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

Question

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

Bunuel · Accepted Answer

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

GMAT TIGER · Answer

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

vomhorizon · Answer

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

bhavinshah5685 · Answer

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

Kinshook · Answer

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

2+4+6+....50 terms = (2+100)/2*50 = 51*50 = 
1+3+5+....n terms = nˆ2
51*50/nˆ2 = 51/2
nˆ2 = 100
n = 10

IMO D

MartyMurray · Answer

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

The Sum of an Evenly-Spaced Set of Integers  =  The Average of the Integers × The Number of Integers

For the Numerator:

The Average of the Integers  = \frac{2 + 100}{2} = 51

The Number of Integers  = 50

The Average of the Integers × The Number of Integers  = 51 × 50

For the Denominator:

The Average of the Integers  = \frac{1 + 2n - 1}{2} = n

The Number of Integers  = n

The Average of the Integers × The Number of Integers =  n^2

So, we have the following:

\frac{51 × 50}{n^2} = \frac{51}{2}

\frac{50}{n^2} = \frac{1}{2}

100 = n^2

10 = n

A. 12

B. 13

C. 9

D. 10

Correct answer:   D

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

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

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards