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
Answer: A
Raffle tickets numbered consecutively from 101 through 350
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Hi boomgoesthegmat,
This is an example of a 'fence post' problem (meaning that you have to remember to count the tickets at the 'beginning' and 'end' of each sub-list.
We're asked for the probability of selecting a ticket with a "2" in the hundreds digit from a group of tickets numbered 101 through 350, inclusive.
The number of tickets is 350 - 101 + 1 = 250 total tickets
The number that have a 2 in the hundreds spot = 100 (200 through 299, inclusive).
So the probability is 100/250 = 2/5
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This is an example of a 'fence post' problem (meaning that you have to remember to count the tickets at the 'beginning' and 'end' of each sub-list.
We're asked for the probability of selecting a ticket with a "2" in the hundreds digit from a group of tickets numbered 101 through 350, inclusive.
The number of tickets is 350 - 101 + 1 = 250 total tickets
The number that have a 2 in the hundreds spot = 100 (200 through 299, inclusive).
So the probability is 100/250 = 2/5
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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This is a straight forward probability question.boomgoesthegmat wrote: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
Answer: A
Always remember, the total numbers between a and b = b - a + 1
Total number of tickets = 350 - 101 + 1 = 250
Tickets with 2 in the hundreds digit = 299 - 200 + 1 = 100
Probability of picking a ticket with 2 in the hundredth digit = 100/250 = 2/5
Correct Option: A
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Rich and Ankur have provided nice solutions, so I won't solve the question again.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
However, I do want to add a pro tip to remember when answering questions using calculating probabilities using the formula:
P(event A occurs) = (# of outcomes where event A occurs)/(total # of outcomes)
In these cases, calculate the denominator first
There are two reasons for this:
1) The denominator is usually the easier value to calculate
2) If you can't calculate the numerator, you can probably use the denominator to eliminate answer choices.
Here's what I mean:
In this question, P(number has a hundreds digit of 2) = (# of integers with hundreds digit of 2)/(# of integers to choose from)
# of integers to choose from = 350 - 101 + 1 = 250
So, P(number has a hundreds digit of 2) = ??)/(250)
This tells us that the correct answer EITHER has 250 in its denominator OR, when the probability is simplified, the new denominator is a factor of 250
At this point, if we can't calculate the numerator, we eliminate some answer choices
A) 2/5 [5 is a factor of 250, so this answer COULD be correct]
B) 2/7 [7 is NOT a factor of 250. ELIMINATE B]
C) 33/83 [83 is NOT a factor of 250. ELIMINATE C]
D) 99/250 [250 is a factor of 250, so this answer COULD be correct]
E) 100/249 [249 is NOT a factor of 250. ELIMINATE E]
So, we were able to deduce that the correct answer is either A or D.
For more on this concept, see the following videos:
- Introduction to Probability: https://www.gmatprepnow.com/module/gmat ... /video/742
- General Probability Strategies: https://www.gmatprepnow.com/module/gmat ... /video/757
Cheers,
Brent
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How do you simply 100/250 to 2/5?OptimusPrep wrote:This is a straight forward probability question.boomgoesthegmat wrote: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
Answer: A
Always remember, the total numbers between a and b = b - a + 1
Total number of tickets = 350 - 101 + 1 = 250
Tickets with 2 in the hundreds digit = 299 - 200 + 1 = 100
Probability of picking a ticket with 2 in the hundredth digit = 100/250 = 2/5
Correct Option: A
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Hi boomgoesthegmat,
When simplifying a fraction, you can do the math in 'stages' or you can do it all at once (depending on your comfort level with the work involved). When dealing with a fraction, you can multiply BOTH the numerator and the denominator by the same number or you can divide BOTH the numerator and the denominator by the same number.
With 100/250, if you recognize that both numbers are multiples of 50, then you can divide 100 by 50 and 250 by 50... you end up with 2/5.
You could also divide in 'stages' though. Notice how both 100 and 250 both end in a 0... That means that you can divide both by 10:
100/250 = 10/25
Now you can divide both by 5... and you'll still end up with 2/5.
GMAT assassins aren't born, they're made,
Rich
When simplifying a fraction, you can do the math in 'stages' or you can do it all at once (depending on your comfort level with the work involved). When dealing with a fraction, you can multiply BOTH the numerator and the denominator by the same number or you can divide BOTH the numerator and the denominator by the same number.
With 100/250, if you recognize that both numbers are multiples of 50, then you can divide 100 by 50 and 250 by 50... you end up with 2/5.
You could also divide in 'stages' though. Notice how both 100 and 250 both end in a 0... That means that you can divide both by 10:
100/250 = 10/25
Now you can divide both by 5... and you'll still end up with 2/5.
GMAT assassins aren't born, they're made,
Rich
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In this problem,
Probability = # of target events / # of possible events
The target is "hundreds digit of 2". We have 200 -> 299, or 00 -> 99. That's 00 + (01 -> 99), for a total of 100 numbers.
The total is "anything from 101 to 350". We want everything from 1 to 350 MINUS everything from 1 to 100, or 350 - 100, or 250 numbers.
That gives us
100 / 250 => 2/5
Probability = # of target events / # of possible events
The target is "hundreds digit of 2". We have 200 -> 299, or 00 -> 99. That's 00 + (01 -> 99), for a total of 100 numbers.
The total is "anything from 101 to 350". We want everything from 1 to 350 MINUS everything from 1 to 100, or 350 - 100, or 250 numbers.
That gives us
100 / 250 => 2/5
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There are a total of 350 - 101 + 1 = 250 raffle tickets in the box, and there are 299 - 200 + 1 = 100 raffle tickets with a hundreds digit of 2; thus, the probability isboomgoesthegmat wrote: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
100/250 = 2/5
Answer: A
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