Is a + b = a^2 + b^2? (1) a and b are natural numbers. (2) a b

Question

Is a + b = a^2 + b^2?

(1) a and b are natural numbers.
(2) a > b

(A) Statement I ALONE is sufficient, but statement II alone is not sufficient.
(B) Statement II ALONE is sufficient, but statement I alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements I and II TOGETHER are NOT sufficient

Bunuel · Answer

1. GMAT does not use the term "natural numbers"; it uses "positive integers" instead.

2. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

HarshaBujji · Answer

As mentioned earlier this is not part of GMAT focus syllabus. But just to let you know the solution:

Stmt 1 : a and b are natural numbers.

Case 1 : a=1, b=1 ; Equation is satisfied. 
Case 2: a=1, b=2 ; Equation is not satisfied.

Stmt 2: a>b
Case 1 : a=1, b=0; Equation is satisfied
Case 2: a=-1, b=0; Equation is not satisfied.

Both stmt together ::

Both has to be natural, So a,b>=1;

So a has to be 2,3......
b can be 1,2,3,...

Hence in all the cases this will not satisfy the existing equation. Hence C is the answer.

Kinshook · Answer

Is a + b = a^2 + b^2?
Is a + b = (a+b)^2 - 2ab ? 
Is (a+b)^2 - (a+b) = 2ab = (a+b)(a+b-1) = 2ab ?

(1) a and b are natural numbers.
Case 1: a = b = 1; a + b = 2 = a^2 + b^2; Equation is correct
Case 2: a = 1; b = 2; a + b = 3; a^2 + b^2 = 1 + 4 = 5; Equation is incorrect
NOT SUFFICIENT

(2) a > b
Case 1: a = 1; b = 0; a + b = 1 = a^2 + b^2; Equation is correct
Case 2: a = 2; b = 1; a + b = 3; a^2 + b^2 = 4+1 = 5; Equation is incorrect
NOT SUFFICIENT

(1) + (2) 
(1) a and b are natural numbers.
(2) a > b
Equation hold true only when a = b = 1; or a=1; b=0; Both are not possible but a>b; and b = 0 is not possible since b is a a natural number.
SUFFICIENT

IMO C

Is a + b = a^2 + b^2? (1) a and b are natural numbers. (2) a > b

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