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a, b, and c are three integers such that a and b are less [#permalink]
18 Apr 2012, 05:05

Expert's post

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

38% (01:05) correct
63% (01:49) wrong based on 16 sessions

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).

Re: a, b, and c are three integers such that a and b are less [#permalink]
18 Apr 2012, 05:37

1

This post received KUDOS

Expert's post

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. _________________

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

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

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

Re: a, b, and c are three integers such that a and b are less [#permalink]
20 Apr 2012, 03:12

Expert's post

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. _________________