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n is an integer greater than 2 and t = 10n 132. If t is represented
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12 Jul 2023, 00:57
12 Jul 2023, 00:57
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n is an integer greater than 2 and \(t = 10^n – 132\). If t is represented in decimal notation, which of the following can be the sum of all digits of t?
A. 183
B. 184
C. 185
D. 186
E. 187
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
A. 183
B. 184
C. 185
D. 186
E. 187
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE NUMBER PROPERTIES
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Re: n is an integer greater than 2 and t = 10n 132. If t is represented
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15 Jul 2023, 03:21
15 Jul 2023, 03:21
2
Given that n is an integer greater than 2 and \(t = 10^n – 132\) and we need to find the sum of all digits of t?
Let n = 3
=> \(t = 10^3 – 132\) = 1000 - 132 = 868
Sum of the digits = 8 + 6 + 8 = 22
Now if n was 4
t = 9868
if n was 5
t = 99868
So, the last three digits will remain same as 868 and we will have more 9's getting added in the front
=> Sum of the digits = 9 + 9+ ...9 + 8 + 6 + 8
= 9*(k) + 22 (where k is an integer)
Since the numbers are close to 180 so we will take 9k close to 180-18 (so that 9k + 22 comes between 180-190)
= 162 + 22 = 184
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Sequence problems
Let n = 3
=> \(t = 10^3 – 132\) = 1000 - 132 = 868
Sum of the digits = 8 + 6 + 8 = 22
Now if n was 4
t = 9868
if n was 5
t = 99868
So, the last three digits will remain same as 868 and we will have more 9's getting added in the front
=> Sum of the digits = 9 + 9+ ...9 + 8 + 6 + 8
= 9*(k) + 22 (where k is an integer)
Since the numbers are close to 180 so we will take 9k close to 180-18 (so that 9k + 22 comes between 180-190)
= 162 + 22 = 184
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Sequence problems
gmatclubot
Re: n is an integer greater than 2 and t = 10n 132. If t is represented [#permalink]
15 Jul 2023, 03:21
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