
(00:58)
wrong
based on 129
sessions
History
Date
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Not Attempted Yet
What is the value of the integer r ?
(1) The only prime factors of r are 3 and 7.
(2) Each of the integers 3, 7, and 21 are factors of r.
(1) The only prime factors of r are 3 and 7.
(2) Each of the integers 3, 7, and 21 are factors of r.
03 Feb 2020, 05:20
Kudos
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Using both Statements, r could be 3*7 = 21, or r could be 3^100 * 7^100, say, so the answer is E.
03 Feb 2020, 05:35
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Bunuel
Solution:
- \(r\) is an integer.
- \(r =3^a *7^b\), where \(a\) and \(b\) are integers.
Here, we don’t know the value of \(a\) and \(b\), we can’t find the value of \(r\).
Statement 2:
- \(\frac{r}{3}, \frac{r}{7},\) and \(\frac{r}{21}\) are integers.
- If \(r = 21,\) then \(3, 7,\) and \(21\) are factors of \(r\).
If \(r = 42,\) then \(3, 7,\) and \(21\) are factors of \(r\).
Hence, statement 2 is also not sufficient, we can eliminate the answer options B.
By combining the statements:
From statement 1:\( r =3^a*7^b\)
From statement 2: \(3, 7,\) and \(21\) are factors of \(r\).
By combining the statements also, we can’t infer anything.
- If \(r= 21\), then both the statements are satisfied.
If \(r = 63,\) then also both the statements are satisfied.
