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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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

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

Source: Beat The GMAT — Problem Solving | Sun Jun 14, 2020 8:22 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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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