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What could be the range of a set consisting of odd multiples

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by Brent@GMATPrepNow » Sun Feb 25, 2018 9:39 am
ardz24 wrote:What could be the range of a set consisting of odd multiples of 7?

A. 21
B. 24
C. 35
D. 62
E. 70
We could just test numbers.
7, 21 and 77 are odd multiples of 7.
The range of these numbers = 77 - 7 = 70

Answer: E

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by [email protected] » Sun Feb 25, 2018 6:08 pm
Hi ardz24,

We're asked for what COULD be the RANGE of a set consisting of ODD multiples of 7. This question can be solved in a couple of different ways. Here's how you can use Number Properties - and the answer choices - to find the correct answer.

To start, we know that all of the numbers in the set are ODD numbers. The RANGE of that set will be the (biggest odd multiple of 7) - (smallest odd multiple of 7)....
(Odd) - (Odd) = Even
Thus, the range MUST be EVEN

In addition, subtracting a multiple of 7 from another multiple of 7 will give us a number that is ALSO a multiple of 7.

There's only one answer choice that is an EVEN multiple of 7...

Final Answer: E

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by deloitte247 » Sun Mar 04, 2018 12:28 pm
Let 'S' be the set of odd multiples of 7. i.e S={7,21,35,49,...}
where Tn=7(2n-1)
Range of a set is the difference between the largest and smallest numbers in the set. For set 'S' that contain 'n' elements, the smallest number is 7=T1
$$or\left[T1=7[2(1-1\right]=\ 7$$
$$l\arg est\ number\ is\ Tn\ =\ 7\left(2n-1\right)$$
$$Therefore,\ Tn-T1=7\left(2n-1\right)-7$$
$$=7\left(2n-2\right)$$
$$=7\left(2\right)\left(n-1\right)=14\left(n-1\right)$$
$$The\ value\ of\ \left(Tn-T1\right)\ is\ always\ a\ even\ multiple\ of\ 7.\ i.e$$
$$Tn-T1=\left[7\left(n-1\right)\right]2\ \ \ \ \left(multiples\ of\ 2\ are\ even\right)$$
$$from\ the\ options\ given,\ only\ '70'\ is\ an\ even\ multiple\ of\ '7'$$
$$Answer\ =\ 70....\ Option\ E$$
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