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If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of the

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If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of the

by VJesus12 » Sun Jun 14, 2020 8:22 am

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If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of the number \(N?\)

(A) \(0\)
(B) \(1\)
(C) \(x\)
(D) \(y\)
(E) \(z\)

[spoiler]OA=A[/spoiler]

Source: Official Guide
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Re: If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of

by Jay@ManhattanReview » Mon Jun 15, 2020 9:38 pm
VJesus12 wrote: ↑
Sun Jun 14, 2020 8:22 am
 If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of the number \(N?\)

(A) \(0\)
(B) \(1\)
(C) \(x\)
(D) \(y\)
(E) \(z\)

[spoiler]OA=A[/spoiler]

Source: Official Guide
So, we have \(N=100(x) + 1,000(y) + 10(z) => 10(100y+10x+z)\)

Noe that any integer multiplied by 10 will have its units digit equal to 0. So, the correct answer is A.

Correct answer: A

Hope this helps!

-Jay
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Re: If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of

by swerve » Tue Jun 16, 2020 4:07 am
VJesus12 wrote: ↑
Sun Jun 14, 2020 8:22 am
 If \(x, y,\) and \(z\) are single-digit integers and \(100(x) + 1,000(y) + 10(z) = N,\) what is the units' digit of the number \(N?\)

(A) \(0\)
(B) \(1\)
(C) \(x\)
(D) \(y\)
(E) \(z\)

[spoiler]OA=A[/spoiler]

Source: Official Guide
We have:

\(10\cdot z = z0, 100\cdot x = x00, 1000\cdot y = y000\)

Sum will be \(y000 + x00 + z0 = yxz0\)

So, units' digit will be \(0\).

Therefore, A
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