Last visit was: 31 Dec 2024, 07:59 It is currently 31 Dec 2024, 07:59
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

QOTD#14 When x is divided by 3, the remainder is 1. When x

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4815
Own Kudos [?]: 11279 [5]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink] New post   14 Nov 2016, 15:14
2
Expert Reply
3
Bookmarks
00:00

Question Stats:

57% (02:42) correct 42% (02:46) wrong based on 45 sessions

Hide Show timer Statistics

When x is divided by 3, the remainder is 1. When x is divided by 7, the remainder is 2. How many positive integers less than 100 could be values for x?


Drill 4
Question: 5
Page: 293


Show: :: OA
4
User avatar
sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4815
Own Kudos [?]: 11279 [3]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
Re: QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink] New post   14 Nov 2016, 15:21
3
Expert Reply
Explanation

To solve this question, write it out.

Since there are fewer numbers that yield a remainder of 2 when divided by 7, start there. The first such number is 2, and thereafter they increase by 7; the rest of the list is thus 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, and 93. Rather than list out all the numbers that yield a remainder of 1 when divided by 3, just select the numbers that meet the requirement from the list you already have: Only 16, 37, 58, and 79 do, so there are 4 values for x.

Hence the correct answer is 4.
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12239 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink] New post   25 Nov 2016, 17:46
2
sandy wrote:
When x is divided by 3, the remainder is 1. When x is divided by 7, the remainder is 2. How many positive integers less than 100 could be values for x?



When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Now onto the question....
When x is divided by 7, the remainder is 2
Possible values of x are: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, 93

When x is divided by 3, the remainder is 1
Possible values of x are: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97

The two sets have 4 numbers in common.
Answer:
Show: ::
4


ASIDE: Notice that each of the shared values (16, 37, 58, and 79) are 21 greater than the previous shared value. Also notice that 21 is the least common multiple (LCM) of 3 and 7.
So, once we found 1 value in common, we could have just kept adding 21 to that value to find the subsequent values.

RELATED VIDEO
avatar
tejalbharade
Intern
Intern
Joined: 24 Oct 2017
Posts: 36
Own Kudos [?]: 17 [0]
Given Kudos: 0
Send PM
Re: QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink] New post   22 Jan 2018, 08:19
1
in 1st case when N=4/3..remainder=1
2nd case when N=9/7...remainder=2
looking at condition we can conclude that 3,9,27,81.....in short, the power of 3 is increasing there and the limit is till 100 hence last number to consider is 81...making it total 4 numbers.
answer 4
User avatar
G
BrushMyQuant
Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1126
Own Kudos [?]: 980 [0]
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)
Send PM
Re: QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink] New post   20 Oct 2022, 08:36
Given that When x is divided by 3, the remainder is 1. When x is divided by 7, the remainder is 2. And we need to find How many positive integers less than 100 could be values for x

Theory: Dividend = Divisor*Quotient + Remainder

When x is divided by 3, the remainder is 1

x -> Dividend
3 -> Divisor
a -> Quotient (Assume)
1 -> Remainders
=> x = 3*a + 1 = 3a + 1

When x is divided by 7, the remainder is 2

x -> Dividend
7 -> Divisor
b -> Quotient (Assume)
2 -> Remainders
=> x = 7*b + 2 = 7b + 2

x = 3a + 1 = 7b + 2
=> a = \(\frac{7b + 1}{3}\)

Only those values of b which will also give a as integer will give us the common values of x
b = 2, 5, 8, 11, 14,...
But for b = 14, we will get x = 7b + 2 = 7*14 + 2 = 100 which is NOT less than 100

=> 4 values of x less than 100 are possible

So, Answer will be 4
Hope it helps!

Watch the following video to learn the Basics of Remainders

Prep Club for GRE Bot
gmatclubot
Re: QOTD#14 When x is divided by 3, the remainder is 1. When x [#permalink]
20 Oct 2022, 08:36
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1126 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact