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The sum of the first V positive integers is W. What is the sum of the

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Bunuel
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The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:27
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The sum of the first V positive integers is W. What is the sum of the next V positive integers?

A. VW
B. (V + W)/N
C. V + W
D. W + V^2
E. W - V^2
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D
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nkme2007
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The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:36
Bunuel wrote:
The sum of the first V positive integers is W. What is the sum of the next V positive integers?

A. VW
B. (V + W)/N
C. V + W
D. W + V^2
E. W - V^2


Let V be 2

Sum of first 2 positive integers = 1+2 = 3 = W

Sum of next 2 positive integers = 3+4 = 7

POE of given options:

A: VW = 6 Wrong
B: (V + W)/N Wrong, as we don't know N
C: V+W = 5 Wrong
D: W + V^2 = 3+2^2 = 7 Fits
E: W - V^2 = 3-2^2 = 7 Wrong

Hence, OA: D
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Re: The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:39
Let sum of first three(v) positive integers 1,2,3 = 6 {w}

The sum of next V positive integers= (4,5,6) = 15

That is
A. VW = 3*6 = 18 ≠ 15
B. (V + W)/N = (3+6) /N = 9/N ≠ 15
C. V + W = 3+6 = 9 ≠ 15
D. W + V^2 = 6 + 9 = 15 = 15
E. W - V^2 = 6 - 9 = -3 ≠ 15

Answer is D

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Re: The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:41
Sum of first V integers = V(V+1)/2 = W

Sum of next V integers = V[2*(V+1)+(V-1)1]/2
=> Sum = V[2V + 2 + V - 1]/2
=> Sum = V(2V + V+1)/2
=> Sum = V^2 + W

Ans: D
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Re: The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:41
i was picking numbers to get D
v=3 numbers 1-2-3 so w=6
v2=3 , numbers 4-5-6 so w2=15
6+3^2=15
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The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:43
nkme2007 wrote:
Bunuel wrote:
The sum of the first V positive integers is W. What is the sum of the next V positive integers?

A. VW
B. (V + W)/N
C. V + W
D. W + V^2
E. W - V^2


Let V be 2

Sum of first 2 positive integers = 1+2 = 3 = W

Sum of next 2 positive integers = 3+4 = 7

POE of given options:

A: VW = 6 Wrong
B: (V + W)/N Wrong, as we don't know N
C: V+W = 5 Wrong
D: W + V^2 = 3+2^2 = 7 Fits
E: W - V^2 = 3-2^2 = 7 Wrong

Hence, OA: D

nkme2007 Just curious how did you know that you should try and put in values?
Coz I intially started solving taking variables only. But i liked your approach better.

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nkme2007
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Re: The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Jul 2020, 04:54
bratbg wrote:
nkme2007 wrote:
Bunuel wrote:
The sum of the first V positive integers is W. What is the sum of the next V positive integers?

A. VW
B. (V + W)/N
C. V + W
D. W + V^2
E. W - V^2


Let V be 2

Sum of first 2 positive integers = 1+2 = 3 = W

Sum of next 2 positive integers = 3+4 = 7

POE of given options:

A: VW = 6 Wrong
B: (V + W)/N Wrong, as we don't know N
C: V+W = 5 Wrong
D: W + V^2 = 3+2^2 = 7 Fits
E: W - V^2 = 3-2^2 = 7 Wrong

Hence, OA: D

nkme2007 Just curious how did you know that you should try and put in values?
Coz I intially started solving taking variables only. But i liked your approach better.

Posted from my mobile device


Thanks for liking my approach bratbg. Just try to think if you can substitute any numbers when the question contains variables. This may save a lot of time when the algebraic solution takes time.

All the best.
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The sum of the first V positive integers is W. What is the sum of the [#permalink] New post   10 Sep 2020, 20:34
out of curiosity, does anyone have an Algebra Approach? I Plugged in Numbers also....


EDIT: Nevermind, I missed a post above. Apologies.
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The sum of the first V positive integers is W. What is the sum of the [#permalink]
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