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GMAT Diagnostic Test Question 23 [#permalink]
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29 Sep 2013, 12:03
GMAT Diagnostic Test Question 23Field: 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 07 Oct 2013, 00:24, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 23 [#permalink]
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29 Sep 2013, 12:03
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Explanation:Official Answer: BSet 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. Answer: B. 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 nonnegative 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 2s and/or 5s 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: doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.html
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Re: GMAT Diagnostic Test Question 23 [#permalink]
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13 Oct 2013, 11:19
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]
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13 Oct 2013, 11:33
Armada0023 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.
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Re: GMAT Diagnostic Test Question 23 [#permalink]
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19 Nov 2013, 12:53
Bunuel wrote: Armada0023 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]
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19 Nov 2013, 15:27
Anshulmodi wrote: Bunuel wrote: Armada0023 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]
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20 Nov 2013, 03:05
Hey sorry I missed the division by 2. Thanks
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Re: GMAT Diagnostic Test Question 23 [#permalink]
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03 Jan 2014, 08:47
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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]
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03 Jan 2014, 08:53



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Re: GMAT Diagnostic Test Question 23 [#permalink]
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05 Jan 2014, 18:01
Bunuel wrote: Armada0023 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]
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05 Jan 2014, 18:57
lindt123 wrote: Bunuel wrote: Armada0023 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]
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05 Jan 2014, 21:55
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]
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06 Jan 2014, 03:24




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