GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
How many positive integers less than 500 begin
[#permalink]
20 Jun 2018, 04:49
20 Jun 2018, 04:49
4
19
Bookmarks
00:00
Question Stats:
34% (02:38) correct
65% (02:33) wrong based on 123 sessions
Hide Show timer Statistics
How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149
B) 150
C) 159
D) 199
E) 200
*I'll post a full solution in 2 days
A) 149
B) 150
C) 159
D) 199
E) 200
*I'll post a full solution in 2 days
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many positive integers less than 500 begin
[#permalink]
22 Jun 2018, 05:07
22 Jun 2018, 05:07
4
2
Bookmarks
GreenlightTestPrep wrote:
How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149
B) 150
C) 159
D) 199
E) 200
*I'll post a full solution in 2 days
A) 149
B) 150
C) 159
D) 199
E) 200
*I'll post a full solution in 2 days
There are 499 integers from 1 to 499 inclusive.
Let's determine how many of those 499 integers DO NOT meet the condition of beginning with a 3, ending with a 3, or both
1-digit integers that DO NOT begin with a 3, end with a 3, or both
1, 2, 4, 5, 6, 7, 8, and 9
TOTAL = 8
2-digit integers that DO NOT begin with a 3, end with a 3, or both
In the tens position, we can have 1, 2, 4, 5, 6, 7, 8, or 9 (8 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (9 possibilities)
TOTAL number of 2-digit integers that DO NOT begin with a 3, end with a 3, or both = (8)(9) = 72
3-digit integers that DO NOT begin with a 3, end with a 3, or both
In the hundreds position, we can have 1, 2, or 4 (3 possibilities)
In the tens position, we can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 (10 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (9 possibilities)
TOTAL number of 3-digit integers that DO NOT begin with a 3, end with a 3, or both = (3)(10)(9) = 270
So, the TOTAL number of integers that DO NOT meet the given condition = 8 + 72 + 270 = 350
TOTAL number of integers that MEET the given condition
So, the = 499 - 350 = 149
Answer: A
Cheers,
Brent
General Discussion
Re: How many positive integers less than 500 begin
[#permalink]
11 Jul 2018, 00:03
11 Jul 2018, 00:03
1
2
Bookmarks
Less than 500, we have 1 digit, 2 digits, 3 digits number.
+1 digit numbers: only 3 ( 1 outcome)
+2 digits, we can have: a3 (9 outcomes since a cannot be 0) or 3b (b cannot be 3 since overlap, hence only 9 outcomes)
+3 digits, we can have: 3bc (100 outcomes)or 1b3,2b3,4b3(each has 10 outcomes, then total 30)
Total 149 outcomes
+1 digit numbers: only 3 ( 1 outcome)
+2 digits, we can have: a3 (9 outcomes since a cannot be 0) or 3b (b cannot be 3 since overlap, hence only 9 outcomes)
+3 digits, we can have: 3bc (100 outcomes)or 1b3,2b3,4b3(each has 10 outcomes, then total 30)
Total 149 outcomes
