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

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.

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?

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

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.

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

B is the answer.

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.

Answer: E.

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.