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Sub 505 (Easy)|   Sequences|      
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 26 Aug 2020, 00:24
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

86% (01:55) correct 14% (02:16) wrong based on 254 sessions

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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is the value of K ?

(A) −282
(B) −84
(C) −30
(D) −15
(E) −3

Source: Advanced Quant Manhattan Prep 2020
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D
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 26 Aug 2020, 00:37
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Long Method:

K = 5(80)+94+5(82)+94+5(84) - 5(81)-94-5(83)-94-5(85)-94

Simplifying

K=5(80+82+84-81-83-85)

K=5(-3)=-15

Concise method:

Observe that there are 3 terms to be added and 3 terms to be subtracted

So in Sn=5n+94, we can remove 94 as they will eventually cancel out

Now taking a closer look at K=(S80+S82+S84) - (S81+S83+S85)

We can directly substitute values to get K=-15
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 26 Aug 2020, 07:13
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The term can be written as

K = 5(80) + 94 + 5(82) + 94 + 5(84) + 94 - [5(81) + 94 + 5(83) + 94 + 5(85) + 94]

Rearranging

K = 5[80 - 81 + 82 - 83 + 84 - 84] + 3 * 94 - 3 * 94

K = 5 * -3 = -15

Option D

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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 26 Aug 2020, 09:36
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If you subtract consecutive terms in this sequence, i.e. if you compute S_n - S_(n+1), you just get 5n - 5(n + 1) = -5 (I'm omitting the "+94" each time since it will cancel). In the calculation we're asked to do in this question, we're just subtracting three pairs of consecutive terms, and adding what we get, so the answer is -15.
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 29 Aug 2020, 16:59
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rakshit21
If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is the value of K ?

(A) −282
(B) −84
(C) −30
(D) −15
(E) −3

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Solution:

S80 = 5(80) + 94

S81 = 5(81) + 94

S82 = 5(82) + 94

S83 = 5(83) + 94

S84 = 5(84) + 94

S85 = 5(85) + 94

We see that the 3 terms of 94 from S80, S82 and S84 will cancel the same three 3 terms in S81, S83 and S85 when you subtract the two sums. Therefore, we have:

(S80 + S82 + S84) − (S81 + S83 + S85)

= [5(80)+ 5(82) + 5(84)] - [5(81)+ 5(83) + 5(85)]

= 5(80 + 82 + 84 - 81 - 83 - 85)

= 5(-1 - 1 - 1)

= -15

Answer: D
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 10 Dec 2020, 20:35
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is the value of K ?

First of all, let's consider only the units as the tens will cancel out with the sustraction
Then, let's dump the +94 because it will cancel out too.

We are left with 5n and (S0+S2+S4)-(S1+S3+S5) = (0+10+20)-(5+15+25) = 30-45 = -15

With this method, it will only take you seconds to solve the question

Answer D)
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If Sn = 5n + 94 and K = (S80 + S82 + S84) − (S81 + S83 + S85), what is 03 Nov 2023, 09:21
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