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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is Updated on: 24 Nov 2018, 08:18
Originally posted by Sajjad1994 on 12 Feb 2017, 23:14.
Last edited by Sajjad1994 on 24 Nov 2018, 08:18, edited 2 times in total.
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C
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71% (01:50) correct 29% (02:02) wrong based on 507 sessions

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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
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C
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 12 Feb 2017, 23:38
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SajjadAhmad
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

I have tried to write 10 raise to power n minus 4 in question according to (Writing Mathematical Formulas on the Forum) but failed so z= 10 raise to power n minus 4 which is highlited
Show more

To write 10 raise to power n minus 4 you have used the "highlight" tag instead of the "m" tag.

Consider the following,
when n= 1; z=6
n=2; z=96
n=3; z=996
n=4; z=9996

when n=k; \(z = 10^n – 4\) will have (k-1) times 9 and the last digit will always be 6
therefore 186-6 = 180 => 180/9=20
so the value of k-1 =20 thus k=21

Hence Option C is correct.
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 13 Feb 2017, 02:07
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SajjadAhmad
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

I have tried to write 10 raise to power n minus 4 in question according to (Writing Mathematical Formulas on the Forum) but failed so z= 10 raise to power n minus 4 which is highlited
Show more

You can write it as \(z = 10^{n – 4}\) or as 10^(n – 4).
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 13 Feb 2017, 13:07
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Hi SajjadAhmad,

Based on the answers choices (and the correct answer), the "intent" of this question is that that Z = (10^N) - 4. We're also told that the sum of the DIGITS of Z is 186. We're asked for the value of N.

Consider the following examples...

IF....
N = 1, then Z = 10 - 4 = 6 and the sum of the digits is 6
N = 2, then Z = 100 - 4 = 96 and the sum of the digits is 15
N = 3, then Z = 1000 - 4 = 996 and the sum of the digits is 24

Notice that when N increases by 1, the sum of the digits of Z increases by 9. To answer this question, we just have to determine how many additional "9s" we have to add to get the sum of the digits up to 186.

Since N = 1 led to a sum of 6, we need twenty 9s to get the sum up to 186. Thus, N would have to be 1 + 20 = 21

Final Answer:
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C

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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 13 Feb 2017, 13:59
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Hello :)
try finding the pattern...
10^2-4=96
10^3-4=996
10^4-4=9996
conclude that sum of digits=9(n-1)+6 --> 9(n-1)+6=186 n=21 answer:c
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 02 Apr 2017, 21:31
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SajjadAhmad
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

I have tried to write 10 raise to power n minus 4 in question according to (Writing Mathematical Formulas on the Forum) but failed so z= 10 raise to power n minus 4 which is highlited
Show more

For any n>2, \(10^n-4\) will have 96 in the end. Sum of 96 = 15.

186 - 15 = 171.

All the numbers in \(10^n-4\), apart from 96, should to be 9. So numbers of 9's will be

\(\frac{171}{9}= 19\)

19(9's) + 2(96) = 21.

Answer C.

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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 22 Jul 2017, 00:33
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[quote="SajjadAhmad"]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

I have tried to write 10 raise to power n minus 4 in question according to (Writing Mathematical Formulas on the Forum) but failed so z= 10 raise to power n minus 4 which is highlited[/quote

sum of digits =186 =180+6
repeatition of 9 = 180/9=20 times
10-4=6
whereas 10^2-4=96
power of 10 must be one greater than the power of 9.
power of 10 = n= 20+1=21
ans C
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 15 Nov 2018, 04:37
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It needs to be clear at the outset that the question states ((10^n) – 4)
(10^1) – 4 = 6 (i.e. 0 times 9 & 6)
(10^2) – 4 = 96 (i.e. 1 times 9 & 6)
(10^3) – 4 = 996 (i.e. 2 times 9 & 6)
(10^4) – 4 = 9996 (i.e. 3 times 9 & 6)
(10^5) – 4 = 99996 (i.e. 4 times 9 & 6)

Hence we can conclude that
(10^n) – 4 = (n-1) times 9 & 6

Total sum of digits = 186 & 6 is always present hence sum of 9’s should be = 186 -6 = 180
i.e. 9(n-1)=180 that implies n = 21

Hence C
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The sum of the digits of integer z is 186 and z = 10^(n – 4). What is 07 Apr 2025, 05:16
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