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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]

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New post 18 Apr 2012, 06:05
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Question Stats:

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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.

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Re: a, b, and c are three integers such that a and b are less  [#permalink]

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New post 18 Apr 2012, 06:37
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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.
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Re: a, b, and c are three integers such that a and b are less  [#permalink]

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New post 18 Apr 2012, 06:52
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Re: a, b, and c are three integers such that a and b are less  [#permalink]

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New post 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 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]

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New post 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 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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Re: a, b, and c are three integers such that a and b are less  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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 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.



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.


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Re: a, b, and c are three integers such that a and b are less   [#permalink] 12 Jul 2017, 14:40
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