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a, b, and c are three integers such that a and b are less
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18 Apr 2012, 06:05
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a, b, and c are three integers such that a and b are less than 100, and c is less than 10. If a and b each have 2 more distinct prime factors than c has, is ab/c an integer? (1) The ratio a/b is greater than 1, and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of nonzero digits (for example, 3.4, 2.004, and 12 are terminating decimals). (2) The integer c is not prime.
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Re: a, b, and c are three integers such that a and b are less
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18 Apr 2012, 06:37
carcass wrote: a, b, and c are three integers such that a and b are less than 100, and c is less than 10. If a and b each have 2 more distinct prime factors than c has, is ab/c an integer?
(1) The ratio a/b is greater than 1, and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of nonzero digits (for example, 3.4, 2.004, and 12 are terminating decimals).
(2) The integer c is not prime.
Can someone help me ho to approach this problem ??? They've used a lot of words for this question. Frankly not clear why. Answer is E and the easiest way to solve this problem is number picking: If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^2=4 then the answer is YES; If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^3=8 then the answer is NO.
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Re: a, b, and c are three integers such that a and b are less
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18 Apr 2012, 06:52
thanks. Bunuel I thought the same thing. This is not help the students however .
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Re: a, b, and c are three integers such that a and b are less
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18 Apr 2012, 20:26
Bunuel wrote: carcass wrote: a, b, and c are three integers such that a and b are less than 100, and c is less than 10. If a and b each have 2 more distinct prime factors than c has, is ab/c an integer?
(1) The ratio a/b is greater than 1, and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of nonzero digits (for example, 3.4, 2.004, and 12 are terminating decimals).
(2) The integer c is not prime.
Can someone help me ho to approach this problem ??? They've used a lot of words for this question. Frankly not clear why. Answer is E and the easiest way to solve this problem is number picking: If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^2=4 then the answer is YES; If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^3=8 then the answer is NO. Any way to explain the solution differently? Or maybe point to what is the best way to pick numbers here? I tried the number picking method and got lost. Also, when they say distinct prime factors...doesn't it mean that a and b cannot have the same primes as in your example? Thank you.



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Re: a, b, and c are three integers such that a and b are less
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19 Apr 2012, 02:08
bohdan01 wrote: Bunuel wrote: carcass wrote: a, b, and c are three integers such that a and b are less than 100, and c is less than 10. If a and b each have 2 more distinct prime factors than c has, is ab/c an integer?
(1) The ratio a/b is greater than 1, and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of nonzero digits (for example, 3.4, 2.004, and 12 are terminating decimals).
(2) The integer c is not prime.
Can someone help me ho to approach this problem ??? They've used a lot of words for this question. Frankly not clear why. Answer is E and the easiest way to solve this problem is number picking: If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^2=4 then the answer is YES; If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^3=8 then the answer is NO. Any way to explain the solution differently? Or maybe point to what is the best way to pick numbers here? I tried the number picking method and got lost. Also, when they say distinct prime factors...doesn't it mean that a and b cannot have the same primes as in your example? Thank you. a and b each have 2 more distinct prime factors than c has means that if c has 1 distinct prime factor then a and b each have 3 distinct prime factors (it does not mean a, b, and c cannot have the same primes).
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Re: a, b, and c are three integers such that a and b are less
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19 Apr 2012, 22:00
Agreed , answer is E.
I need some clarification though.
Initially i read the second statement as " c IS a prime number ". Using that premise I concluded that the answer option should be C. Do you agree if the premise were indeed "IS" versus "NOT" the answer would be C and not E?



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Re: a, b, and c are three integers such that a and b are less
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20 Apr 2012, 04:12
shreya717 wrote: Agreed , answer is E.
I need some clarification though.
Initially i read the second statement as " c IS a prime number ". Using that premise I concluded that the answer option should be C. Do you agree if the premise were indeed "IS" versus "NOT" the answer would be C and not E? The answer still would be E. Consider the following cases: If a=2^2*3*5=60, b=2*3*5=30 (a/b=2) and c=5 then the answer is YES; If a=2^2*3*5=60, b=2*3*5=30 (a/b=2) and c=7 then the answer is NO.
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Re: a, b, and c are three integers such that a and b are less
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12 Jul 2017, 14:40
bicu17 wrote: Bunuel wrote: carcass wrote: a, b, and c are three integers such that a and b are less than 100, and c is less than 10. If a and b each have 2 more distinct prime factors than c has, is ab/c an integer?
(1) The ratio a/b is greater than 1, and when expressed as a decimal it is a terminating decimal, meaning that its decimal expression has a finite number of nonzero digits (for example, 3.4, 2.004, and 12 are terminating decimals).
(2) The integer c is not prime.
Can someone help me ho to approach this problem ??? They've used a lot of words for this question. Frankly not clear why. Answer is E and the easiest way to solve this problem is number picking: If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^2=4 then the answer is YES; If a=2*3*7=42, b=2*3*5=30 (a/b=1.4) and c=2^3=8 then the answer is NO. Any way to explain the solution differently? Or maybe point to what is the best way to pick numbers here? I tried the number picking method and got lost. Also, when they say distinct prime factors...doesn't it mean that a and b cannot have the same primes as in your example? Thank you. I'm trying to explain differently. Here, a, b are less than 100. So their prime number range is 2 to 10 that means their possible prime factors are 2;3;5;7. (i) doesn't help. Only we know now ab has at least 2 and 5 as prime factors (ii) ab may or may not have 2 and 3. ( because c may be 1;4;6, or 8) Both. If c is (1 or) 6, ab/c is integer. But if c is 4 or 8? ab may or may not have more that one 2!! So, ans is E. *********** Plz give kudos!!!! Posted from my mobile device




Re: a, b, and c are three integers such that a and b are less
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