nonameee wrote:

Can I ask someone to provide a solution for this? I don't understand the solution provided by Paul. Thank you.

Is (x^2 + y^2) a perfect square?

(1) x is even, y is odd --> clearly insufficient: if

x=0 and

y=1 then

x^2+y^2=1^2 and the answer will YES but if

x=2 and

y=1 then

x^2+y^2=5 and the answer will be NO. Not sufficient.

(2) x and y are odd -->

x=2m+1 and

y=2n+1 for some integers

m and

n -->

x^2+y^2=(2m+1)^2+(2n+1)^2=2*(2(m^2+m+n^2+n)+1)=2*odd (as

2(m^2+m+n^2+n)+1=even+odd=odd), so

x^2+y^2 is not a perfect square (an even perfect square must be multiple of 2^2=4, in other words

x^2+y^2 to be a perfect square since it's a multiple of 2 it must be multiple of 2^2 as a perfect square has even powers of its primes, but as

x^2+y^2=2*odd then it's not a multiple of 2^2). Sufficient.

But even though formal answer to the question is B (Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient), this is not a realistic GMAT question, as:

on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other, and in this question (1) says that x is even and (2) says that x is odd, so the statements clearly contradict each other.

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership