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

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

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New post 03 Jul 2018, 11:08
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A
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C
D
E

Difficulty:

  75% (hard)

Question Stats:

22% (00:43) correct 78% (01:00) 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  [#permalink]

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New post 03 Jul 2018, 11:45
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
nothing about r
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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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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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New post 03 Jul 2018, 15:40
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.
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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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New post 03 Jul 2018, 17:36
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

Use same examples.............No clear answer

Insufficient

Answer: 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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New post 03 Jul 2018, 20:16
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.

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Re: Is q^r + 1 an odd number? (1) q + r is even (2) q is even &nbs [#permalink] 03 Jul 2018, 20:16
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