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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

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

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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, 04:50

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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
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