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Manager  Joined: 19 Aug 2009
Posts: 77
If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 69% (02:32) correct 31% (02:54) wrong based on 222 sessions

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If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find value of n

A. 12
B. 13
C. 9
D. 10

Originally posted by virtualanimosity on 06 Nov 2009, 15:44.
Last edited by Bunuel on 28 Sep 2012, 05:59, edited 1 time in total.
Renamed the topic.
Math Expert V
Joined: 02 Sep 2009
Posts: 58453

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virtualanimosity wrote:
Q.If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find value of n

1.12
2.13
3.9
4.10

Nominator sum of first n even integers = $$n*(n+1)=50*51$$
Denominator sum of first n odd integers = $$n^2$$

$$\frac{50*51}{n^2}=\frac{51}{2}$$

$$n^2=100$$

$$n=10$$
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virtualanimosity wrote:
Q.If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find value of n

1.12
2.13
3.9
4.10

Sum of 2+4+....+100 = 2(1+2+3+....+50) = 2(50x51/2) = 50x51

(50x51)/(1+3+5+....n terms) = 51/2
100 = 1+3+5+....n terms
100 = n (First term + last term)/2
100 = n (1 + 19)/2
n = 10
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Is this a 700 Category question ??
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Intern  Joined: 01 Jun 2012
Posts: 18
Location: United States
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Bunuel wrote:
virtualanimosity wrote:
Q.If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find value of n

1.12
2.13
3.9
4.10

Nominator sum of first n even integers = $$n*(n+1)=50*51$$
Denominator sum of first n odd integers = $$n^2$$

$$\frac{50*51}{n^2}=\frac{51}{2}$$

$$n^2=100$$

$$n=10$$

Hi Bunuel,

How did you know that the sum of the terms in the denominator was $$n^2$$?
Current Student B
Joined: 03 Sep 2012
Posts: 372
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42 GPA: 3.88
WE: Medicine and Health (Health Care)
Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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Quote:
How did you know that the sum of the terms in the denominator was ?

Sum of n terms of an A.P. = n/2 { 2a+(n-1)d}

...

n/2 { 2x1 + (n-1)2}

: n/2 { 2 + 2n - 2}

: n/2 x 2n = n^2

Because the Sum of the first 50 even numbers can be calculated using the same formula to be 2550 , we get the equation:

2550/n^2 = 51/2

and solving for n we get n = 10.

You could also attack this question by plugging in the values in the answer choices :

Given one choice is 10 , we can easily write down the first 10 odd numbers to be : 1 3 5 7 9 11 13 15 17 19 .. So their sum = 10/5 x (A+L) = 10/5 x 20 = 40 ... Divide 2550 by 40 to get the desired ratio...

Hope this helps
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"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas
Manager  Joined: 25 Jun 2012
Posts: 61
Location: India
WE: General Management (Energy and Utilities)
Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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1
Sn=n/2(2a+(n-1)d)...(1)

Here (2+4+...+50th Term)
n=50
a=2
d=2
Putting this in eqn (1) we get numerator = 25*102

Now for denominator,
n=n
a=1
d=2
putting this values in eqn(1) we get denominator = n*n

Now keeping in question stem,
25*102/n*n = 51/2

n = 10
Intern  Joined: 25 Jun 2012
Posts: 29
Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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bhavinshah5685 wrote:
Sn=n/2(2a+(n-1)d)...(1)

Here (2+4+...+50th Term)
n=50
a=2
d=2
Putting this in eqn (1) we get numerator = 25*102

Now for denominator,
n=n
a=1
d=2
putting this values in eqn(1) we get denominator = n*n

Now keeping in question stem,
25*102/n*n = 51/2

n = 10

I can't tell based on this equation what a is in the highlighted equation and what operation we are performing on it. Based on what seems to be happening, it is the first number of the sequence and that is it, the 2 didn't appear to do anything in this equation. help appreciated.
Manager  Joined: 22 Aug 2014
Posts: 136
Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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GMAT TIGER wrote:
virtualanimosity wrote:
Q.If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find value of n

1.12
2.13
3.9
4.10

Sum of 2+4+....+100 = 2(1+2+3+....+50) = 2(50x51/2) = 50x51

(50x51)/(1+3+5+....n terms) = 51/2
100 = 1+3+5+....n terms
100 = n (First term + last term)/2
100 = n (1 + 19)/2
n = 10

Hey ,
how did u get 19 as last term?  Non-Human User Joined: 09 Sep 2013
Posts: 13262
Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find  [#permalink]

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_________________ Re: If (2+4+6+....50 terms)/(1+3+5+....n terms)=51/2, then find   [#permalink] 19 Oct 2018, 10:21
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