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

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by Azizakaria » Thu Feb 11, 2016 5:52 am
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

why the answer is a
is there some kind of a rule here or equation ?
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by GMATGuruNY » Thu Feb 11, 2016 5:54 am
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
Range = biggest - smallest.

Any set of 100 consecutive multiples of 7 will have the SAME RANGE.
Thus, the problem above is the same as the following:
What is the range of the first 100 positive multiples of 7?

First positive multiple of 7 = 1*7 = 7.
100th positive multiple of 7 = 100*7 = 700.
Range = biggest - smallest = 700-7 = 693.

The correct answer is A.
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by Azizakaria » Thu Feb 11, 2016 6:07 am
Range = biggest - smallest.

Any set of 100 consecutive multiples of 7 will have the SAME RANGE.
Thus, the problem above is the same as the following:
What is the range of the first 100 positive multiples of 7?

First positive multiple of 7 = 1*7 = 7.
100th positive multiple of 7 = 100*7 = 700.
Range = biggest - smallest = 700-7 = 693.

The correct answer is A.[/quote]

Yes, but it says " that are greater than 70" how it can be the same as "the first 100 positive multiples of 7" ?
shouldn't I add 70 to the total because I'm skipping the 7 multiplies till 70 ?
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by DavidG@VeritasPrep » Thu Feb 11, 2016 6:19 am
Azizakaria wrote:Range = biggest - smallest.

Any set of 100 consecutive multiples of 7 will have the SAME RANGE.
Thus, the problem above is the same as the following:
What is the range of the first 100 positive multiples of 7?

First positive multiple of 7 = 1*7 = 7.
100th positive multiple of 7 = 100*7 = 700.
Range = biggest - smallest = 700-7 = 693.

The correct answer is A.

Yes, but it says " that are greater than 70" how it can be the same as "the first 100 positive multiples of 7" ?
shouldn't I add 70 to the total because I'm skipping the 7 multiplies till 70 ?
No - the first multiple of 7 greater than 70 is 70 + 1*7 = 77.
The 100th multiple of 7 greater than 70 is 70 + 100*7 = 770.
Range = 770 - 77 = 693.

Mitch was simply showing that the range from 77 to 770 will be identical to the range from 7 to 700, because you're changing both the high and the low by 70, and thus not altering the range.
Last edited by DavidG@VeritasPrep on Thu Feb 11, 2016 6:54 am, edited 1 time in total.
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by GMATGuruNY » Thu Feb 11, 2016 6:27 am
Azizakaria wrote:
Range = biggest - smallest.

Any set of 100 consecutive multiples of 7 will have the SAME RANGE.
Thus, the problem above is the same as the following:
What is the range of the first 100 positive multiples of 7?

First positive multiple of 7 = 1*7 = 7.
100th positive multiple of 7 = 100*7 = 700.
Range = biggest - smallest = 700-7 = 693.

The correct answer is A
.

Yes, but it says " that are greater than 70" how it can be the same as "the first 100 positive multiples of 7" ?
shouldn't I add 70 to the total because I'm skipping the 7 multiplies till 70 ?
ANY SET of 100 consecutive multiples of x will have the SAME RANGE.

Case 1: First 100 positive multiples of 7
smallest = 1*7 = 7.
biggest = 100*7 = 700.
range = biggest - smallest = 700-7 = 693.

Case 2: First 100 positive multiple of 7 greater than 70
To determine the smallest and the biggest, add 70 to each of the blue values in Case 1.
smallest = 7 + 70 = 77.
biggest = 700 + 70 = 770.
range = biggest - smallest = 770 - 77 = 693.

In each case, the range is 693.
The reason:
When we proceed from Case 1 to Case 2, the two values used to calculate the range -- the smallest and the biggest -- each increase by the SAME AMOUNT (70).
Since both values increase by the same amount, their difference does not change.
The result:
The range in each case is THE SAME.
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by Matt@VeritasPrep » Thu Feb 11, 2016 5:42 pm
Or, put in one equation, you're going from

70 + 1*7

to

70 + 100*7

so your range is 77 to 770, or 693.
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by masoom j negi » Fri Dec 21, 2018 9:16 pm
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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by Scott@TargetTestPrep » Mon Feb 18, 2019 6:00 pm
Azizakaria 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 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.

Answer: A

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