Is s an odd integer?(1)

\sqrt{s} is not an even integer.

Notice we are not told that \sqrt{s}=odd, we are told that \sqrt{s}\neq{even}, those ARE NOT the same. \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.

\sqrt{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.

Notice again that we are not told that s^2=odd, we are told that s^2\neq{even}, those ARE NOT the same. 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

s=\frac{1}{3} then the answer will be NO.

Answer: E.

Hope it's clear.

_________________

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.

What are GMAT Club Tests?

25 extra-hard Quant Tests