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

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Manager
Joined: 09 Jun 2015
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Re: What is the range of a set consisting of the first 100 multi  [#permalink]

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14 Mar 2016, 04:59
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

Multiple of 7 greater than 70 is 77 = 11*7 (the first term)
The last term is 110*7=770 ( the last term)
Range = 770-77 = 693 or simply 99*7 =693
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Re: What is the range of a set consisting of the first 100 multi  [#permalink]

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12 Dec 2016, 13:33
Great Question from the Official Source.
Here is what i did in tis Question=>

First term => 77
Last term= 77+(99)*7 => 770
Hence Range = Highest Value-Lowest Value = 770-77=693

Hence A

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16 Feb 2018, 09:31
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Re: What is the range of a set consisting of the first 100 multi  [#permalink]

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26 Sep 2018, 03:57
The Testmaker here is trying to confuse the reader to complicate the math. However, if we conceptually understand the nature of range, we can see the math is fairly simple.
Quote:
The problem begins with the notion of 100 multiples of 7 greater than 70. Naturally, the first multiple would be 77, the second multiple would be 84, etc. In other words, the Nth multiple of N greater than 70 could be calculated with the equation 70 + 7(N). To calculate the range, we would subtract the 100th multiple from the 1st multiple:

[(70 + 7(100)] - [70 + 7(1)]

7(100) - 7(1)

700 - 7

Quote:
There is an even easier solution, however. As we can see, the two values of 70 cancel. This underscores a fundamental notion of range: if we add the same value to every element in a set, this doesn’t change the range. If we recognized this concept from the very beginning, the math to this problem becomes even simpler. We simply need to subtract the 100th multiple of 7 from the 1st multiple of 7 to get our answer (700 – 7 = 693).

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

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21 Dec 2018, 22:24
)The elements of the set are (70+1x7) , (70+2x7), ………………., (70+100 x 7).
This will be an A.P with positive common difference. So, first term is the lowest and last term is the highest.
First term = 77 & last term = 770
Range = 770 – 77 = 693
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Re: What is the range of a set consisting of the first 100 multi  [#permalink]

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18 Feb 2019, 19:15
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 first multiple of 7 that works is 11 x 7 = 77.

The 100th multiple of 7 (after 77) is 77 + 99 x 7 = 770.

So the range is 770 - 77 = 693.

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Re: What is the range of a set consisting of the first 100 multi   [#permalink] 18 Feb 2019, 19:15

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