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M22-15

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:16
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Difficulty:

45% (medium)

Question Stats:

70% (01:10) correct 30% (02:06) wrong based on 37 sessions

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If after a number was added to a set consisting of all distinct one-digit prime integers, the median of the set grew by 25%, which of the following cannot be the value of the number added?

A. 4.8
B. 5.0
C. $$\sqrt{29}$$
D. 7.7
E. $$\frac{49}{4}$$
[Reveal] Spoiler: OA

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Kudos [?]: 135450 [0], given: 12695

Math Expert
Joined: 02 Sep 2009
Posts: 42577

Kudos [?]: 135450 [0], given: 12695

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16 Sep 2014, 00:16
Expert's post
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Official Solution:

If after a number was added to a set consisting of all distinct one-digit prime integers, the median of the set grew by 25%, which of the following cannot be the value of the number added?

A. 4.8
B. 5.0
C. $$\sqrt{29}$$
D. 7.7
E. $$\frac{49}{4}$$

The original set was $$\{2, 3, 5, 7\}$$. Its median was $$\frac{3 + 5}{2} = 4$$. The median of the new set $$= 4*1.25 = 5$$. Thus, the number added cannot be less than 5.

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Joined: 11 Nov 2014
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Concentration: Technology, Strategy
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WE: Consulting (Consulting)

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01 Jul 2015, 18:07
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It´s not clear that the set has all 4 one-digit integers that are prime. One may understand that all items in the set are one digit integers (which would give you {2,3} or {3,5} or {2,3,5}.... just the way it´s written there is room for misunderstanding...

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31 Oct 2015, 02:10
michaelyb wrote:
It´s not clear that the set has all 4 one-digit integers that are prime. One may understand that all items in the set are one digit integers (which would give you {2,3} or {3,5} or {2,3,5}.... just the way it´s written there is room for misunderstanding...

Also, nowhere is it mentioned that all of them are positive.

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Math Expert
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31 Oct 2015, 03:00
jamesav wrote:
michaelyb wrote:
It´s not clear that the set has all 4 one-digit integers that are prime. One may understand that all items in the set are one digit integers (which would give you {2,3} or {3,5} or {2,3,5}.... just the way it´s written there is room for misunderstanding...

Also, nowhere is it mentioned that all of them are positive.

Only positive integers can be primes.
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07 Mar 2017, 03:29
hi Brunel how can you pick these numbers.For example if set is 2,3,5 then median is 3.after adding x median will become 3.75 so as per your statement number can't be less than 3.75

kindly clear where I am going wrong in my understanding

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07 Mar 2017, 04:02
sidagar wrote:
hi Brunel how can you pick these numbers.For example if set is 2,3,5 then median is 3.after adding x median will become 3.75 so as per your statement number can't be less than 3.75

kindly clear where I am going wrong in my understanding

The question says that the set consists of single-digit prime integers. There are four single digit primes: 2, 3, 5, and 7. So, the set is {2, 3, 5, 7} not {2, 3, 5}
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04 Sep 2017, 10:22
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I think this is a poor-quality question. It says all distinct one digit prime numbers, however it can be unclear. I understood it as ALL the numbers in the set were distinict prime digits, not that they set included ALL the prime single digits

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06 Nov 2017, 05:10
Bunuel wrote:
the number added cannot be less than 5.

Hello Bunuel, can you please explain this in more detail? Would be happy to understand this.

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15 Nov 2017, 21:54
since the new median is 5, all options except B are wrong....????

in other words, if the question mentioned that the median grew by atleast 35%, A would be the answer.

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15 Nov 2017, 22:18
sevenplusplus wrote:
If after a number was added to a set consisting of all distinct one-digit prime integers, the median of the set grew by 25%, which of the following cannot be the value of the number added?

A. 4.8
B. 5.0
C. $$\sqrt{29}$$
D. 7.7
E. $$\frac{49}{4}$$

The original set was $$\{2, 3, 5, 7\}$$. Its median was $$\frac{3 + 5}{2} = 4$$. The median of the new set $$= 4*1.25 = 5$$. Thus, the number added cannot be less than 5.

since the new median is 5, all options except B are wrong....????

in other words, if the question mentioned that the median grew by atleast 35%, A would be the answer.

You are wrong.

The original set = {2, 3, 5, 7}.
The original median = 4.

B. New number = 5;
New set = {2, 3, 5, 5, 7}.
New median = 5.

C. New number = $$\sqrt{29}$$;
New set = 2, 3, 5, $$\sqrt{29}$$, 7}.
New median = 5.

D. New number = 7.7;
New set = {2, 3, 5, 7, 7.7}.
New median = 5.

E. New number = $$\frac{49}{4}$$;
New set = {2, 3, 5, 7, 49/4}.
New median = 5.
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16 Nov 2017, 07:07
Bunuel wrote:
sevenplusplus wrote:
If after a number was added to a set consisting of all distinct one-digit prime integers, the median of the set grew by 25%, which of the following cannot be the value of the number added?

A. 4.8
B. 5.0
C. $$\sqrt{29}$$
D. 7.7
E. $$\frac{49}{4}$$

The original set was $$\{2, 3, 5, 7\}$$. Its median was $$\frac{3 + 5}{2} = 4$$. The median of the new set $$= 4*1.25 = 5$$. Thus, the number added cannot be less than 5.

since the new median is 5, all options except B are wrong....????

in other words, if the question mentioned that the median grew by atleast 35%, A would be the answer.

You are wrong.

The original set = {2, 3, 5, 7}.
The original median = 4.

B. New number = 5;
New set = {2, 3, 5, 5, 7}.
New median = 5.

C. New number = $$\sqrt{29}$$;
New set = 2, 3, 5, $$\sqrt{29}$$, 7}.
New median = 5.

D. New number = 7.7;
New set = {2, 3, 5, 7, 7.7}.
New median = 5.

E. New number = $$\frac{49}{4}$$;
New set = {2, 3, 5, 7, 49/4}.
New median = 5.

Thanks. That clarifies.

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