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
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.