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The sum of the digits of integer z is 186 and

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by Gmat_mission » Sat Apr 06, 2019 4:54 am
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The sum of the digits of integer z is 186 and z=10^n -4. What is the value of positive integer n?

(A) 19
(B) 20
(C) 21
(D) 22
(E) 23

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
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by deloitte247 » Wed Apr 10, 2019 6:52 am
$$Z=10^n-4$$
$$When\ n=1,\ z=6$$
$$When\ n=2,\ z=96$$
$$When\ n=3,\ z=996$$
$$When\ n=4,\ z=9996$$
$$When\ n=k,\ z=10^n-4\ will\ have\ \left(k-1\right)\cdot9\ and\ the\ last\ digit\ will\ always\ ne\ 6$$
$$Therefore,\ 186-6=180$$
$$and\ \frac{180}{9}=20$$
$$Hence,\ k-1=20$$
$$k=20+1=21\ \ \ \ \ \ OPTION\ C$$
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by Scott@TargetTestPrep » Sat Apr 13, 2019 5:39 pm
Gmat_mission wrote:The sum of the digits of integer z is 186 and z=10^n -4. What is the value of positive integer n?

(A) 19
(B) 20
(C) 21
(D) 22
(E) 23

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
If z = 10^n - 4, then z = 99...996 where there are (n - 1) nines (for example, if n = 3, z = 10^3 - 4 = 996). So the sum of the digits of z is 9(n - 1) + 6 and we are given that it is 186. So we have:

9(n - 1) + 6 = 186

9(n - 1) = 180

n - 1 = 20

n = 21

Answer: C

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