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Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

(A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249

Practice Questions Question: 10 Page: 153 Difficulty: 600

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

(A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249

The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 100/250=2/5.

Then if it didn't mean inclusive, how else it could present the problem? Could you answer, pls?

Tickets numbered consecutively from 101, for me, naturally means including 101. There are other ways to write that if 101 were not included, for example "tickets numbered consecutively from 102".
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Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

(A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249

Practice Questions Question: 10 Page: 153 Difficulty: 600

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Total numbers = 350 -101 +1 = 250 favorable cases = 299-200 +1 = 100 Probability = 100/250 = 2/5

option A.
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Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

(A) 2/5 (B) 2/7 (C) 33/83 (D) 99/250 (E) 100/249

The probability of an event is equal to: favorable outcomes/total outcomes

In this particular problem we have:

favorable outcomes = numbers with a hundreds digit of 2

total outcomes = consecutive integers from 101 through 350

Let’s start with the total outcomes. Although the word “inclusive” is not actually used, it is implied because we are told the raffle tickets start at 101 and end at 350. Thus, the number of tickets from 101 to 350, inclusive, is 350 – 101 + 1 = 250. (Note that we had to add 1 because we counted BOTH tickets 101 and 350.)

The favorable outcomes are the number of tickets with a hundreds digit of 2. Since all the numbers from 200 to 299 are included, there are 299 – 200 +1 = 100 numbers with a hundreds digit of 2.

Therefore, the probability that a randomly selected ticket with have a hundreds digit of 2 is 100/250 = 2/5.

Answer A.
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Re: Raffle tickets numbered consecutively from 101 through 350 [#permalink]

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02 Nov 2017, 08:52

GGrunthal wrote:

Can someone please explain to me when we have to add 1?

If it includes both 101 and 350, we have to + 1.

When it does not include neither 101 nor 350, we do not add.

What hapens when we include just 101, or just 350?

Thank you!

(i) Lets say you have consecutive numbers from a to b, then the total numbers would be b - a + 1.

(ii) But if we are asked for consecutive numbers between a & b (in this case a and b are not included), then we would have the total number as b - a - 1

However, if we are asked for consecutive numbers between a & b inclusive then we use the same as (i), which is b - a + 1.