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If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470,

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If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470,  [#permalink]

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New post 26 Apr 2016, 05:34
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Question Stats:

84% (01:25) correct 16% (01:55) wrong based on 93 sessions

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If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?

I. x = 115, y = 146, z = 173
II. x = 114, y = 142, z = 171
III. x = 110, y = 108, z = 179

A. I only
B. II only
C. III only
D. I​ and II
E. I and III

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Re: If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470,  [#permalink]

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New post 26 Apr 2016, 07:32
We can just go by the units digit of the square of the numbers

I. x = 115, y = 146, z = 173 > Sum of the square of the unit digits 5 +6 +9 = 0
II. x = 114, y = 142, z = 171 > Sum of the square of the unit digits 6 +4+1 = 1
III. x = 110, y = 108, z = 179> Sum of the square of the unit digits 0+4+1 = 5

So the answer is A
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If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470,  [#permalink]

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New post 26 Apr 2016, 07:33
Bunuel wrote:
If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?

I. x = 115, y = 146, z = 173
II. x = 114, y = 142, z = 171
III. x = 110, y = 108, z = 179

A. I only
B. II only
C. III only
D. I​ and II
E. I and III


10 sec answer if you know how to find the units digit of a number

The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0

x = 115, so x^2 will have units digit 5
y = 146, so y^2 will have units digit 6
z = 173, so z^2 will have units digit 9

Calculate the units digit , the units digit will be 0

Test with options II and III, only option I will satisfy the condition , hence this will be our answer.
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Re: If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470,  [#permalink]

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New post 08 Oct 2017, 23:58
Bunuel If I prepare quant from GMAT directory
is it sufficient to get Q50 score?
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Re: If x, y, and z are positive integers such that x2 + y2 + z2 = 64,470, &nbs [#permalink] 08 Oct 2017, 23:58
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