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M22-15

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:16
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67% (01:00) correct 33% (01:35) wrong based on 126 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. $$\frac{49}{4}$$

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16 Sep 2014, 01:16
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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01 Jul 2015, 19:07
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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, 03:10
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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31 Oct 2015, 04:00
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, 04:29
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, 05:02
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, 11:22
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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, 06:10
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, 22:54
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, 23:18
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, 08:07
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.

Sent from my iPhone using GMAT Club Forum mobile app
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19 Apr 2018, 11:24
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...

Hi Bunuel,

I agree with michaelyb. It is possible to revise the question?

"If after a number was added to a set consisting entirely of all the 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?"

Thank you.
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09 May 2018, 11:30
In my opionion the question is absolutely clear. No revision needed...
"...set consisting of all distinct one-digit prime integers..."
all one-digit primes (2,3,5,7) and no other integers.
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