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# If x is to be selected at random from T, what is the probabi

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If x is to be selected at random from T, what is the probabi [#permalink]  18 Aug 2008, 11:17
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If x is to be selected at random from T, what is the probability that \frac{1}{4}*x-5\leq{0}?

(1) T is a set of 8 integers.
(2) T is contained in the set of integers from 1 to 25, inclusive.
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Re: DS: probability [#permalink]  18 Aug 2008, 11:35
vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

1/4x - 5 <=0
x<=20
1) T is a set of 8 integers
Can be any 8 integers >20 or can be any integers <20..

insuffcient.
2) {1,2,...25}

probablity = 20/25

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Re: DS: probability [#permalink]  18 Aug 2008, 13:26
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I think the answer is E.

First the inequality simplifies to x <= 20.
1/4x - 5 <=0
1/4x <= 5
4*(1/4x) <= 4*5
x <= 20

We need to know what the options are in set T before we know the probability of selecting a value for x that is <= 20.

vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
This doesn't give us enough information. We know the total number, but all numbers in Set T could be greater than 20 thus giving us probability of 0, or they could all be less than 20 giving us a probability of 1, or anything in between. INSUFFICIENT
2. T is contained in the set of integers from 1 to 25, inclusive
INSUFFICIENT. We need to know how many of the integers in the set of integers from 1 to 25 make up T. since we do not know this, we do not know the total number of integers in the pool, and since some integers are higher than 20, some will satisfy the inequality and others will not. Once we know how many integers we would need to know which ones make up T.

TOGETHER: Insufficient. Together we know that T consists of 8 integers from 1 to 25, but because we could have all that are <= 20 and probability would be 1, or we could include any number of integers from 21 to 25 inclusive thus giving us many different probability values.

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Re: DS: probability [#permalink]  18 Aug 2008, 14:23
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

Simplifying the question, we get, x<=20; From the choices, can we find if x<=20?
Choice 1: No
Choice 2: No
Combined: No

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Re: DS: probability [#permalink]  20 Aug 2008, 03:29
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vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

E.

(1) Insufficient

Could be any set of 8 integers. Tells us nothing.

(2) Insufficient

Does not tell us how many and/or what numbers comprise T.
T could = {1,2,3,4), where probability = 1
T could = {1,2,3,25}, where probability = 3/4

(1) and (2) Insufficient
Tells us how many integers are in T but does not tells us which integers are in T.
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Re: DS: probability [#permalink]  20 Aug 2008, 05:46
zoinnk wrote:
vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

E.

(1) Insufficient

Could be any set of 8 integers. Tells us nothing.

(2) Insufficient

Does not tell us how many and/or what numbers comprise T.
T could = {1,2,3,4), where probability = 1
T could = {1,2,3,25}, where probability = 3/4

(1) and (2) Insufficient
Tells us how many integers are in T but does not tells us which integers are in T.

Thanks everyone.. I agree with E

2. T is contained in the set of integers from 1 to 25, inclusive

I missed the highlighted part.
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Re: DS: probability [#permalink]  20 Aug 2010, 01:46
x2suresh wrote:
vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

1/4x - 5 <=0
x<=20
1) T is a set of 8 integers
Can be any 8 integers >20 or can be any integers <20..

insuffcient.
2) {1,2,...25}

probablity = 20/25

I defininetly agree with you however OA is E,

it is written from 1 to 25 so it means t= (1,2,3,4...23,24,25) why it is not B couldnt understand...

Bunuel Can you check and help us plz?
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Re: DS: probability [#permalink]  20 Aug 2010, 05:34
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fatihaysu wrote:
x2suresh wrote:
vksunder wrote:
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

1/4x - 5 <=0
x<=20
1) T is a set of 8 integers
Can be any 8 integers >20 or can be any integers <20..

insuffcient.
2) {1,2,...25}

probablity = 20/25

I defininetly agree with you however OA is E,

it is written from 1 to 25 so it means t= (1,2,3,4...23,24,25) why it is not B couldnt understand...

Bunuel Can you check and help us plz?

First of all: 1/4x - 5 <=0 should be written as 1/4*x - 5 <=0.

1. If x is to be selected at random from T, what is the probability that \frac{1}{4}*x-5\leq{0}?

\frac{1}{4}*x-5\leq{0} --> is x\leq{20}?

(1) T is a set of 8 integers. Clearly insufficient.
(2) T is contained in the set of integers from 1 to 25, inclusive. Though the wording is a little bit strange but it means that set T is a subset of a set of integers from 1 to 25, inclusive. Set T can be {1,5,7} or {21,22,25}... Also insufficient.

(1)+(2) T can be set of 8 integers, which are ALL less than or equal to 20 and in this case P(x\leq{20})=1 or T can be set of 8 integers which are NOT ALL all less than or equal to 20 and in this case P(x\leq{20})<1. Not sufficient.

You should spotted that there was something wrong with your approach as (1) say that T is a set of 8 integers and if (2) says that T is a set of integers from 1 to 25 inclusive, so set of 25 integers (as you suggested) then it would mean that statements contradict each other and on GMAT two statements never contradict.

Hope it's clear.
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Re: DS: probability [#permalink]  20 Aug 2010, 05:43
Good tip about contradiction bunuel, whatever I asked you,you are perfect on it buddy I think you should write a book,

If you don't mind What was your GMAT score?
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Re: DS: probability [#permalink]  20 Aug 2010, 20:39
This is why I like the contradiction, one statement can hint at the parameters or bounds. If I had looked at statement 2 first, I probably would have forgotten about the limit that the number of the set is not yet defined. But you look at the other statement, and see they limit the set to 8 digits, and it sets off a lightbulb in my head. If the set had 1 number or 25 numbers, would give different answers.
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Re: DS: probability [#permalink]  06 Jan 2011, 10:11
If x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?
x<= 20

1. T is a set of 8 integers
2. T is contained in the set of integers from 1 to 25, inclusive

St.1 [IS] set of the same integers? integers less than 20? negative integers?
St.2 [IS] 1-25 inclusive maybe all the integers are the same no. 25 or no. 10

With both, you can conclude that there is a set of 8 integers between the no. 1-25 inclusive. They can still be all the same integers or all int less than 20 or all int greater than 20 or consist of random proportion of int greater/less than 20. Therefore you can not conclude a definite answer so ---> (E)
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Re: DS: probability [#permalink]  11 Jan 2011, 17:52
some people (like myself) thought that 1/4x is 1/(4x). In this case B is the answer with a probability of 1. Otherwise the answer is E
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Re: If x is to be selected at random from T, what is the probabi [#permalink]  07 Jun 2013, 05:12
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Re: If x is to be selected at random from T, what is the probabi [#permalink]  09 Jun 2013, 00:02
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Solving the equation for x : 1/4x – 5 <= 0

(x – 20)/4 <= 0

x – 20 <=0

x <= 20,hence the question can be reframed as,what is the probability that x <= 20?

Stmt 1 : T is a set of 8 integers – here x could be any integer so it could be <20 or = 20 or > 20

Since we can not arrive at a definite answer,this statement is insufficient

Stmt 2 : T is contained in the set of integers from 1 to 25, inclusive

Here again,x could be any integer so it could be <20 or = 20 or > 20

Since we can not arrive at a definite answer,this statement is insufficient

Both : x could be any integer so it could be <20 or = 20 or > 20

Since we can not arrive at a definite answer,both statements are insufficient
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Re: DS: probability [#permalink]  15 Jul 2013, 04:46
Bunuel wrote:
f x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

First of all: 1/4x - 5 <=0 should be written as 1/4*x - 5 <=0.

1. If x is to be selected at random from T, what is the probability that \frac{1}{4}*x-5\leq{0}?

\frac{1}{4}*x-5\leq{0} --> is x\leq{20}?

(1) T is a set of 8 integers. Clearly insufficient.
(2) T is contained in the set of integers from 1 to 25, inclusive. Though the wording is a little bit strange but it means that set T is a subset of a set of integers from 1 to 25, inclusive. Set T can be {1,5,7} or {21,22,25}... Also insufficient.

(1)+(2) T can be set of 8 integers, which are ALL less than or equal to 20 and in this case P(x\leq{20})=1 or T can be set of 8 integers which are NOT ALL all less than or equal to 20 and in this case P(x\leq{20})<1. Not sufficient.

You should spotted that there was something wrong with your approach as (1) say that T is a set of 8 integers and if (2) says that T is a set of integers from 1 to 25 inclusive, so set of 25 integers (as you suggested) then it would mean that statements contradict each other and on GMAT two statements never contradict.

Hope it's clear.

Bunuel,

Is it not possible to arrive at the answer by combining the two statements? Theoretically, we can identify all the subsets of 8 integers from 1 to 25, find the probability of X>=20 in all those subsets and add those probabilities.

What is wrong in my approach here?

Thank you.
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Re: DS: probability [#permalink]  15 Jul 2013, 04:55
Expert's post
keenys wrote:
Bunuel wrote:
f x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

First of all: 1/4x - 5 <=0 should be written as 1/4*x - 5 <=0.

1. If x is to be selected at random from T, what is the probability that \frac{1}{4}*x-5\leq{0}?

\frac{1}{4}*x-5\leq{0} --> is x\leq{20}?

(1) T is a set of 8 integers. Clearly insufficient.
(2) T is contained in the set of integers from 1 to 25, inclusive. Though the wording is a little bit strange but it means that set T is a subset of a set of integers from 1 to 25, inclusive. Set T can be {1,5,7} or {21,22,25}... Also insufficient.

(1)+(2) T can be set of 8 integers, which are ALL less than or equal to 20 and in this case P(x\leq{20})=1 or T can be set of 8 integers which are NOT ALL all less than or equal to 20 and in this case P(x\leq{20})<1. Not sufficient.

You should spotted that there was something wrong with your approach as (1) say that T is a set of 8 integers and if (2) says that T is a set of integers from 1 to 25 inclusive, so set of 25 integers (as you suggested) then it would mean that statements contradict each other and on GMAT two statements never contradict.

Hope it's clear.

Bunuel,

Is it not possible to arrive at the answer by combining the two statements? Theoretically, we can identify all the subsets of 8 integers from 1 to 25, find the probability of X>=20 in all those subsets and add those probabilities.

What is wrong in my approach here?

Thank you.

When a DS question asks to find some value, then the statement is sufficient ONLY if you can get the single numerical value.

Since we cannot get the single numerical value of the probability alsed, thee the answer is E.

Hope it's clear.
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If x is to be selected at random from T, what is the probabi [#permalink]  02 Jul 2014, 16:25
Bunuel wrote:
keenys wrote:
Bunuel wrote:
f x is to be selected at random from T, what is the probability that 1/4x - 5 <=0?

First of all: 1/4x - 5 <=0 should be written as 1/4*x - 5 <=0.

1. If x is to be selected at random from T, what is the probability that \frac{1}{4}*x-5\leq{0}?

\frac{1}{4}*x-5\leq{0} --> is x\leq{20}?

(1) T is a set of 8 integers. Clearly insufficient.
(2) T is contained in the set of integers from 1 to 25, inclusive. Though the wording is a little bit strange but it means that set T is a subset of a set of integers from 1 to 25, inclusive. Set T can be {1,5,7} or {21,22,25}... Also insufficient.

(1)+(2) T can be set of 8 integers, which are ALL less than or equal to 20 and in this case P(x\leq{20})=1 or T can be set of 8 integers which are NOT ALL all less than or equal to 20 and in this case P(x\leq{20})<1. Not sufficient.

You should spotted that there was something wrong with your approach as (1) say that T is a set of 8 integers and if (2) says that T is a set of integers from 1 to 25 inclusive, so set of 25 integers (as you suggested) then it would mean that statements contradict each other and on GMAT two statements never contradict.

Hope it's clear.

Bunuel,

Is it not possible to arrive at the answer by combining the two statements? Theoretically, we can identify all the subsets of 8 integers from 1 to 25, find the probability of X>=20 in all those subsets and add those probabilities.

What is wrong in my approach here?

Thank you.

When a DS question asks to find some value, then the statement is sufficient ONLY if you can get the single numerical value.

Since we cannot get the single numerical value of the probability alsed, thee the answer is E.

Hope it's clear.

Bunuel,

I find myself in the same position as Keenys'.

Won't we get a single numerical value though if we do identify all the subsets and add all those "OR" possibilities?

Or the reason why this approach is wrong is that the question asks us for the probability of getting an x from a subset T that is supposed to be "fixed," not variable? And for this reason, we cannot get a single numerical value since we can have multiple possibilities for the subset T?

Thank you.
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Re: If x is to be selected at random from T, what is the probabi [#permalink]  02 Jul 2014, 21:59
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francoimps wrote:
Bunuel,

I find myself in the same position as Keenys'.

Won't we get a single numerical value though if we do identify all the subsets and add all those "OR" possibilities?

Or the reason why this approach is wrong is that the question asks us for the probability of getting an x from a subset T that is supposed to be "fixed," not variable? And for this reason, we cannot get a single numerical value since we can have multiple possibilities for the subset T?

Thank you.

I don't think it is possible to arrive at single answer with the information given by the statements.

Both statements together tell us that T is a subset of 8 integers of superset of 25 integers starting from 1 to 25

So we can easily create a few subsets of 8 integers that give is different probabilities.
Subset 1 -------> 1,2,3,4,5,6,7,8 ---------> Probability of x being <= 20 is 1
Subset 2 --------> 1,2,8,10,21,22,24,25 -------> Probability of x being <= 20 is 0.5
Subset 3 --------> 25,25,25,25,25,25,25,25 --------> Probability of x being <= 20 is 0 (Note that we are not told that the integers in set of 8 integers are all distinct)
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Re: If x is to be selected at random from T, what is the probabi   [#permalink] 02 Jul 2014, 21:59
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