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25 Jul 2018, 21:45
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B
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Difficulty:
25%
(medium)
Question Stats:
75% (01:55) correct
25%
(02:09)
wrong
based on 150
sessions
History
Date
Time
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Not Attempted Yet
Is \(3^x < 300\)?
(1) \(3^{(x – 1)} < 250\)
(2) \(3^{(x+ 1)} = 3^x+ 486\)
(1) \(3^{(x – 1)} < 250\)
(2) \(3^{(x+ 1)} = 3^x+ 486\)
25 Jul 2018, 21:53
Kudos
Bookmarks
Find 3^x < 300
If x <= 4 ---(1)
Statement 1:
If x=4 . True satisfies equation 1
If x=5 . Doesn't satisfy equation 1
Insufficient
Statement 2:
Substitute x = 4
729 = 729
Hence x=4. True
Sufficient
+1 for B
Posted from my mobile device
If x <= 4 ---(1)
Statement 1:
If x=4 . True satisfies equation 1
If x=5 . Doesn't satisfy equation 1
Insufficient
Statement 2:
Substitute x = 4
729 = 729
Hence x=4. True
Sufficient
+1 for B
Posted from my mobile device
25 Jul 2018, 21:57
Kudos
Bookmarks
To determine whether \(3^x < 300\)
Statement 1
\(3^{(x-1)} < 250\)
=> \(3^x * 3^{-1} < 250\)
=> \(\frac{3^x}{3^{1}} < 250\)
=> \(3^x < 250 * 3\)
=> \(3^x < 750\)
=> \(3^x\) can be 81 or 729 or any value less than 750
Statement 1 is not sufficient
Statement 2
\(3^{x+1} = 3^x + 486\)
=> \(3^x * 3 = 3 * (3^{x-1} + 162)\)
=> \(3^x = (3^{x-1} + 162)\)
=> \(3 * 3^{x-1} = 3^{x-1} + 162\)
=> \(2 * 3^{x-1} = 162\)
=> \(3^{x-1} = 81\)
=> \(3^x = 81 * 3 = 243 < 300\)
Statement 2 is sufficient
Hence option B
Statement 1
\(3^{(x-1)} < 250\)
=> \(3^x * 3^{-1} < 250\)
=> \(\frac{3^x}{3^{1}} < 250\)
=> \(3^x < 250 * 3\)
=> \(3^x < 750\)
=> \(3^x\) can be 81 or 729 or any value less than 750
Statement 1 is not sufficient
Statement 2
\(3^{x+1} = 3^x + 486\)
=> \(3^x * 3 = 3 * (3^{x-1} + 162)\)
=> \(3^x = (3^{x-1} + 162)\)
=> \(3 * 3^{x-1} = 3^{x-1} + 162\)
=> \(2 * 3^{x-1} = 162\)
=> \(3^{x-1} = 81\)
=> \(3^x = 81 * 3 = 243 < 300\)
Statement 2 is sufficient
Hence option B
