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.
What is the least positive integer which when divided by 2, 3, 4, 5 an
[#permalink]
16 Dec 2021, 03:11
16 Dec 2021, 03:11
Expert Reply
1
Bookmarks
00:00
Question Stats:
93% (01:36) correct
6% (03:11) wrong based on 15 sessions
Hide Show timer Statistics
What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder ?
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the least positive integer which when divided by 2, 3, 4, 5 an
[#permalink]
16 Dec 2021, 04:39
16 Dec 2021, 04:39
Carcass wrote:
What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder ?
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
(A) 109
(B) 119
(C) 126
(D) 154
(E) 210
Let's deal with each piece of information individually.
We are told that, when the number is divided by 2, the remainder is 1.
This tells us that the number must be ODD, which means we can eliminate answer choices C, D and E they are all EVEN.
We're also told that, when the number is divided by 7, the reminder is 0.
In other words, the number must be divisible by 7.
Let's check the two remaining answer choices...
109 is NOT divisible by 7, which means we can eliminate answer choice A.
119 IS divisible by 7, so the correct answer must be B.
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: What is the least positive integer which when divided by 2, 3, 4, 5 an
[#permalink]
02 Oct 2022, 10:31
02 Oct 2022, 10:31
We need to find What is the least positive integer which when divided by 2, 3, 4, 5 and 6 leaves 1, 2, 3, 4 and 5 as remainders, respectively, but when divided by 7 leaves no remainder
Number when divided by 2 gives 1 remainder
=> Number is odd
Only odd choices are A and B
Number when divided by 3 gives 1 remainder
Remainder of 109 when divided by 3 = Remainder of (1+0+9) when divided by 3 = Remainder of 10 when divided by 3 = 1 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
Watch the following video to learn the Basics of Remainders
Number when divided by 2 gives 1 remainder
=> Number is odd
Only odd choices are A and B
Number when divided by 3 gives 1 remainder
Remainder of 109 when divided by 3 = Remainder of (1+0+9) when divided by 3 = Remainder of 10 when divided by 3 = 1 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Divisibility Rules
Watch the following video to learn the Basics of Remainders
