GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2019, 13:14

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a and b are both positive integers, is b^(a+1) - ba^b odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58434
if a and b are both positive integers ,is b(a+1)-ba^b odd?  [#permalink]

Show Tags

New post 05 May 2011, 00:56
1
19
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:48) correct 69% (02:44) wrong based on 498 sessions

HideShow timer Statistics

Most Helpful Expert Reply
SVP
SVP
User avatar
P
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1882
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 09 Aug 2011, 11:11
15
8
Quote:
If a and b are both positive integers, is b^(a+1) - ba^b odd?
(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd


Using statement (1):
5a-8 is odd
=> a is odd

Now evaluating b^(a+1) - ba^b, we get b^even -b*odd
If b is even, the expression is even^even - even = even
If b is odd, the expression is odd^even - odd = even
Therefore in either case, we can say that the expression is not odd. Sufficient.

Using statement 2:
b^3 + 3b^2 + 5b + 7 is odd
=> b^3 + 3b^2 + 5b is even
=> b is even (because if b is odd, the expression would be odd + odd + odd = odd)

Now evaluating b^(a+1) - ba^b
we get even^(a+1) - even*a^odd
= even - even*a^odd
= even
Therefore statement (2) is sufficient.

The answer should therefore be (D).
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Most Helpful Community Reply
Manager
Manager
User avatar
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 175
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 09 Aug 2011, 05:20
6
25
If a and b are both positive integers, is b^(a+1) - ba^b odd?

(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd
_________________
WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post. :)
General Discussion
GMAT Tutor
avatar
G
Joined: 24 Jun 2008
Posts: 1805
If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 05 May 2011, 14:56
6
1
7
Bunuel wrote:
If a and b are both positive integers, is \(b^{a + 1}– b*(a^b)\) odd?

(1) \(a + (a + 4) + (a – 8 ) + (a + 6) + (a – 10)\) is odd
(2) \(b^3 + 3b^2 + 5b + 7\) is odd


The answer is D here; each statement alone guarantees that the expression in the question is *even* so we know the answer is 'no'.

A bit of theory first: when you are dealing with positive integers b and x, then when b^x is odd, b is odd, and when b^x is even, then b is even. That is, the exponent never makes any difference at all - we only care about the base. So as long as we know we're dealing with positive integers, we can always ignore exponents in an even/odd question, because they change nothing.

So if a question asks if b^(a+1)-b(a^b) is odd, it's really just asking if b-ba is odd. From Statement 1 we learn that a is odd, so b-ba = b(1-a) will be even. In Statement 2, again you can just ignore all the exponents; Statement 2 then tells you that b+3b+5b+7 is odd, so 9b+7 is odd and b is even, and thus b-ba is even.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1572
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 10 Jul 2011, 07:33
3
1
AnkitK wrote:
If a and b are both positive integers, is b^(a+1)– b*(a^b)odd?
(1) a + (a + 4) + (a – 8 ) + (a + 6) + (a – 10) is odd
(2) b^3+ 3b^2+ 5b + 7 is odd


1.
a + (a + 4) + (a – 8 ) + (a + 6) + (a – 10) is odd
5a-8 odd
5*Integer-even=odd
odd*Integer=odd
Integer=odd
a=odd

b^(a+1)– b*(a^b)
Integer^(odd+1)-Integer*(Odd^Integer)
Integer^(even)-Integer*(Odd)

If Integer=Even
Even^Even-Even*(Odd)=even-even=even

If Integer=Odd
Odd^Even-Odd*(Odd)=odd-odd=even

Sufficient.

(2) b^3+ 3b^2+ 5b + 7 is odd
Integer^Odd+Odd*Integer^Even+Odd*Integer+Odd is odd

If Integer=Even
Even^Odd+Odd*Even^Even+Odd*Even+Odd
Even+Even+Even+odd=odd
b could be EVEN.

If Integer=Odd
Odd^Odd+Odd*Odd^Even+Odd*Odd+Odd
Odd+Odd+Odd+odd=EVEN
Thus, b cannot be ODD.
b=Even

b^(a+1)– b*(a^b)
Even^(Integer+Odd)-Even*Integer^Even
Even-even=even
Sufficient.

Ans: "D"
_________________
Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 348
Schools: Simon '16 (M$)
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 10 Jul 2011, 12:55
AnkitK wrote:
If a and b are both positive integers, is b^(a+1)– b*(a^b)odd?
(1) a + (a + 4) + (a – 8 ) + (a + 6) + (a – 10) is odd
(2) b^3+ 3b^2+ 5b + 7 is odd


1. 5a-8 is odd
5a must be odd. a must be odd.
let a=1

Question: b^(a+1) - b(a^b)= b^a.b^1 - b. a^b = b(b^a-a^b) is odd?
let b=even=2
Expression: b(b^a-a^b)
2(2^1-1^2)=2=even
let b=odd=3
Expression : b(b^a-a^b)
3(3^1-1^3)=6=even.
Hence for b=even and b= odd, expression in question is even.
b(b^a-a^b) is odd? NO. Sufficient.

2. b(b^2+3b+5) + 7 is odd
even + odd = odd
hence expression b(b^2+3b+5) must be even. b must be even. let b=2
let a=even=2
Expression : b(b^a-a^b)
2(2^2-2^2)=0 = even
let a=odd=1
Expression: b(b^a-a^b)
2(2^1-1^2)=2=even
Hence for a=even and a= odd, expression in question is even.
b(b^a-a^b) is odd? NO. Sufficient.

OA D
_________________
My dad once said to me: Son, nothing succeeds like success.
Intern
Intern
avatar
Joined: 17 May 2009
Posts: 27
Location: United States
GMAT 1: 770 Q51 V44
GPA: 3.62
WE: Corporate Finance (Manufacturing)
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 13 Aug 2011, 19:56
1
We can factor b^(a+1) - ba^b and rephrase the question stem as "\(b(b^a-a^b)\) odd?"

\(b(b^a-a^b)\) is odd only when both \(b\) and \((b^a-a^b)\) are odd, since \(O * O = O\). Since \(b^a\) is odd if \(b\) is odd and \(a>0\), \((b^a-a^b)\) is odd when \(a^b\) is even, since \(O - E = O\). \(a^b\) is even when \(a\) is even (and it's given that \(b>0\)).

We can rephrase once again: "Is both \(b\) odd and \(a\) even?"

Statement 1) \(5a - 8\) is odd, so \(5a\) is \(odd + even = odd\). \(a\) is thus odd since \(a = \frac{odd}{odd}\) cannot be even and it's given that \(a\) is an integer.

We are given that \(a\) is odd, so it cannot be that both \(b\) is odd and \(a\) is even. Sufficient.

Statement 2) \(b^3 + 3b^2 + 5b + 7\) is odd, so \(b^3 + 3b^2 + 5b\) is \(odd - odd = even\).

We can factor as \(b(b^2+3b+5) = even\) and test \(b\) as odd: \(O(O*O + 3(O) + 5) = O(O+O+O)=O\), so \(b\) cannot be odd. \(b\) must be even.

We are given that \(b\) is even, so it cannot be that both \(b\) is odd and \(a\) is even. Sufficient.

Intern
Intern
avatar
Joined: 11 Feb 2013
Posts: 1
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 18 May 2013, 16:48
GyanOne wrote:
Quote:
If a and b are both positive integers, is b^(a+1) - ba^b odd?
(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd


Using statement (1):
5a-8 is odd
=> a is odd

Now evaluating b^(a+1) - b(a^b), we get b^even -b*odd
If b is even, the expression is even^even - even = even
If b is odd, the expression is odd^even - odd = even
Therefore in either case, we can say that the expression is not odd. Sufficient.

Using statement 2:
b^3 + 3b^2 + 5b + 7 is odd
=> b^3 + 3b^2 + 5b is even
=> b is even (because if b is odd, the expression would be odd + odd + odd = odd)

Now evaluating b^(a+1) - ba^b
we get even^(a+1) - even*a^odd
= even - even*a^odd
= even
Therefore statement (2) is sufficient.

The answer should therefore be (D).


Hi guys,

I have a question about statement 1

Simplifying main stem: b^(a+1) - b(a^b) gives us b[(b^a) - (a^b)]

From statement 1 we get that a has to be odd
Then to see if statement 1 is S, we try odd/even values for b and see that all of them give even answers, except when a=3 b=3, which yield and answer of 0, which isnt considered neither even or odd.
Am I not understanding something here, which prevents the use of these values?

Thanks in advance!
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 590
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 18 May 2013, 22:00
1
Quote:
Then to see if statement 1 is S, we try odd/even values for b and see that all of them give even answers, except when a=3 b=3, which yield an answer of 0, which isnt considered neither even or odd.

All even numbers are divisible by 2 integrally. Thus 0 is EVEN.
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58434
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 19 May 2013, 03:20
1
1
retropecexy82 wrote:
GyanOne wrote:
Quote:
If a and b are both positive integers, is b^(a+1) - ba^b odd?
(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd


Using statement (1):
5a-8 is odd
=> a is odd

Now evaluating b^(a+1) - b(a^b), we get b^even -b*odd
If b is even, the expression is even^even - even = even
If b is odd, the expression is odd^even - odd = even
Therefore in either case, we can say that the expression is not odd. Sufficient.

Using statement 2:
b^3 + 3b^2 + 5b + 7 is odd
=> b^3 + 3b^2 + 5b is even
=> b is even (because if b is odd, the expression would be odd + odd + odd = odd)

Now evaluating b^(a+1) - ba^b
we get even^(a+1) - even*a^odd
= even - even*a^odd
= even
Therefore statement (2) is sufficient.

The answer should therefore be (D).


Hi guys,

I have a question about statement 1

Simplifying main stem: b^(a+1) - b(a^b) gives us b[(b^a) - (a^b)]

From statement 1 we get that a has to be odd
Then to see if statement 1 is S, we try odd/even values for b and see that all of them give even answers, except when a=3 b=3, which yield and answer of 0, which isnt considered neither even or odd.
Am I not understanding something here, which prevents the use of these values?

Thanks in advance!


Zero is an even integer.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it's clear.
_________________
Manager
Manager
avatar
Joined: 14 Dec 2014
Posts: 51
Location: India
Concentration: Technology, Finance
GPA: 3.87
WE: Programming (Computer Software)
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 22 Dec 2014, 03:00
Using statement 1:
5a-8 is odd. so a is odd.

we know that odd^(positive integer) is odd and even ^(positive integer) is even.
So by evaluating the given expression we get b^even-b*odd
if b is odd>> we get odd-odd=even
if b is even >> we get even-even=even
Sufficient

Using Statement 2:
b^3 + 3b^2 + 5b + 7 is odd So b^3 + 3b^2 + 5b is even

so b is even. By evaluating expression we get even^(a+1)-even*(a^even)
even-even=even
Suffieint
So Ans D
_________________
If you like my posts appreciate them with Kudos :)
Cheers!!
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 23 Dec 2015, 23:24
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are both positive integers, is b^(a+1) - ba^b odd?

(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd
(2) b^3 + 3b^2 + 5b + 7 is odd

In the original condition, there are 2 variables(a,b), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. In 1)&2), 5a-8=odd, a=odd and b^3+3b^2+5b+7=odd -> b=odd. Then, b^(a+1)-ba^b=odd^even-odd(odd)^odd=even, which is no and sufficient. However, since this is an integers questions which is one of the key questions, apply the mistake type 4(A). In 1), when 5a-8=odd, a=odd and b=odd is even, which is b^(a+1) - ba^b=even. So it is no and sufficient. In 2), when b=odd, a=odd, which is even. Then it becomes b^(a+1) - ba^b=even, which is no and sufficient. Therefore the answer is D. You should get this type of question right in order to score 50-51.


-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7991
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 14 Aug 2017, 23:34
1
\(b^{a+1}-b*a^b.......b(b^a-a^b)\)..

So cases..
I) if b is even, ans is NO as equation will be EVEN.
2) if b is odd, and can be yes when a is even AND no when a is odd.
3) if a is even, can be yes or no
4) if a is odd, always NO

Let's see the statements...

(1) a + (a + 4) + (a – 8 ) + (a + 6) + (a – 10) is odd
Or 5a-8 is odd...
Possible only when 5a is odd, thus a is odd.
Case 4 above.
\(b(b^a-a^b)\)
If b is odd..Odd(odd-odd)=odd*even=even
If b is even... Even (even-odd)=even*odf=even
Sufficient

(2) \(b^3 + 3b^2 + 5b + 7\) is odd
So B is even..
Case I..
Sufficient

D
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13316
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?  [#permalink]

Show Tags

New post 05 Sep 2019, 23:22
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.
_________________
GMAT Club Bot
Re: If a and b are both positive integers, is b^(a+1) - ba^b odd?   [#permalink] 05 Sep 2019, 23:22
Display posts from previous: Sort by

If a and b are both positive integers, is b^(a+1) - ba^b odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne