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Is s an odd integer?

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Is s an odd integer? [#permalink] New post 19 Dec 2010, 18:45
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Is s an odd integer?

(1) \sqrt{s} is not an even integer.
(2) s^2 is not an even integer.

When not mentioned do we consider irrational numbers as well? Please clarify. Thanks !
[Reveal] Spoiler: OA

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Re: ODD vs EVEN Trick Question? [#permalink] New post 19 Dec 2010, 23:38
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MasterGMAT12 wrote:
Please help with the below question.. When not mentioned do we consider irrational numbers as well? Please clarify. Thanks !

Is s an odd integer?
(1) sqrt(s) is not an even integer.
(2) s^2 is not an even integer.


GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So, if there is no restriction then you must consider irrational numbers as well.

Note that only integers can be even or odd. So, for example there is no difference in asking "is s an odd integer" and "is s odd".

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Back to the original question:

Is s an odd integer?

(1) sqrt(s) is not an even integer --> \sqrt{s} might be an odd integer, for example 1, 3, ... and in this case s will be an odd integer, but \sqrt{s} might as well be a fraction, for example 1/3, 7/5 and in this case s won't be an integer at all. s also might be an irrational number, for example \sqrt{2}, \sqrt{3}, \sqrt{{\frac{1}{3}}} ... and in this case s might or might not be an odd integer. Not sufficient.

(2) s^2 is not an even integer --> the same here: s^2 might be a square of an odd integer, for example 1, 9, ... and in this case s will be an odd integer, but s^2 might as well not be a perfect square, for example 1/3, 17, and in this case s won't be an integer at all. Not sufficient.

(1)+(2) When combined still insufficient: if s=1 then the answer will be YES but if if s=\frac{1}{3} then the answer will be NO.

Answer: E.

Hope it's clear.
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Re: ODD vs EVEN Trick Question? [#permalink] New post 02 Jul 2012, 01:44
Bunuel wrote:
MasterGMAT12 wrote:
Please help with the below question.. When not mentioned do we consider irrational numbers as well? Please clarify. Thanks !

Is s an odd integer?
(1) sqrt(s) is not an even integer.
(2) s^2 is not an even integer.


GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So, if there is no restriction then you must consider irrational numbers as well.

Note that only integers can be even or odd. So, for example there is no difference in asking "is s an odd integer" and "is s odd".

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Back to the original question:

Is s an odd integer?

(1) sqrt(s) is not an even integer --> \sqrt{s} might be an odd integer, for example 1, 3, ... and in this case s will be an odd integer, but \sqrt{s} might as well be a fraction, for example 1/3, 7/5 and in this case s won't be an integer at all. s also might be an irrational number, for example \sqrt{2}, \sqrt{3}, \sqrt{{\frac{1}{3}}} ... and in this case s might or might not be an odd integer. Not sufficient.

(2) s^2 is not an even integer --> the same here: s^2 might be a square of an odd integer, for example 1, 9, ... and in this case s will be an odd integer, but s^2 might as well not be a perfect square, for example 1/3, 17, and in this case s won't be an integer at all. Not sufficient.

(1)+(2) When combined still insufficient: if s=1 then the answer will be YES but if if s=\frac{1}{3} then the answer will be NO.

Answer: E.

Hope it's clear.

Dear Bunuel

Can you please elaborate a bit further... not clear with the explanation.
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Re: ODD vs EVEN Trick Question? [#permalink] New post 02 Jul 2012, 01:47
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Re: ODD vs EVEN Trick Question? [#permalink] New post 03 Jul 2012, 06:47
Bunuel wrote:
narangvaibhav wrote:
Can you please elaborate a bit further... not clear with the explanation.


Can you please tell what exactly didn't you understand?

Couldn't get why option1 and 2 together are not sufficient

Posted from my mobile device Image
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Re: ODD vs EVEN Trick Question? [#permalink] New post 03 Jul 2012, 06:50
Expert's post
narangvaibhav wrote:
Bunuel wrote:
narangvaibhav wrote:
Can you please elaborate a bit further... not clear with the explanation.


Can you please tell what exactly didn't you understand?

Couldn't get why option1 and 2 together are not sufficient

Posted from my mobile device Image


It's explained in the solution.

Consider two cases: if s=1 then the answer will be YES but if if s=\frac{1}{3} then the answer will be NO.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is s an odd integer? [#permalink] New post 29 Jul 2014, 19:58
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Re: Is s an odd integer?   [#permalink] 29 Jul 2014, 19:58
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