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

 It is currently 18 Dec 2018, 22:21

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# If P and y are positive integers ; is (P^17) - 2*y^3 Odd?

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If P and y are positive integers ; is (P^17) - 2*y^3 Odd?  [#permalink]

### Show Tags

25 Aug 2016, 19:00
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:44) correct 48% (02:18) wrong based on 75 sessions

### HideShow timer Statistics

If p and y are positive integers, is (p^17) - 2*y^3 Odd?

A) The median of p consecutive even integers is an even integer.
B) 2p has twice as many factors as p

Do not forget to try this similar Question from MGMAT => http://gmatclub.com/forum/is-k-2-odd-118591.html

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Manager
Joined: 04 Jan 2014
Posts: 117
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If P and y are positive integers ; is (P^17) - 2*y^3 Odd?  [#permalink]

### Show Tags

25 Aug 2016, 21:10
1
stonecold wrote:
If P and y are positive integers ; is (P^17) - 2*y^3 Odd?

A) The median of P consecutive Even integers is an Even integer.
B) 2P has twice as many factors as P

Do not forget to try this similar Question from MGMAT => is-k-2-odd-118591.html

Main question: Is (P^17) - 2*y^3 Odd?
Since 2*y^3 is always even, the question becomes -> is (P^17) odd? -> is P odd?

St1:

If P is even, median will be odd.
Example: if the set is 0,2,4,6 -> median = average of 2 and 4 which is 3.

If P is odd, median will be even.
Example: if the set is 0,2,4,6,8 -> median = 4.

Hence P is odd.
Sufficient.

St2: This is only possible if P is odd. We can try with different pairs such as (2,1) and (6,3).
Sufficient.

Senior Manager
Joined: 03 Apr 2013
Posts: 273
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: If P and y are positive integers ; is (P^17) - 2*y^3 Odd?  [#permalink]

### Show Tags

16 Mar 2017, 22:45
1
stonecold wrote:
If P and y are positive integers ; is (P^17) - 2*y^3 Odd?

A) The median of P consecutive Even integers is an Even integer.
B) 2P has twice as many factors as P

Do not forget to try this similar Question from MGMAT => http://gmatclub.com/forum/is-k-2-odd-118591.html

Okay..The answer is (D). I'm gonna try to explain this in detail, so that others enjoy it as much as I did it in exploring it

(1) The median of P consecutive Even integers is an Even integer.

Okay..consider the following series

2 4 6 8 10 12 14 16

as you can see..if you take any consecutive numbers here..one is a multiple of 4..and the other 2*(odd number)..in other words..one is an even multiple of 2 and another is an odd multiple. Now, if the number of terms are even, then the median is always the mean of the middle two numbers..say a and b are those two numbers..so it will be..
$$(a+b)/2$$

which will become..
Odd + Even or Even + Odd
in either case..odd.
Thus is has to be Even number of numbers. Sufficient.

(2) 2P has twice as many factors as P

Okay..now there are two possibilities..P is either an Odd number or an Even number. In other words

$$P = a^p*b^q*c^r...$$

where a,b,c.. are all odd primes and each p,q,r.. is at least 1

or

$$P = 2^k*a^p*b^q*c^r...$$ in other words

$$2^{some power}*Odd Number$$

Lets call this Odd Number = x for convenience...

Now pay attention...

If its the second case..i.e. $$P = 2^k*x$$

$$2P = 2^{k+1}*x$$

where $$x = a^p*b^q*c^r...$$

The number of factors of x will be = $$(p+1)(q+1)(r+1)...$$
Let this number be = F(can be either even or odd)

Coming back to what the statement says..and putting it all into an equation...we get

$$(k+2)*F = 2(k+1)*F$$

on solving..
$$k = 2k$$

but this can only be possible if k is 0. Therefore, k=0, and this is nothing but the first case
i.e.

$$P = a^p*b^q*c^r...$$ or P is an Odd number. Sufficient.

hope you enjoyed

_________________

Spread some love..Like = +1 Kudos

Manager
Joined: 30 Mar 2017
Posts: 135
GMAT 1: 200 Q1 V1
Re: If P and y are positive integers ; is (P^17) - 2*y^3 Odd?  [#permalink]

### Show Tags

20 Feb 2018, 18:02
Can a math expert pls opine on Statement 2. My analysis was different from the other users' but I arrived at the same answer.
Bunuel chetan2u

"2P has twice as many factors as P"
I interpreted this as total # of factors, not prime factors. I reasoned that for 2P to have twice as many factors as P, P has to have 1 factor. The only positive integer that has 1 factor is 1. Thus, P is odd.
Current Student
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If P and y are positive integers ; is (P^17) - 2*y^3 Odd?  [#permalink]

### Show Tags

20 Feb 2018, 20:37
aserghe1 wrote:
Can a math expert pls opine on Statement 2. My analysis was different from the other users' but I arrived at the same answer.
Bunuel chetan2u

"2P has twice as many factors as P"
I interpreted this as total # of factors, not prime factors. I reasoned that for 2P to have twice as many factors as P, P has to have 1 factor. The only positive integer that has 1 factor is 1. Thus, P is odd.

Hi,
Your logic and reasoning are incorrect.
Every number has 1 as a factor. In other words -> 1 is the factor of every number.

If the question says factors, it is specifying total number of factors and not the prime factors.

Next, If the question mentions that 2p has twice as many factors as p => p is always odd. It can be 3 or 5 or 5001 etc. The point is that it is always odd.
You can verify it by using examples too.

Here is a GMAT-prep question based on the same logic -> https://gmatclub.com/forum/is-the-integ ... 91399.html

Best
Stone

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

If P and y are positive integers ; is (P^17) - 2*y^3 Odd? &nbs [#permalink] 20 Feb 2018, 20:37
Display posts from previous: Sort by