[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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If neither x nor y is divisible by 3, which of the following
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Max@Math Revolution
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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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As it stands, all of the answer choices are correct.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
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
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Max@Math Revolution
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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
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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