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

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a, b, and c are three integers such that a and b are less [#permalink] New post 18 Apr 2012, 05:05
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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 non-zero digits (for example, 3.4, 2.004, and 12 are terminating decimals).

(2) The integer c is not prime.
[Reveal] Spoiler: OA

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Re: a, b, and c are three integers such that a and b are less [#permalink] New post 18 Apr 2012, 05:37
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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 non-zero 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 [#permalink] New post 18 Apr 2012, 05:52
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Re: a, b, and c are three integers such that a and b are less [#permalink] New post 18 Apr 2012, 19:26
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 non-zero 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 [#permalink] New post 19 Apr 2012, 01:08
Expert's post
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 non-zero 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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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.


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Re: a, b, and c are three integers such that a and b are less [#permalink] New post 19 Apr 2012, 21:00
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 [#permalink] New post 20 Apr 2012, 03:12
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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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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.


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Re: a, b, and c are three integers such that a and b are less [#permalink] New post 30 Aug 2015, 09:48
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Re: a, b, and c are three integers such that a and b are less   [#permalink] 30 Aug 2015, 09:48
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