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# GMAT Diagnostic Test Question 23

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GMAT Diagnostic Test Question 23 [#permalink]  29 Sep 2013, 11:03
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GMAT Diagnostic Test Question 23
Field: Statistics, Number properties
Difficulty: 750

Set A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the set less than 1/5?

(1) Reciprocal of the median is a prime number
(2) The product of any two terms of the set is a terminating decimal
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Last edited by Bunuel on 06 Oct 2013, 23:24, edited 1 time in total.
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Founder
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Joined: 04 Dec 2002
Posts: 13021
Location: United States (WA)
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Followers: 2918

Kudos [?]: 15193 [4] , given: 3940

Re: GMAT Diagnostic Test Question 23 [#permalink]  29 Sep 2013, 11:03
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Explanation:

Set A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the set less than 1/5?

(1) Reciprocal of the median is a prime number. If all the terms equal 1/2, then the median=1/2 and the answer is NO but if all the terms equal 1/7, then the median=1/7 and the answer is YES. Not sufficient.

(2) The product of any two terms of the set is a terminating decimal. This statement implies that the set must consists of 1/2 or/and 1/5. Thus the median could be 1/2, 1/5 or (1/5+1/2)/2=7/20. None of the possible values is less than 1/5. Sufficient.

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^3$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html
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Re: GMAT Diagnostic Test Question 23 [#permalink]  13 Oct 2013, 10:19
Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!
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Re: GMAT Diagnostic Test Question 23 [#permalink]  13 Oct 2013, 10:33
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Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.
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Re: GMAT Diagnostic Test Question 23 [#permalink]  19 Nov 2013, 11:53
Bunuel wrote:
Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.

Just want to confirm the following:

1. (1/5+1/2)/2 = 7/10 and not 7/20 (as its mentioned twice)

2. If the theory part of 2^n*5^m was not known than it would not had been possible to answer the question, right? I mean is there any other way?
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Re: GMAT Diagnostic Test Question 23 [#permalink]  19 Nov 2013, 14:27
Expert's post
Anshulmodi wrote:
Bunuel wrote:
Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.

Just want to confirm the following:

1. (1/5+1/2)/2 = 7/10 and not 7/20 (as its mentioned twice)

2. If the theory part of 2^n*5^m was not known than it would not had been possible to answer the question, right? I mean is there any other way?

1. (1/5+1/2)/2 = 7/20, not 7/10. Check your math.
2. Yes, you need to know this property to solve the question.
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Re: GMAT Diagnostic Test Question 23 [#permalink]  20 Nov 2013, 02:05
Hey sorry I missed the division by 2.

Thanks
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Re: GMAT Diagnostic Test Question 23 [#permalink]  03 Jan 2014, 07:47
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bb wrote:
For example: is a terminating decimal , as (denominator) equals to .

Is there a typo in the explanation, under the theory portion - for the denominator 250?
2*5^3= 250 instead of 2*5^2 = 50?
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Re: GMAT Diagnostic Test Question 23 [#permalink]  03 Jan 2014, 07:53
Expert's post
alpsang wrote:
bb wrote:
For example: is a terminating decimal , as (denominator) equals to .

Is there a typo in the explanation, under the theory portion - for the denominator 250?
2*5^3= 250 instead of 2*5^2 = 50?

Yes, it was a typo. Sorry for that. Edited. Thank you.
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Re: GMAT Diagnostic Test Question 23 [#permalink]  05 Jan 2014, 17:01
Bunuel wrote:
Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.

hi i did not understand why statement b is right??
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Re: GMAT Diagnostic Test Question 23 [#permalink]  05 Jan 2014, 17:57
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lindt123 wrote:
Bunuel wrote:
Hi bb,

Could you elaborate your work for statement 2? I'm confused how (1/5+1/2)/2=7/20 comes into play. The statement mentions product of two terms (which would be 1/10), how does that play a role?

Thanks!

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.

hi i did not understand why statement b is right??

Can you please specify which part is unclear? Thank you.
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Re: GMAT Diagnostic Test Question 23 [#permalink]  05 Jan 2014, 20:55
Thanks![/quote]

From (2) it follows that the set must consists of 1/2 or/and 1/5. It cannot have any other reciprocal of a prime since in this case the product of ANY two terms in the set won't be a terminating decimal (refer to Theory part in the post). For example if there is 1/3 and say 1/2 in the set, then 1/3*1/2=1/6, which is not a terminating decimal.

Now, if the set has only 1/2 or/and 1/5 in it, then the median of the set can be 1/5 (if the two middle terms are 1/5), 1/2 (if the two middle terms are 1/2) or (1/5+1/2)/2=7/20 (if the two middle terms are 1/5 and 1/2).

Hope it' clear.[/quote]

hi i did not understand why statement b is right?? [/quote]

Can you please specify which part is unclear? Thank you.[/quote]

WHY THE ANSWER IS B AND NOT A..I WAS NOT ABLE TO UNDERSTAND THE REASONING BEHIND STATEMENT B
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Re: GMAT Diagnostic Test Question 23 [#permalink]  06 Jan 2014, 02:24
Expert's post
lindt123 wrote:
WHY THE ANSWER IS B AND NOT A..I WAS NOT ABLE TO UNDERSTAND THE REASONING BEHIND STATEMENT B

That's given in the solution. I meant what part of the solution didn't you understand?
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Re: GMAT Diagnostic Test Question 23   [#permalink] 06 Jan 2014, 02:24
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# GMAT Diagnostic Test Question 23

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