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If a and b are non-negative integers, is a > b?

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Math Expert
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If a and b are non-negative integers, is a > b?  [#permalink]

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24 Jun 2015, 07:16
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Difficulty:

75% (hard)

Question Stats:

45% (01:07) correct 56% (00:54) wrong based on 200 sessions

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If $$a$$ and $$b$$ are non-negative integers, is $$a > b$$?

(1) $$6^a = 36^b$$

(2) $$5^a = 35^b$$

Kudos for a correct solution.

M31-53

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Re: If a and b are non-negative integers, is a > b?  [#permalink]

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24 Jun 2015, 07:39
1
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^(a-b) = 7^b
Now this is possible only if a = b = 0.
Hence Sufficient !!
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Re: If a and b are non-negative integers, is a > b?  [#permalink]

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24 Jun 2015, 08:21
1
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 non-negative integers, is a > b?  [#permalink]

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24 Jun 2015, 10:31
1
(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^(a-b) = 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 a-b=0, a=0....a is not greater than b

Sufficient
Ans B
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Re: If a and b are non-negative integers, is a > b?  [#permalink]

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25 Jun 2015, 10:05
2
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^( a-b) = 7^b *5^0 therefore a-b=0 and a=b; hence ais not greater than b; hence Sufficient.

Thanks,
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Posts: 51067
Re: If a and b are non-negative integers, is a > b?  [#permalink]

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20 Jul 2015, 04:51
Bunuel wrote:
If $$a$$ and $$b$$ are non-negative integers, is $$a > b$$?

(1) $$6^a = 36^b$$

(2) $$5^a = 35^b$$

Kudos for a correct solution.

M31-53

Official Solution:

If $$a$$ and $$b$$ are non-negative 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,

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Re: If a and b are non-negative integers, is a > b?  [#permalink]

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19 Nov 2018, 08:48
A quick and important tip for such questions!

ALWAYS REMEMBER IN DS questions statement 1 can never contradict statement 2!
So even in case u made mistake of taking $$a > b$$ from statement 1, while doing statement 2 u realize $$a=b=0$$.
You should immediately stop and check to see why statement 1 and 2 are contradicting.
Probably because u made some mistake.
This simple tip will help u avoid in a lot of DS questions.
Re: If a and b are non-negative integers, is a > b? &nbs [#permalink] 19 Nov 2018, 08:48
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