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If p = 10^x – 6 and the sum of the digits of integer p is 274 then

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Bunuel
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If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 22:20
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If \(p = 10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?

A. 28
B. 29
C. 30
D. 31
E. 32
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D
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 22:28
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274 = 270+4 = 9*30 + 4

Therefore p must have 30 9's followed by a 4 that is 31 digits.

When 6 is added to p, the result will have 32 digits that is 1 followed by 31 0's which is 10^31

So, x=31

Answer is (D)

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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 22:48
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Bunuel wrote:
If \(p = 10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?

A. 28
B. 29
C. 30
D. 31
E. 32


Let us assume x = 1 => p =10 -6 = 4 => sum of digits =4
Let us assume x>1 say 4 => p = 10000 - 6 = 9994 having (x-1)=3 9s followed by 4 => sum of digits = (x-1)9+4 in general
Given that 9(x-1) + 4 = 274 => (x-1) = 30 => x =31

Answer D is correct.
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 23:08
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P=10^x-6
Sum of digits of P equal 274.
10^1-6=4
10^2-6=94
10^3-6=994
It can be deduced that the number of 9s in P is (x-1).
We can therefore write this equation for the sum of digits of P: 9(x-1)+4=274
x-1=30
Which means x=31.
In my opinion the answer is D.

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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 22:45
Number of 9's will be x-1 and there will be one 4 .

Sum of the digits will be 9*(x-1)+4 =274

On solving we get X=31 hence answer is D
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   30 Jun 2019, 22:54
Bunuel wrote:
If \(p = 10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?

A. 28
B. 29
C. 30
D. 31
E. 32



For 10^4-9 we will have digits as 3-9's and 1-4 so the form is for sum of digits 9(n-1)+4

9(n-1)+4 = 274; n =31 IMO D
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   01 Jul 2019, 01:43
Bunuel wrote:
If \(p = 10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?

A. 28
B. 29
C. 30
D. 31
E. 32


\(10^2 - 6 = 94\), Sum = 9*1 + 4
\(10^3 - 6 = 994\), Sum = 9*2 + 4
\(10^4 - 6 = 9994\), Sum = 9*3 + 4
.
.
.
\(10^x - 6 = 999.....[(x-1)times]4\), Sum = 9*(x - 1) + 4

Given, 9*(x - 1) + 4 = 274
--> 9(x - 1) = 270
--> x - 1 = 30
--> x = 31

IMO Option D

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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   01 Jul 2019, 07:25
Bunuel wrote:
If \(p = 10^x – 6\) and the sum of the digits of integer p is 274 then what is the value of positive integer x?

A. 28
B. 29
C. 30
D. 31
E. 32


\(p = 10^x – 6\)
x=1 ; 10-6; 4
x=2; 100-6; 94 ; 13
x=3; 1000-6 ; 994 ; 22
we can say the eqn would be ; 9*(x-1)+4 ;
so for sum 274=9x-9+4
x=31
IMO D
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink] New post   07 Sep 2020, 01:37
Expert Reply
Given

    • p =\( 10^x\) – 6.
    • Sum of the digits of p is 274.

To Find

    • The value of x.

Approach and Working Out

    • Let us visualize what happens if we plug in values for x.
      o x = 1, p = 10 – 6 = 4.
      o x = 2, p = 100 – 6 = 94.
      o x = 3, p = 1000 – 6 = 994.
      o x = 4, p = 10000 – 6 = 9994.

    • So, we can say for x = n, there will be (n – 1) number of 9s and one 4 in P.
      o 9 (n – 1) + 4 = 274
      o 9 (n – 1) = 270
      o (n – 1) = 30
      o n = 31

Correct Answer: Option D
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Re: If p = 10^x – 6 and the sum of the digits of integer p is 274 then [#permalink]
07 Sep 2020, 01:37
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