Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Apr 2015, 23:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Director
Joined: 10 Feb 2006
Posts: 664
Followers: 3

Kudos [?]: 119 [0], given: 0

What is the range of a set consisting of the first 100 multi [#permalink]  21 Jun 2008, 19:08
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:00) correct 38% (00:57) wrong based on 139 sessions
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

_________________

GMAT the final frontie!!!.

Last edited by Bunuel on 14 Jan 2014, 23:49, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 23 Sep 2007
Posts: 797
Followers: 5

Kudos [?]: 99 [0], given: 0

Re: Range [#permalink]  21 Jun 2008, 19:16
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
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2035
Followers: 135

Kudos [?]: 1098 [1] , given: 376

Re: range [#permalink]  23 Mar 2011, 21:28
1
KUDOS
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"
_________________
Senior Manager
Joined: 12 Oct 2009
Posts: 268
Followers: 2

Kudos [?]: 52 [0], given: 4

Re: range [#permalink]  09 Apr 2011, 10:08
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5429
Location: Pune, India
Followers: 1324

Kudos [?]: 6709 [0], given: 176

Re: range [#permalink]  09 Apr 2011, 20:12
Expert's post
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
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Director
Status: Up again.
Joined: 31 Oct 2010
Posts: 543
Concentration: Strategy, Sustainability
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 17

Kudos [?]: 130 [0], given: 75

Re: range [#permalink]  10 Apr 2011, 09:31
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: from-620-to-710-my-gmat-journey-114437.html

Director
Joined: 01 Feb 2011
Posts: 763
Followers: 14

Kudos [?]: 68 [0], given: 42

Re: range [#permalink]  10 Apr 2011, 10:36
sequence is as follows.

77,84,....770

Range = 770-77 = 693

Intern
Joined: 01 Oct 2010
Posts: 20
Schools: Ross,Duke,Emory
Followers: 0

Kudos [?]: 3 [1] , given: 5

Re: range [#permalink]  11 Apr 2011, 11:11
1
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: 662
Followers: 36

Kudos [?]: 346 [0], given: 38

Re: range [#permalink]  13 Apr 2011, 06:49
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: 2035
Followers: 135

Kudos [?]: 1098 [1] , given: 376

Re: range [#permalink]  13 Apr 2011, 06:59
1
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 Instructor
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 280

Kudos [?]: 793 [2] , given: 3

Re: range [#permalink]  13 Apr 2011, 08:29
2
KUDOS
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.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 247
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Followers: 4

Kudos [?]: 54 [1] , given: 46

Re: range [#permalink]  14 Apr 2011, 11:50
1
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: 16
Followers: 1

Kudos [?]: 4 [1] , given: 2

Re: Range of multiples of 7 [#permalink]  22 Nov 2011, 18:41
1
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: 41
Followers: 1

Kudos [?]: 16 [0], given: 0

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

A.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5429
Location: Pune, India
Followers: 1324

Kudos [?]: 6709 [2] , given: 176

Re: Range of multiples of 7 [#permalink]  23 Nov 2011, 04:50
2
KUDOS
Expert's post
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

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Manager
Joined: 28 Jul 2011
Posts: 218
Followers: 0

Kudos [?]: 52 [0], given: 14

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
Current Student
Joined: 08 Jan 2009
Posts: 331
GMAT 1: 770 Q50 V46
Followers: 23

Kudos [?]: 105 [1] , given: 7

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

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

$$99*7 = 693$$
Senior Manager
Joined: 06 Aug 2011
Posts: 409
Followers: 2

Kudos [?]: 78 [0], given: 82

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..

_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Intern
Joined: 30 Apr 2010
Posts: 21
Followers: 0

Kudos [?]: 11 [0], given: 2

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.

$$(7x110) - (7x11) = 7x99 = 693$$
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4668
Followers: 290

Kudos [?]: 52 [0], given: 0

Re: range [#permalink]  14 Jan 2014, 16:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: range   [#permalink] 14 Jan 2014, 16:49

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
What is the range of set S? 1 21 Jun 2014, 00:35
3 Set S contains 100 consecutive integers. If the range of the 2 06 Apr 2014, 14:40
What is the range of a set consisting of the first 100 0 12 Sep 2013, 22:51
14 What could be the range of a set consisting of odd multiples 14 27 May 2010, 00:48
What is the price range for 100 books? (1) The most 3 05 Sep 2008, 18:02
Display posts from previous: Sort by