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.
How many positive integers less than 30 are either a multiple of 2, an
[#permalink]
10 Sep 2021, 09:39
10 Sep 2021, 09:39
Expert Reply
00:00
Question Stats:
25% (02:58) correct
75% (01:51) wrong based on 4 sessions
Hide Show timer Statistics
How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many positive integers less than 30 are either a multiple of 2, an
[#permalink]
10 Sep 2021, 09:49
10 Sep 2021, 09:49
1
Carcass wrote:
How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
Multiples of 2: 2, 4, 6, 8, 10, . . .26, 28
Sum of a positive multiple of 2 and an odd prime
3 is the smallest ODD prime
So, let's add multiples of 2 to 3.
We get: 3 + 2, 3 + 4, 3 + 6, 3 + 8, etc
Evaluate to get: 5, 7, 9, 11, . . . 27, 29
At this point, our list of numbers includes 2 as well as all integers from 4 to 29
All we're missing is 1 and 3
An odd prime number
3 is odd, so, now our list becomes: 2, 3, 4, 5, 6, . . . 27, 28, 29
So, the ONLY value that is NOT in the list is 1 (1 is NOT prime)
So, there are 28 numbers that meet the given conditions.
Answer: B
Cheers,
Brent
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
How many positive integers less than 30 are either a multiple of 2, an
[#permalink]
10 Sep 2021, 10:10
10 Sep 2021, 10:10
1
multiples of 2 less than 30 include \(2(1+2+...14)\), 14 numbers
odd prime numbers less than 30 include \({3,5,7,11,13,17,19,23,29}\), 9 numbers
now every odd prime is resulting from the previous one by adding even numbers, e.g. 3+2=5, 7+6=13, etc.
to find the sum by excluding (9-1) odd prime numbers, continue \((30-3)/2=13\) and \(13-(9-1)\)=5
answer is \(14+9+5=28\) and B
odd prime numbers less than 30 include \({3,5,7,11,13,17,19,23,29}\), 9 numbers
now every odd prime is resulting from the previous one by adding even numbers, e.g. 3+2=5, 7+6=13, etc.
to find the sum by excluding (9-1) odd prime numbers, continue \((30-3)/2=13\) and \(13-(9-1)\)=5
answer is \(14+9+5=28\) and B
Carcass wrote:
How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
