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18 Mar 2020, 09:12
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:58) correct
52%
(02:07)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
If a^5 ≥ −32 and a is an integer, what is the value of a?
(1) 6a + 18 ≤ 12
(2) a^2 > 2
(1) 6a + 18 ≤ 12
(2) a^2 > 2
Bunuel
Asked: If a^5 ≥ −32 and a is an integer, what is the value of a?
a >= -2
(1) 6a + 18 ≤ 12
a + 3 <= 2
a <= -1
-2<=a <=-1
Since a is an integer
a = -2 or a = -1
NOT SUFFICIENT
(2) a^2 > 2
a < - 1.4 or a>1.4
Since a is an integer >=-2
a = -2 or a>=2
NOT SUFFICIENT
(1) + (2)
(1) 6a + 18 ≤ 12
-2<=a <=-1
a = -2 or a = -1
(2) a^2 > 2
a < - 1.4 or a>1.4
Since a is an integer >=-2
a = -2 or a>=2
a = -2
SUFFICIENT
IMO C
20 Mar 2020, 03:55
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If \(a^{5} ≥ −32\) and a is an integer, what is the value of a?
--> \(a ≥ -2.\)
(Statement1): \(6a + 18 ≤ 12\)
\(a ≤-1\) and \(a ≥ -2\)
\(-2≤ a ≤ -1\)
--> a could be \(-2\) or \(-1\)
Insufficient
(Statement2): \(a^{2} > 2\)
--> \((a -√2)(a +√2) >0\)
and \(a ≥ -2\)
--> \(-2 ≤ a < -√2\) and \(a > √2\)
Insufficient
Taken together 1&2,
\(-2≤ a ≤ -1\)
\(-2 ≤ a < -√2\) and \(a > √2\)
---------------------------
--> \(-2 ≤ a < -√2\)
a could be only -2.
Sufficient
Answer (C)
--> \(a ≥ -2.\)
(Statement1): \(6a + 18 ≤ 12\)
\(a ≤-1\) and \(a ≥ -2\)
\(-2≤ a ≤ -1\)
--> a could be \(-2\) or \(-1\)
Insufficient
(Statement2): \(a^{2} > 2\)
--> \((a -√2)(a +√2) >0\)
and \(a ≥ -2\)
--> \(-2 ≤ a < -√2\) and \(a > √2\)
Insufficient
Taken together 1&2,
\(-2≤ a ≤ -1\)
\(-2 ≤ a < -√2\) and \(a > √2\)
---------------------------
--> \(-2 ≤ a < -√2\)
a could be only -2.
Sufficient
Answer (C)
