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Director  Joined: 09 Jul 2007
Posts: 865
Location: London
If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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1
10 00:00

Difficulty:   65% (hard)

Question Stats: 61% (02:02) correct 39% (02:34) wrong based on 361 sessions

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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

Originally posted by Ravshonbek on 03 Jan 2008, 15:40.
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.
Director  Joined: 12 Jul 2007
Posts: 664
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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2
2
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 SVP  Joined: 29 Mar 2007
Posts: 1874
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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: 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
Director  Joined: 12 Jul 2007
Posts: 664
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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4
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 Senior Manager  Joined: 19 Nov 2007
Posts: 321
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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1
if the question is modified by taking out the word 'respecitively' from this question, how would one approach it?
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VP  Joined: 07 Nov 2007
Posts: 1203
Location: New York
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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

{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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Manager  Joined: 27 Oct 2008
Posts: 130
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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

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
Intern  Joined: 17 Jan 2010
Posts: 23
Schools: SSE, LSE
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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?

(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
Intern  Joined: 24 Feb 2012
Posts: 29
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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.
Senior Manager  Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44 Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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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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Joined: 17 Jul 2014
Posts: 2496
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
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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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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
Intern  Joined: 28 Apr 2015
Posts: 19
GMAT 1: 600 Q46 V27 GMAT 2: 630 Q47 V30 Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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1
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 Intern  B
Joined: 01 Jun 2019
Posts: 9
Re: If two numbers, a and b, are to be chosen from a set of 4  [#permalink]

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1
siv 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?

(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 You are not. The question is worded poorly. Re: If two numbers, a and b, are to be chosen from a set of 4   [#permalink] 20 Oct 2019, 06:16
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