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If a, b, c, d and e are integers and p=2^a3^b and q=2^c3

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Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3 [#permalink]

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New post 21 Sep 2017, 20:35
goalMBA1990 wrote:
Bunuel wrote:
goalMBA1990 wrote:
Thank you very much for clarification. So answer we would be B for above question. Correct?

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In the below question:
Is P/Q a terminating decimal?

(1) P is a factor of 100
(2) Q is a factor of 100

Does the solution mention that p can be 1/6 for the first statement or for the second? If for (2), then yes p could be 1/6 and in this case (2) is not sufficient. When combined, since p is a factor of 100, then it must be an integer, thus p/q will be terminating decimal and the answer would be C.


Whether it is mentioned or not, how any fraction become factor of any integer? How can we assume fraction for P or Q?

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For (1) since p is a factor of 100, then it must be an integer. But q can be any real number: fraction, integer, irrational, ...
For (2) since q is a factor of 100, then it must be an integer. But p can be any real number: fraction, integer, irrational, ...
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Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3 [#permalink]

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New post 23 Oct 2017, 23:19
Bunuel wrote:
enigma123 wrote:
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?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a 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 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.

BACK TO THE ORIGINAL QUESTION:
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?

Question: is \(\frac{2^a*3^b}{2^c*3^d*5^e}\) a terminating decimal? The question basically asks whether we cans reduce 3^d in the denominator so to have only powers of 2 and 5 left, which can be rephrased is b (the power of 3 in the nominator) greater than or equal to d (the power of 3 in the denominator): is b>=d?

(1) a > c. Not sufficient.
(2) b > d. Sufficient.

Answer: B.

Hope it helps.




-----------------

as you said that both the numerator and denominator should be reduced to the lower term ,,, but as in the question, it was clearly seen that 2^a and 2^c is present in both numerator and denominator so the term is not reduced to its lowest term...

now from statement 1, we can clearly state that 2 will not present in the denominator and we have to have only 2 and 5 in the denominator to say that the term would be terminating. Hence statement 1 looks sufficient to me

could you please help me explain this ?

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Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3 [#permalink]

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New post 24 Oct 2017, 00:06
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Expert's post
priyanknema wrote:
Bunuel wrote:
enigma123 wrote:
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?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a 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 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.

BACK TO THE ORIGINAL QUESTION:
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?

Question: is \(\frac{2^a*3^b}{2^c*3^d*5^e}\) a terminating decimal? The question basically asks whether we cans reduce 3^d in the denominator so to have only powers of 2 and 5 left, which can be rephrased is b (the power of 3 in the nominator) greater than or equal to d (the power of 3 in the denominator): is b>=d?

(1) a > c. Not sufficient.
(2) b > d. Sufficient.

Answer: B.

Hope it helps.




-----------------

as you said that both the numerator and denominator should be reduced to the lower term ,,, but as in the question, it was clearly seen that 2^a and 2^c is present in both numerator and denominator so the term is not reduced to its lowest term...

now from statement 1, we can clearly state that 2 will not present in the denominator and we have to have only 2 and 5 in the denominator to say that the term would be terminating. Hence statement 1 looks sufficient to me

could you please help me explain this ?


If the denominator of a reduced fraction has only 2's OR only 5's OR only 2's and 5's the fraction will be a terminating decimal.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135256 [1], given: 12679

Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3   [#permalink] 24 Oct 2017, 00:06

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