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If two numbers, a and b, are to be chosen from a set of 4

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If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 03 Jan 2008, 15:40
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If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Sep 2014, 20:07, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 03 Jan 2008, 16:04
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I'm going to assume it's B/A and give that a shot.

A: 1, 2, 3, 4
B: 4, 6, 8

Total # of outcomes: 4*3 = 12

Choose 4: only 3 makes a non-integer
Choose 6: only 4 makes a non-integer
Choose 8: only 3 makes a non-integer

3/12 = 1/4 probability of B/A not being an integer.

Sorry if this isn't actually the problem :-D
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 04 Jan 2008, 00:45
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

Answers:
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


A: 1,2,3,4
B: 4,6,8

b/a=i? 4/3, 6/4, 8/3

so: 1/4*1/3 = 1/12 (3) --> 1/4

B
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 04 Jan 2008, 07:07
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kazakhb wrote:
I can't understand why i can't think the way as you guys do, especially "wisconsin", generally he answers every question in this forum, if i was to solve that problem I would need million years(


Most people feel like this when they first start studying for the GMAT. It's not that the math is extremely difficult, it's how the math is being tested that's strange and new. When I first started out I spent lots of time on this forum and made sure I really understood the concepts and reasoning behind each question. In my opinion it's not enough to blindly memorize formulas for this test, you need to understand WHY a question is solved the way it's solved. This way, when the GMAT throws you for a loop, you have solid math founded in an understanding that allows you to apply it to a broad spectrum of problems...and not just on problems and problem types you've seen in the past.

so keep asking questions and digging deeper on here and before long you'll be a pro! there are also great books out there to help you brush up on math skills. I love the MGMAT series for most quant topics and Veritas Project GMAT for combinatorics. You may want to give them a look as well 8-)
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 04 Jan 2008, 10:51
if the question is modified by taking out the word 'respecitively' from this question, how would one approach it?
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 25 Aug 2008, 10:51
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

Answers:
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


{1,2,3,4}
{4,6,8}
b/a not integer 4/3,6/3,8/3
p = 3/12 =1/4
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 27 Sep 2009, 11:06
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

Answers:
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3

Soln:
a is from the following set {1,2,3,4}
b is from the following set {4,6,8}

Total number of ways of choosing 2 integers, one from each set is = 4* 3 = 12 ways

Now the number of possibilities where b/a is not an integer is for the following outcomes
{b,a} => {4,3},{6,4},{8,3} = 3 ways

Hence probability is = 3/12 = 1/4

ans is B
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 05 Mar 2010, 07:45
x2suresh wrote:
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

Answers:
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


{1,2,3,4}
{4,6,8}
b/a not integer 4/3,6/3,8/3
p = 3/12 =1/4


Hey suresh,

you probably meant:
b/a not integer 4/3,6/4,8/3
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 29 Feb 2012, 11:44
OK, here's an example of how to get an easy question wrong.
I assumed (misread) the question to mean that a and b sets are interchangeable.
Implying that a and b could be selected from either {1,2,3,4} or {4,6,8}.

I now realize that I had misread the question, but if that was the original question, then:
P(b/a is not an integer)
= P(b/a not an integer where b in {1234} and a in {468})
+ P(b/a not an integer where b in {468} and a in {1234})
= 11/12 + 3/12
= 7/12.

Going back to the question that was asked:
P(b/a not an integer where b in {468} and a in {1234})
= 3/12
= 1/4.
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 18 Oct 2015, 23:52
Expert's post
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


In such problems, it is better to first write down all the cases that are in cosideration

Set A = {1, 2, 3, 4}
Set B = {4, 6, 8}

Total outcomes: 4*3 = 12

Favourable outcomes:
We need B/A, hence considering one element of the set B at a time

4: only 3 satisfies our condition (4 is divisible by 1, 2 and 4)
6: only 4 satisfies our condition (6 is divisible by 1, 2 and 3)
8: only 3 satisfies our condition (8 is divisible by 1, 2 and 4)

Favourable outcomes = 3
Probability = 3/12 = 1/4
Option B
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 06 Apr 2016, 18:18
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


a relatively easy question that can be solved by enumerating all the outcomes:
1st list: 1, 2, 3, 4
2nd list: 4, 6, 8

now, possible options:
4/1
4/2
4/3 - non-integer
4/4

6/1
6/2
6/3
6/4 - non-integer

8/1
8/2
8/3 - non-integer
8/4

total 12 outcomes, out of which 3 are "successful" outcomes. 3/12 = 1/4
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Re: If two numbers, a and b, are to be chosen from a set of 4 [#permalink]

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New post 20 Jul 2016, 04:47
Ravshonbek wrote:
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?

(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3


Am I the only one who interpreted the question in the following manner?

Given that the first set consists of 4 consecutive integers starting with 1, I assumed the set will be something like this {10, 11, 12, 13} or {102,103,104,105} and same for the second set {404, 406, 408}. This made me lose my mind on how to go about :(
Re: If two numbers, a and b, are to be chosen from a set of 4   [#permalink] 20 Jul 2016, 04:47
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