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# When counting from 3 to 201, 53 is the 51 st number counted. When coun

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Senior Manager
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Joined: 02 Nov 2018
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When counting from 3 to 201, 53 is the 51 st number counted. When coun  [#permalink]

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20 Mar 2019, 04:25
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Difficulty:

55% (hard)

Question Stats:

55% (01:29) correct 45% (01:30) wrong based on 51 sessions

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When counting from 3 to 201, 53 is the 51 st number counted. When counting backwards from 201 to 3, 53 is the n th number counted. What is n?

(A) 146 (B) 147 (C) 148 (D) 149 (E) 150

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Re: When counting from 3 to 201, 53 is the 51 st number counted. When coun  [#permalink]

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20 Mar 2019, 08:42
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Top Contributor
When counting from 3 to 201, 53 is the 51 st number counted. When counting backwards from 201 to 3, 53 is the n th number counted. What is n?

(A) 146
(B) 147
(C) 148
(D) 149
(E) 150

Counting backwards from 201 to 3
term1 = 201
term2 = 201 - 1 [we're subtracting ONE 1]
term3 = 201 - 1 - 1 = 201 - 2 [we're subtracting TWO 1's]
term4 = 201 - 1 - 1 - 1 = 201 - 3 [we're subtracting THREE 1's]
term5 = 201 - 1 - 1 - 1 - 1 = 201 - 4 [we're subtracting FOUR 1's]
.
.
.
See the pattern?
The number we subtract from 201 is one less than the term number.
For example, term40 = 201 - 39

In general, term n = 201 - (n-1)
We're told that term n = 53
So, we can write: 53 = 201 - (n-1)
Simplify: 53 = 202 - n
Solve: n = 202 - 53 = 149

Cheers,
Brent
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Re: When counting from 3 to 201, 53 is the 51 st number counted. When coun  [#permalink]

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20 Mar 2019, 09:45
When counting from 3 to 201, 53 is the 51 st number counted. When counting backwards from 201 to 3, 53 is the n th number counted. What is n?

(A) 146 (B) 147 (C) 148 (D) 149 (E) 150

total terms = 201-3 + 1 = 199 terms
so from 201 to 53 we will have ; 201-53 = 148 +1 ; 149 terms
IMO D
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Re: When counting from 3 to 201, 53 is the 51 st number counted. When coun  [#permalink]

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25 Mar 2019, 14:37
1
Archit3110 wrote:
When counting from 3 to 201, 53 is the 51 st number counted. When counting backwards from 201 to 3, 53 is the n th number counted. What is n?

(A) 146 (B) 147 (C) 148 (D) 149 (E) 150

total terms = 201-3 + 1 = 199 terms
so from 201 to 53 we will have ; 201-53 = 148 +1 ; 149 terms
IMO D

Hello Archit3110!

Is it also ok to do it this way?

$$201 = 53 + (n-1)$$

$$n = 149$$

Kind regards!
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Re: When counting from 3 to 201, 53 is the 51 st number counted. When coun  [#permalink]

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26 Mar 2019, 00:54
jfranciscocuencag wrote:
Archit3110 wrote:
When counting from 3 to 201, 53 is the 51 st number counted. When counting backwards from 201 to 3, 53 is the n th number counted. What is n?

(A) 146 (B) 147 (C) 148 (D) 149 (E) 150

total terms = 201-3 + 1 = 199 terms
so from 201 to 53 we will have ; 201-53 = 148 +1 ; 149 terms
IMO D

Hello Archit3110!

Is it also ok to do it this way?

$$201 = 53 + (n-1)$$

$$n = 149$$

Kind regards!

jfranciscocuencag
well its same formula what I have mentioned in the solution ..
Re: When counting from 3 to 201, 53 is the 51 st number counted. When coun   [#permalink] 26 Mar 2019, 00:54
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