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# Which of the following cannot be the range of a set consisting of 5 od

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Joined: 02 Sep 2009
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Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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19 Aug 2015, 02:03
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75% (01:33) correct 25% (01:50) wrong based on 218 sessions

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Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

(A) 72
(B) 144
(C) 288
(D) 324
(E) 436

Kudos for a correct solution.

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Posts: 62457
Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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23 Aug 2015, 12:00
4
5
Bunuel wrote:
Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

(A) 72
(B) 144
(C) 288
(D) 324
(E) 436

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

There are infinite possibilities regarding the multiples of 9 that can be included in the set. The set could be any one of the following (or any one of the other infinite possibilities):

S = {9, 27, 45, 63, 81} or

S = {9, 63, 81, 99, 153} or

S = {99, 135, 153, 243, 1071}

The range in each case will be different. The question asks us for the option that ‘cannot’ be the range. Let’s figure out the constraints on the range.

A set consisting of only odd multiples of 9 will have a range that is an even number (Odd Number – Odd Number = Even number)
Also, the range will be a multiple of 9 since both, the smallest and the greatest numbers, will be multiples of 9. So their difference will also be a multiple of 9.

Only one option will not satisfy these constraints. Do you remember the divisibility rule of 9? The sum of the digits of the number should be divisible by 9 for the number to be divisible by 9. The sum of the digits of 436 is 4 + 3 + 6 = 13 which is not divisible by 9. Hence 436 cannot be divisible by 9 and therefore, cannot be the range of the set.

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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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19 Aug 2015, 02:21
1
1
Bunuel wrote:
Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

(A) 72
(B) 144
(C) 288
(D) 324
(E) 436

Ans: E

Solution: sequence of 9 lets say sequence is 9n, 9(n+1), 9(n+2), 9(n+3), 9(n+4)
so range is 9n+36-9n = 36
if we put the different values of n we will get different but the range will be multiple of 36
and only 436 is not multiple of 36
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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20 Aug 2015, 08:00
If the odd multiples of 9 are consecutive then in each case range is a multiple of 72.
If not consecutive then it is coming different no. In each case.
In such case option D is also not a multiple of 72 though it is a multiple of 36.

Then how to choose between D and E?
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Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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20 Aug 2015, 10:39
4
A multiple of 9 minus a multiple of 9 will be a multiple of 9. The only answer that is not a multiple of 9 is E. 4+6+3=13
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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23 Aug 2015, 21:38
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Bunuel wrote:
Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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12 Dec 2016, 12:08
1
Here is my solution to this one->
Questions talks about odd multiples of 9
Lets see some examples =>
9
27
45
etc.

Range = highest value - Lowest value
Range will always be a multiple of 18.

Hence only option that satisfies the given criteria is E.

We could also do this by saying => Since all the numbers are mutes of 9 => Range will be a multiple of 9.
We would still get an E.To be more precise here => Range must be a multiple of 18

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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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18 Dec 2017, 18:10
Best solved by going through the options. Need to check for only 2 properties:
1. Should be even (as it is Odd minus Odd)
2. Should be divisble by 9 (as 9a - 9b = 9(a-b))
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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31 Mar 2018, 06:23
Bunuel wrote:
Bunuel wrote:
The sum of the digits of the number should be divisible by 9 for the number to be divisible by 9.

or be divisible by 3 two times
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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01 May 2018, 10:28
Bunuel wrote:
Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

(A) 72
(B) 144
(C) 288
(D) 324
(E) 436

Kudos for a correct solution.

If you are not able to find solutions, then in such "Cannot be question" always look for an Odd man out in answer options, all are multiple of 9, except E.
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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03 May 2018, 09:57
The difference between the multiple of 9, should be a multiple of 9. So in the given question Option A,B,C,D are multiple of 9. Only E is not a multiple of 9.
So the solution is E.
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Re: Which of the following cannot be the range of a set consisting of 5 od  [#permalink]

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03 May 2018, 15:10
Bunuel wrote:
Which of the following cannot be the range of a set consisting of 5 odd multiples of 9?

(A) 72
(B) 144
(C) 288
(D) 324
(E) 436

When two numbers, each of which is a multiple of 9, are subtracted from each other, their difference is always divisible by 9. For example, 180 - 72 = 108. Thus, in this problem, since the greatest and least values in the set are multiples of 9, then the range of the set = (greatest - least) must be a multiple of 9.

Recall that a quick test for the divisibility of a number by 9 is to add the digits in the number; if that sum is evenly divisible by 9, then the number itself is divisible by 9. Let’s use this rule to test the answer choices.

In answer choice E, we see that 4 + 3 + 6 = 13, which is not divisible by 9; therefore, 436 cannot be the range.

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