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If set Q consists of all three digit numbers divisible by 4, what is

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Bunuel
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If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   17 Jun 2019, 01:09
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If set Q consists of all three digit numbers divisible by 4, what is the mean of the set?

(A) 498
(B) 499.5
(C) 548
(D) 549.5
(E) 550
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C
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Lampard42
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   17 Jun 2019, 02:16
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Bunuel wrote:
If set Q consists of all three digit numbers divisible by 4, what is the mean of the set?

(A) 498
(B) 499.5
(C) 548
(D) 549.5
(E) 550


The set will be in a AP with starting term 100 and last term = 996.

Last term = 996 = 100+(n-1)4 solving for n we get 225.

Mean in a AP will be the middle most term (Odd numbers) = t113= 100+112*4= 548 IMO C
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   17 Jun 2019, 10:22
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Bunuel wrote:
If set Q consists of all three digit numbers divisible by 4, what is the mean of the set?

(A) 498
(B) 499.5
(C) 548
(D) 549.5
(E) 550


The 3 digit numbers which are multiples of 4 are 100, 104, 108, . . . . . . . 996
The above series is in AP.

Formula:
If a series is in AP, Mean = Median = \(\frac{(First term + Last term)}{2}\)


So, Mean = \(\frac{(First term + Last term)}{2}\)
= \(\frac{(100 + 996)}{2}\)
= \(\frac{1096}{2}\)
= 548

IMO Option C

Pls Hit Kudos if you like the solution
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   17 Jun 2019, 10:37
Bunuel wrote:
If set Q consists of all three digit numbers divisible by 4, what is the mean of the set?

(A) 498
(B) 499.5
(C) 548
(D) 549.5
(E) 550


total terms of 3 digit no divisible by 4 ; 100 to 996 ; 996-100 +1 ; 225
and sum of these 225 terms ;
sn=225/2* ( 2*225+(224*4) = 548*225
sum / total terms = mean ;; 548*225/225 = 548
IMO C
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   17 Jun 2019, 22:23
I did it this way.... since all numbers in the set are divisible by 4, mean should also be divisible by 4. Only 548 is divisible by 4 among all the options. Can anybody tell me if my approach is right or not?
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   20 Jun 2019, 18:45
Bunuel wrote:
If set Q consists of all three digit numbers divisible by 4, what is the mean of the set?

(A) 498
(B) 499.5
(C) 548
(D) 549.5
(E) 550



Can we directly select option C as the answer because it is the only option perfectly divisible by 4 (as all 3 digits are divisible by 4 there mean should also be divisible by 4) ?
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink] New post   11 Dec 2020, 11:24
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Re: If set Q consists of all three digit numbers divisible by 4, what is [#permalink]
11 Dec 2020, 11:24
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