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# Is q^r + 1 an odd number? (1) q + r is even (2) q is even

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
Is q^r + 1 an odd number? (1) q + r is even (2) q is even  [#permalink]

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03 Jul 2018, 10:08
00:00

Difficulty:

75% (hard)

Question Stats:

19% (01:07) correct 81% (01:07) wrong based on 49 sessions

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Is $$q^r + 1$$ an odd number?

(1) q + r is even
(2) q is even

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7100
Is q^r + 1 an odd number? (1) q + r is even (2) q is even  [#permalink]

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03 Jul 2018, 10:45
Is $$q^r + 1$$ an odd number?
$$q^r+1$$ odd means $$q^r$$ is even
Easy to wrong by believing q as even would be sufficient----
NO we have to know
a) q and r are positive integers
b) q is even

(1) q + r is even
3+(-1) is even
but $$q^r+1=3^{-1}+1=\frac{1}{3}+1$$.. not odd
2+2 is even.. yes $$q^r+1$$ is odd
insuff

(2) q is even
insuff

Combined
q is2 and r is 0...2^0+1=2.... Even
wish 2 and r is -2.....2^-2+1=5/2.... fraction
q is 2 and r is 4..... 2^4+1=17...odd
Insufficient

E
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Re: Is q^r + 1 an odd number? (1) q + r is even (2) q is even  [#permalink]

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03 Jul 2018, 14:40
Bunuel wrote:
Is $$q^r + 1$$ an odd number?

(1) q + r is even
(2) q is even

we are asked to determine whether $$q^r$$ + 1 = odd or not.

Statement 1 :

q + r = even . This fact can be proved by 2 ways.

1. even + even = even . 2 +2 = 4
2. odd + odd = even . 3 + 1 = 4

If both q and r are even , we will always get odd number but the scenario is different when q and r are odd.

NOT sufficient.

Statement 2 :

This statement is a trap. anyone can say that if q is even $$q^r$$ + 1 will be odd. But we don't sufficient information about r. Thus this statement becomes fruitless. r could be anything. so, NOT sufficient .

combining both statements:

if q is even r has to be even if we consider statement 1. even or odd can't be fraction .

So, both statements together are sufficient.

Thus the best answer is C.
SVP
Joined: 26 Mar 2013
Posts: 1904
Re: Is q^r + 1 an odd number? (1) q + r is even (2) q is even  [#permalink]

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03 Jul 2018, 16:36
Bunuel wrote:
Is $$q^r + 1$$ an odd number?

(1) q + r is even
(2) q is even

(1) q + r is even

Let q=2 & r= 0..........$$2^0 + 1$$=2..........Answer No

Let q=2 & r= 2..........$$2^2 + 1$$=5..........Answer Yes

Insufficient

(2) q is even

Use same examples above

Insufficient

Combine 1 & 2

Insufficient

Intern
Joined: 28 Nov 2016
Posts: 7
Re: Is q^r + 1 an odd number? (1) q + r is even (2) q is even  [#permalink]

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03 Jul 2018, 19:16
selim wrote:
Bunuel wrote:
Is $$q^r + 1$$ an odd number?

(1) q + r is even
(2) q is even

we are asked to determine whether $$q^r$$ + 1 = odd or not.

Statement 1 :

q + r = even . This fact can be proved by 2 ways.

1. even + even = even . 2 +2 = 4
2. odd + odd = even . 3 + 1 = 4

If both q and r are even , we will always get odd number but the scenario is different when q and r are odd.

NOT sufficient.

Statement 2 :

This statement is a trap. anyone can say that if q is even $$q^r$$ + 1 will be odd. But we don't sufficient information about r. Thus this statement becomes fruitless. r could be anything. so, NOT sufficient .

combining both statements:

if q is even r has to be even if we consider statement 1. even or odd can't be fraction .

So, both statements together are sufficient.

Thus the best answer is C.
If you take r=0 then q^r+1=even.so together also it is insufficient to ans.
Hence E is right choice.

Sent from my ONEPLUS A6000 using GMAT Club Forum mobile app
Re: Is q^r + 1 an odd number? (1) q + r is even (2) q is even &nbs [#permalink] 03 Jul 2018, 19:16
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