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If a and b are nonnegative integers, is a > b? [#permalink]
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24 Jun 2015, 08:16
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44% (01:00) correct 56% (00:54) wrong based on 153 sessions
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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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24 Jun 2015, 08:39
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Using statement 1 alone : 6^a = 36^b > 6^a = 6^2b > a = 2b > a>b  Case 1. But, at the same time it is possible that: a = b = 0  Case 2. Also, 6^2 = 36^1 a<b  Case 3. Hence Insufficient.
Using statement 2 alone : 5^a = 7^b * 5^b 5^(ab) = 7^b Now this is possible only if a = b = 0. Hence Sufficient !! Answer is B !!



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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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24 Jun 2015, 09:21
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B
From I > a,b = 0,0 /2, 1/4,2/ ... Hence Not Sufficient
From II > a,b = 0,0 Hence Sufficient



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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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24 Jun 2015, 11:31
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(1) 6^a = 36^b 6^a = 6^2b Or, a=2b
Taking b=1, then a=2.... In this case a> b Taking b=1, then a=2 ..In this case a<b
Hence, insufficient
(2) 5^a = 35^b 5^a = (5*7)^b 5^a = 5^b * 7^b 5^(ab) = 7^b Now, 5 raise to power something (other than zero) can never be equal to 7 raise to power something because 5 raise to something always ends with unit digit as 5 whereas 7 raise to power something will end with unit as {7,9,3,1,7.....}
So, only one value can satisfy the above equation 5^0 = 7^0.
That means b=0 and ab=0, a=0....a is not greater than b
Sufficient Ans B



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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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25 Jun 2015, 11:05
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A ad b are integers, is a>b? 1) 6^a = 36^b =6^2b therefore a=2b; when b=1,a=2 then a<b but when b=1, a=2 then a>b; hence insufficient 2) 5^a = 35^b=5^b * 7^b therefore 5^( ab) = 7^b *5^0 therefore ab=0 and a=b; hence ais not greater than b; hence Sufficient.
Hence answer is B Thanks,



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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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20 Jul 2015, 05:51
Bunuel wrote: If \(a\) and \(b\) are nonnegative integers, is \(a > b\)? (1) \(6^a = 36^b\) (2) \(5^a = 35^b\)
Kudos for a correct solution.
M3153 Official Solution:If \(a\) and \(b\) are nonnegative integers, is \(a > b\)? (1) \(6^a = 36^b\). Simplify: \(6^a = 6^{2b}\). Bases are equal, hence we can equate the powers: \(a=2b\). If \(a=b=0\), then \(a\) is NOT greater than \(b\) but if \(a=2\) and \(b=1\), then \(a\) IS greater than \(b\). Not sufficient. (2) \(5^a = 35^b\). If both \(a\) and \(b\) are positive integers, then we'd have that \(5^a\) is equal to some multiple of 7 (because 35=5*7), which is not possible since 5 in any positive integer power has only 5's in it. Therefore, both \(a\) and \(b\) must be 0, giving a NO answer to the question whether \(a\) is greater than \(b\). Sufficient, Answer: B.
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Re: If a and b are nonnegative integers, is a > b? [#permalink]
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Re: If a and b are nonnegative integers, is a > b?
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