It is currently 23 Mar 2018, 21:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44419
If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

24 Jun 2015, 08:16
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

44% (01:00) correct 56% (00:54) wrong based on 153 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________
Manager
Status: Perspiring
Joined: 15 Feb 2012
Posts: 112
Concentration: Marketing, Strategy
GPA: 3.6
WE: Engineering (Computer Software)
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

24 Jun 2015, 08:39
1
KUDOS
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 !!
Current Student
Joined: 23 Jul 2013
Posts: 40
Location: India
GMAT 1: 690 Q50 V33
GPA: 4
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

24 Jun 2015, 09:21
1
KUDOS
B

From I -> a,b = 0,0 /2, 1/4,2/ ...
Hence Not Sufficient

From II -> a,b = 0,0
Hence Sufficient
Current Student
Joined: 26 Apr 2012
Posts: 94
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 640 Q48 V29
GMAT 2: 660 Q45 V35
GMAT 3: 680 Q48 V35
GPA: 2.8
WE: Information Technology (Computer Software)
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

24 Jun 2015, 11:31
1
KUDOS
(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
Manager
Joined: 26 Dec 2012
Posts: 148
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

25 Jun 2015, 11:05
2
KUDOS
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,
Math Expert
Joined: 02 Sep 2009
Posts: 44419
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

20 Jul 2015, 05:51
Expert's post
1
This post was
BOOKMARKED
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,

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 6544
Re: If a and b are non-negative integers, is a > b? [#permalink]

### Show Tags

27 Nov 2017, 10:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a and b are non-negative integers, is a > b?   [#permalink] 27 Nov 2017, 10:29
Display posts from previous: Sort by