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# A set of data consists of {3, 5, 7, 9, a}. If the range of the set is

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Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [1], given: 12181

A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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22 Aug 2017, 22:48
1
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Question Stats:

84% (01:07) correct 16% (00:10) wrong based on 94 sessions

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A set of data consists of {3, 5, 7, 9, a}. If the range of the set is equal to 2a, what is the value of a?

A. -3
B. 1
C. 3
D. 5
E. 6
[Reveal] Spoiler: OA

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Kudos [?]: 128641 [1], given: 12181

Intern
Joined: 15 Feb 2017
Posts: 39

Kudos [?]: 15 [1], given: 0

A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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22 Aug 2017, 22:57
1
KUDOS
Range = a-3 if a is largest
a-3=2a, a=-3 In this case a is not the largest element as assumed.
so range =3-a=2a, a=1

Kudos [?]: 15 [1], given: 0

Director
Joined: 18 Aug 2016
Posts: 511

Kudos [?]: 139 [0], given: 123

GMAT 1: 630 Q47 V29
Re: A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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22 Aug 2017, 23:36
Bunuel wrote:
A set of data consists of {3, 5, 7, 9, a}. If the range of the set is equal to 2a, what is the value of a?

A. -3
B. 1
C. 3
D. 5
E. 6

range is 2a
Lets substitute value of a
a=-3 then range will be -6...not possible (range cannot be negative)
a=1 then range will be 2....not possible (range will be 9-1=8)
a=3 then range will be 6...correct (range will be 9-3=6)
a=5 then range will be 10...not possible (range will be 9-3=6)
a=6 then range will be 12..not possible (range will be 9-3=6)

Hence C
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Kudos [?]: 139 [0], given: 123

Manager
Joined: 14 Sep 2016
Posts: 136

Kudos [?]: 5 [0], given: 35

A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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23 Aug 2017, 00:46
If a > 9

then in that case a-3 = 2a => a = -3 hence, this is not possible.

ii ) a < 3

then in this case 9-a = 2a > a = 3

if a > 3 then the minimum value of the set will be = 3
since we know "a" cannot be greater than 9

hence range we get

9-3 = 6 => a = 3

Kudos [?]: 5 [0], given: 35

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Joined: 09 Feb 2015
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GPA: 2.8
Re: A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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23 Aug 2017, 01:48
Bunuel wrote:
A set of data consists of {3, 5, 7, 9, a}. If the range of the set is equal to 2a, what is the value of a?

A. -3
B. 1
C. 3
D. 5
E. 6

I found it easier to solve this by evaluating the options! Only C satisfies.

Kudos [?]: 3 [0], given: 196

Director
Joined: 22 May 2016
Posts: 802

Kudos [?]: 254 [0], given: 544

A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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23 Aug 2017, 05:46
Bunuel wrote:
A set of data consists of {3, 5, 7, 9, a}. If the range of the set is equal to 2a, what is the value of a?

A. -3
B. 1
C. 3
D. 5
E. 6

I think the answer is C, but I have a question.

I did this problem in two ways and got the same answer both times. I am uneasy about the second method, however, because I can't explain, with precision, why it works. I think my brain is frozen.

First I just used answer choices, then algebra.

For answer choices, only 3, Answer C, works. If a = 3, (9 - 3) = 6, and 6 = 2a.

Then I wrote:
9 - a = 2a
9 = 3a
a = 3

I think that equation is legitimate here because the range is a multiple of the difference of two numbers in the set. That's as far as I get on the explanation front.

I think I grasp for something I already know about number properties where x is greater than y. Of course x - y CAN be a multiple of y. But there's a difference between possibility and necessity, and I worry that my equation inaccurately suggests the latter.

(Waffling yet again, I think: "But these conditions mandate that necessity.")

IS the equation legitimate? If so, would someone please explain that which I can intuit but can't quite explain? Why does the equation work? Why does "a" have to be the lower limit (9 - a) of the range?

Sorry if this question is a bad case of missing the obvious. I would appreciate greatly any help!

Kudos [?]: 254 [0], given: 544

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A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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23 Aug 2017, 09:04
1
KUDOS
Hi genxer123,

Consider the set {1, 5, 7, 9, a}
In this case, the value for 'a' would be 4 as the range of numbers '2a' is 8

In this case(the problem in hand), it just so happens that a is also the lowest number,
so your equation 9 - a = 2a works.

IMO, the only way we can do this problem is go from the answer choices.
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Kudos [?]: 593 [1], given: 16

Director
Joined: 22 May 2016
Posts: 802

Kudos [?]: 254 [0], given: 544

A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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23 Aug 2017, 11:31
pushpitkc wrote:
Hi genxer123,

Consider the set {1, 5, 7, 9, a}
In this case, the value for 'a' would be 4 as the range of numbers '2a' is 8

In this case(the problem in hand), it just so happens that a is also the lowest number,
so your equation 9 - a = 2a works.

IMO, the only way we can do this problem is go from the answer choices.

Best of all, it confirms my suspicion that something was off about that equation, especially in terms of generalization. My brain is now thawed. Thanks and kudos.

Kudos [?]: 254 [0], given: 544

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Re: A set of data consists of {3, 5, 7, 9, a}. If the range of the set is [#permalink]

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25 Aug 2017, 11:05
Bunuel wrote:
A set of data consists of {3, 5, 7, 9, a}. If the range of the set is equal to 2a, what is the value of a?

A. -3
B. 1
C. 3
D. 5
E. 6

We have to consider the following cases: 1) a is the largest number, 2) a is the smallest number, 3) a is neither the largest number nor the smallest number. Let’s analyze each case.

Case 1: a is the largest number

If a is the largest number (i.e., at least 9), then 3 is the smallest number and we have:

a - 3 = 2a

-a = 3

a = -3

However, since a must be at least 9, this case is not viable.

Case 2: a is the smallest number

If a is the smallest number (i.e., at most 3), then 9 is the largest number and we have:

9 - a = 2a

9 = 3a

a = 3

Since a is indeed at most 3, a can be 3. Although we have found a possible value for a, let’s analyze case 3 also.

Case 3: a is neither the largest number nor the smallest number

If a is neither the largest number nor the smallest number (i.e., 3 < a < 9), then 9 is the largest number and 3 is the smallest number, and hence we have:

9 - 3 = 2a

6 = 2a

a = 3

We have validated that a = 3 works, as was found in Case 2.

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Re: A set of data consists of {3, 5, 7, 9, a}. If the range of the set is   [#permalink] 25 Aug 2017, 11:05
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