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Each factor of 210 is inscribed on its own plastic ball, and

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Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 30 Apr 2012, 06:22
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Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?

A. 1/16
B. 5/42
C. 1/8
D. 3/16
E. 1/4


Please post the fastest method with time.
[Reveal] Spoiler: OA
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 30 Apr 2012, 06:31
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BDSunDevil wrote:
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?

A. 1/16
B. 5/42
C. 1/8
D. 3/16
E. 1/4


Please post the fastest method with time.


210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;

So, the probability is 2/16=1/8.

Answer: C.


Finding the Number of Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

For more on these issues check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 30 May 2012, 11:26
Sorry Bunuel,

i don't get it.

as you said:

210 = 2*5*7*3 and 42 = 2*7*3;
so i would say there are 5 multiples of 42 between 42 and 210.

since I'm obviously wrong, can you please help me to understand where's the mistake?

thanks in advance
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 30 May 2012, 21:23
maffo wrote:
Sorry Bunuel,

i don't get it.

as you said:

210 = 2*5*7*3 and 42 = 2*7*3;
so i would say there are 5 multiples of 42 between 42 and 210.

since I'm obviously wrong, can you please help me to understand where's the mistake?

thanks in advance

By the time we are waiting for Bunuel's reply , I will attempt to answer this. :roll:
I think you mean 42*1, 42*2 ... 42*5 as 5 multiples.
But the plastic balls that we have with us, do not have these numbers inscribed on them, because they are not the factors of 210.

For 42*2 to be on one of the plastic balls, we will need an additional 2 with 42 (which is not there, we only have a 5 left; 42 already takes care of 2*7*3 from 210.)

So, 42*2 = 84 , is not a factor of 210, therefore the assumption does not hold true.

Hope I am making some sense !!
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 31 May 2012, 01:51
Expert's post
maffo wrote:
Sorry Bunuel,

i don't get it.

as you said:

210 = 2*5*7*3 and 42 = 2*7*3;
so i would say there are 5 multiples of 42 between 42 and 210.

since I'm obviously wrong, can you please help me to understand where's the mistake?

thanks in advance


We are not interested in the multiples of 42 between 42 and 210. We are interested in multiples of 42 which are factors of 210. Out of factors of 210 only 2 are multiples of 42: 42 and 210, itself.
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 31 May 2012, 03:05
Bunuel wrote:
BDSunDevil wrote:
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?

A. 1/16
B. 5/42
C. 1/8
D. 3/16
E. 1/4


Please post the fastest method with time.


210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;

So, the probability is 2/16=1/8.

Answer: C.


Finding the Number of Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

For more on these issues check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.


As it said multiples of 42, I had not considered 42 itself.
Where did I went wrong in reasoning?
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Re: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 31 May 2012, 03:20
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manulath wrote:
Bunuel wrote:
BDSunDevil wrote:
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?

A. 1/16
B. 5/42
C. 1/8
D. 3/16
E. 1/4


Please post the fastest method with time.


210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;

So, the probability is 2/16=1/8.

Answer: C.


Finding the Number of Factors of an Integer

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

For more on these issues check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.


As it said multiples of 42, I had not considered 42 itself.
Where did I went wrong in reasoning?


Note that an integer a is a multiple of an integer b (integer a is a divisible by an integer b) means that \frac{a}{b}=integer.

Since 42/42=integer then 42 is a multiple of itself (generally every positive integer is a multiple of itself).

Hope it's clear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: Each factor of 210 is inscribed on its own plastic ball, and [#permalink] New post 21 Jul 2014, 16:41
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Re: Each factor of 210 is inscribed on its own plastic ball, and   [#permalink] 21 Jul 2014, 16:41
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