If c ≠ 1, is ab = a + b? (1) a^2 + b^2 = 0 (2) a = a*c = b

Question

If c ≠ 1, is ab = a+b?

(1)  a^2+b^2=0 
(2)  a=a*c=b

freedom128 · Answer

If c ≠ 1, is ab = a + b?

(1) a^2 + b^2 = 0 
This must be true if a=0 and b=0. Thus, it must also be true that ab = a + b. 
SUFFICIENT

(2) a = a*c = b
Since c≠1, a must be 0 and b must be 0 too. Thus, it must also be true that ab = a + b
SUFFICIENT

FINAL ANSWER IS (D)

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Anjali_1453 · Answer

Could someone please explain how to relate statement 1 and the question stem?

Bunuel · Answer

A square of a number is always non-negative, 0 or positive. So in a^2 + b^2 = 0, the sum of two non-negative numbers is 0, which means both a^2 and b^2 must be 0, and consequently a and b must be 0. Thus, ab = 0 and a + b = 0.

P.S. 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..."

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So, you can ignore this question.

Hope it helps.

MANASH94 · Answer

I tried out in a different way:
 
Question said: 
If c ≠ 1, is ab = a+b? 
 (1)   a^2+b^2=0 
Since squares of numbers cannot be negative, hence only way this seemed possible was if a=0 and b=0.
So sufficient.

(2)   a=a∗c=b 
 so from a = ac we can also say c = 1. But in the question statement it says that c cannot be 1 hence, this seemed impossible for me to achieve a = ac if a is not 0. Hence a = 0 and b = a = 0 hence the second statement has to be also equal to 0. 
 So this is also Sufficient. 
 Hence as per me the answer is D.

If c ≠ 1, is ab = a + b? (1) a^2 + b^2 = 0 (2) a = a*c = b

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GMAT Data Sufficiency (DS) Questions

If c ≠ 1, is ab = a + b? (1) a^2 + b^2 = 0 (2) a = a*c = b

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards