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

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

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

00:00

A

B

C

D

E

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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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