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x is a single-digit positive integer. If the units digit of x^2 and the units digit of

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by BTGmoderatorDC » Sat May 01, 2021 3:57 pm

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x is a single-digit positive integer. If the units digit of x^2 and the units digit of (x+2)^3 is same. How many values of x are possible?


A. 2
B. 3
C. 4
D. 7
E. 9


OA C

Source: e-GMAT
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Re: x is a single-digit positive integer. If the units digit of x^2 and the units digit of

by swerve » Mon May 03, 2021 9:51 am
BTGmoderatorDC wrote: ↑
Sat May 01, 2021 3:57 pm
 x is a single-digit positive integer. If the units digit of x^2 and the units digit of (x+2)^3 is same. How many values of x are possible?


A. 2
B. 3
C. 4
D. 7
E. 9


OA C

Source: e-GMAT
Unit digit, \(x^2 =\) unit digit \((x+2)^3\), so

\(2 \Rightarrow 2^2=4, (2+2)^3 = 64\) unit digit \(4\)

\(3 \Rightarrow 3^2=9, (3+2)^3 = 125\)

\(4 \Rightarrow 4^2=16, (4+2)^3 = 216\) unit digit \(6\)

\(7 \Rightarrow 7^2=49, (7+2)^3 = 729 \) unit digit \(9\)

\(9 \Rightarrow 9^2=81, (9+2)^3= 1331= \) unitdigit \( 1\)

Therefore, C
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