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If neither x nor y is divisible by 3, which of the following

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If neither x nor y is divisible by 3, which of the following

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[GMAT math practice question]

x ans y are integers. If neither x nor y is divisible by 3, which of the following could be the value of x^2+y^2?

A. 333
B. 334
C. 335
D. 336
E. 337

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Last edited by Max@Math Revolution on Sat Mar 10, 2018 12:17 pm; edited 2 times in total

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GMAT/MBA Expert

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Max@Math Revolution wrote:
[GMAT math practice question]

If neither x nor y is divisible by 3, which of the following could be the value of x² + y² ?

A. 333
B. 334
C. 335
D. 336
E. 337
As it stands, all of the answer choices are correct.

A. 333
If x = √300 and y = √33, then x² + y² = (√300)² + (√33)² = 300 + 33 = 333

B. 334
If x = √300 and y = √34, then x² + y² = (√300)² + (√34)² = 300 + 34 = 334

etc

Cheers,
Brent

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=>
Consider the squares of the integers that are not divisible by 3:
1^2 = 1, 2^2 = 4, 4^2 = 16, 5^2 = 25, 7^2 = 49, 8^2=64, ….
They all have a remainder of 1 when they are divided by 3.
Thus, the sum of the squares of two integers which are not divisible by 3 must have a remainder of 2 when it is divided by 3.

The only answer choice having this property is 335.

Therefore, C is the answer.

Answer: C

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