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# What is the range of a set consisting of the first 100

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What is the range of a set consisting of the first 100 [#permalink]  22 Nov 2011, 15:44
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What is the range of a set consisting of the first 100 multiples of 7 that are greater than 70?

A. 693
B. 700
C. 707
D. 777
E. 847

[Reveal] Spoiler:
I got the answer as 693 i.e. A. But, I solved it by counting i.e from 77 to 770. Is there any shortcut guys?
[Reveal] Spoiler: OA

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Last edited by Narenn on 21 Sep 2013, 22:26, edited 1 time in total.
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Re: Range of multiples of 7 [#permalink]  22 Nov 2011, 18:41
I got the answer as 693. Here is how I approached it.
first multiple of 7 after 70 is = 70 + 7.
second multiple of 7 after 70 = 70 + 7 + 7.
Here is a pattern 70 + n x 7.

If n =100 => we get 770.

range 770 - 77 = 693.
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Re: Range of multiples of 7 [#permalink]  23 Nov 2011, 03:52
last term = d*(n-1)
d = 7, n=100
7(99) = 693

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Re: Range of multiples of 7 [#permalink]  23 Nov 2011, 04:50
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enigma123 wrote:
What is the range of a set consisting of the first 100 multiples of 7 that are greater than 70?
(A) 693 (B) 700 (C) 707 (D) 777 (E) 847

I got the answer as 693 i.e. A. But, I solved it by counting i.e from 77 to 770. Is there any shortcut guys?

Another logical approach:
In this question, we talk about only positive multiples.

First multiple of 7 = 7*1
Second multiple of 7 = 7*2
...
100th multiple of 7 = 7*100
But we don't want the first ten multiples (upto 7*10).
First acceptable multiple = 7*11 = 77
So to get a total of 100 multiples, we need to go 10 steps extra after 100 and take upto 110th multiple.
110th multiple of 7 = 7*110 = 770
Range = 770 - 77 = 693
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Re: Range of multiples of 7 [#permalink]  27 Jun 2012, 12:38
A

Solved it following way

number of elements in the set formula = (last multiple of x) - (first multiple of x) / x + 1

first multiple of x >70 = 77
(last multiple of x) = x
number of elements in the set = 100

note (x-77) is also a range of set

therefore
(x-77) / 7 + 1 = 100
(x-77) / 7 = 99
(x-77) = 99 * 7 = 693
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Re: What is the range of a set consisting of the first 100 [#permalink]  28 Jun 2012, 00:46
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a_1 = 77
a_2 = 84
a_3 = 91
a_n = 77 + (n-1)*7

Range:a_{100} - a_{1} = (n-1)*7

99*7 = 693
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Re: What is the range of a set consisting of the first 100 [#permalink]  28 Jun 2012, 08:52
I select B first .. then i cheked the OA.... bt my mistake was i was subtracting 70 from 770.. but question is saying above 70..

but i did this way..

till 70 its 10 multiple of 7 but we dont need those multiples, so we will calculate 110 multiple of 7..

7*110=770..

question is saying multiple of 7 above 70.. so first multiple of 7 after 70 is 77 .. so so so.. to get the range we subtract max-min value..

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Re: What is the range of a set consisting of the first 100 [#permalink]  17 Jul 2012, 15:19
First multiple greater than 70: 7x10 is 7x11. 100 first multiples so our last multiple is 7x110.

Range = Maximum - Minimum of a set S.

(7x110) - (7x11) = 7x99 = 693
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Re: What is the range of a set consisting of the first 100 [#permalink]  12 Sep 2013, 22:51
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Re: What is the range of a set consisting of the first 100   [#permalink] 12 Sep 2013, 22:51
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