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

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What is the range of a set consisting of the first 100 multi [#permalink]

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21 Jun 2008, 20:08
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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: OA

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Last edited by Bunuel on 15 Jan 2014, 00:49, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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21 Jun 2008, 20:16
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A
the first 100 multiples of 7 is 7-700, so the range is 693

It does not matter if you start at 7 or 77
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23 Mar 2011, 22:28
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AnkitK 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

$$a_1=77$$
$$a_{100}=77+(99)*7=693+77$$

Range = 693+77-77=693

Ans: "A"
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09 Apr 2011, 11:08
First Multiple greater than 70 -> 7 * 11 = 77
100th Multiple greater than 70 -> 7 * (11+100) = 770

Range is 770-77 = 693....

Pls can somebody explain where I am making a mistake and why is the answer 777 and not 693
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09 Apr 2011, 21:12
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IEsailor wrote:
First Multiple greater than 70 -> 7 * 11 = 77
100th Multiple greater than 70 -> 7 * (11+100) = 770

Range is 770-77 = 693....

Pls can somebody explain where I am making a mistake and why is the answer 777 and not 693

There are a couple of mistakes you made but they canceled out to give the right answer! (693 is the right answer)

100th multiple greater than 70 will be 7 (10 + 100) or we can say 70 + 7*100 because it has to be the 100th multiple after 70.
When you do 7 * (11+100) i.e. 77 + 7*100, you are calculating the 101th multiple since you are finding the 100th multiple after 77, not 70.

The second error is that 7 * (11+100) = 777, not 770
Actually, 7 (10 + 100) = 770

The range is 770 - 77 = 693
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Status: Up again. Joined: 31 Oct 2010 Posts: 534 Concentration: Strategy, Operations GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Followers: 22 Kudos [?]: 464 [0], given: 75 Re: range [#permalink] ### Show Tags 10 Apr 2011, 10:31 First multiple of 7 after 70= 77 100th multiple of 7 after 70= 110th multiple of 7= 770 Range= 100th multiple-first multiple= 770-77= 693. Ans: A. Ankitk, could you please check whether you've posted the correct OA? Thanks. _________________ My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html Director Joined: 01 Feb 2011 Posts: 755 Followers: 14 Kudos [?]: 125 [0], given: 42 Re: range [#permalink] ### Show Tags 10 Apr 2011, 11:36 sequence is as follows. 77,84,....770 Range = 770-77 = 693 Answer A. Intern Joined: 02 Oct 2010 Posts: 20 Schools: Ross,Duke,Emory Followers: 0 Kudos [?]: 3 [1] , given: 5 Re: range [#permalink] ### Show Tags 11 Apr 2011, 12:11 1 This post received KUDOS 100 multiples of 7 greater than 70 will be as follows : 77+84+91+... = 7 ( 11 + 12 + 13 + .....+110 ) so the last term is 770. Range = 770 - 77 = 693. Ans : A Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 632 Followers: 44 Kudos [?]: 973 [0], given: 39 Re: range [#permalink] ### Show Tags 13 Apr 2011, 07:49 fluke wrote: AnkitK 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 $$a_1=77$$ $$a_{100}=77+(99)*7=693+77$$ Range = 693+77-77=693 Ans: "A" why is 99 is multiplied by 7? _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Math Forum Moderator Joined: 20 Dec 2010 Posts: 2013 Followers: 163 Kudos [?]: 1828 [1] , given: 376 Re: range [#permalink] ### Show Tags 13 Apr 2011, 07:59 1 This post received KUDOS Baten80 wrote: fluke wrote: AnkitK 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 $$a_1=77$$ $$a_{100}=77+(99)*7=693+77$$ Range = 693+77-77=693 Ans: "A" why is 99 is multiplied by 7? In an arithmetic progression $$A_n=A_1+(n-1)*d$$ {77,84,91,98,.....,} $$A_1=First \hspace{2} term=77$$ $$d=Common \hspace{2} Difference=7$$ $$A_{100}=A_1+(n-1)*d$$ $$A_{100}=77+(100-1)*7$$ $$A_{100}=77+99*7$$ $$A_{100}-A_1=77+99*7-77=99*7$$ _________________ GMAT Tutor Joined: 24 Jun 2008 Posts: 1179 Followers: 438 Kudos [?]: 1606 [3] , given: 4 Re: range [#permalink] ### Show Tags 13 Apr 2011, 09:29 3 This post received KUDOS Expert's post 1 This post was BOOKMARKED AnkitK 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 The solutions above are great - just another way to look at things (and the answer certainly is A here): Multiples are equally spaced. If you take any set of 100 consecutive multiples of 7, the range will always be the same; the smallest number in the list is irrelevant. So you can ignore the 'greater than 70' condition in the question, and just look at the first 100 positive multiples of 7: {7, 14, 21, 28, ..., 700}, which has a range of 693. _________________ GMAT Tutor in Toronto If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Manager Status: ==GMAT Ninja== Joined: 08 Jan 2011 Posts: 242 Schools: ISB, IIMA ,SP Jain , XLRI WE 1: Aditya Birla Group (sales) WE 2: Saint Gobain Group (sales) Followers: 5 Kudos [?]: 83 [1] , given: 46 Re: range [#permalink] ### Show Tags 14 Apr 2011, 12:50 1 This post received KUDOS 1 This post was BOOKMARKED fluke wrote: AnkitK 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 $$a_1=77$$ $$a_{100}=77+(99)*7=693+77$$ Range = 693+77-77=693 Ans: "A" why is 99 is multiplied by 7?[/quote] In an arithmetic progression $$A_n=A_1+(n-1)*d$$ {77,84,91,98,.....,} $$A_1=First \hspace{2} term=77$$ $$d=Common \hspace{2} Difference=7$$ $$A_{100}=A_1+(n-1)*d$$ $$A_{100}=77+(100-1)*7$$ $$A_{100}=77+99*7$$ $$A_{100}-A_1=77+99*7-77=99*7$$[/quote] Hey fluke i did it bit simpler without any condition highest no among the first 100 multiple would be 100 x 7 =700 and highest among the first 10 multiple would be 10 x 7 = 70 so if we want to skip the first 10 multiple then we just need to add 70 to the previous 700 right? it came 770 and now first multiple greater than 70 is simply 77 so answer is 770-77 = 693 please guide me if i am right _________________ WarLocK _____________________________________________________________________________ The War is oNNNNNNNNNNNNN for 720+ see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html do not hesitate me giving kudos if you like my post. Intern Joined: 17 Oct 2011 Posts: 11 Followers: 1 Kudos [?]: 5 [2] , given: 2 Re: Range of multiples of 7 [#permalink] ### Show Tags 22 Nov 2011, 19:41 2 This post received KUDOS 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. _________________ We will either find a way, or make one. Please consider giving kudos if you find my post hepful Intern Joined: 20 Aug 2010 Posts: 38 Followers: 1 Kudos [?]: 25 [0], given: 0 Re: Range of multiples of 7 [#permalink] ### Show Tags 23 Nov 2011, 04:52 last term = d*(n-1) d = 7, n=100 7(99) = 693 A. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2291 Kudos [?]: 15146 [2] , given: 224 Re: Range of multiples of 7 [#permalink] ### Show Tags 23 Nov 2011, 05:50 2 This post received KUDOS Expert's post 2 This post was BOOKMARKED 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Range of multiples of 7 [#permalink]

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27 Jun 2012, 13:38
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]

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28 Jun 2012, 01:46
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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]

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28 Jun 2012, 09:52
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]

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17 Jul 2012, 16:19
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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14 Jan 2014, 17:49
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Re: range   [#permalink] 14 Jan 2014, 17:49

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