Last visit was: 12 Nov 2024, 12:15 It is currently 12 Nov 2024, 12:15

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.

Close

Request Expert Reply

Confirm Cancel
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11148 [1]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11148 [2]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
User avatar
Intern
Intern
Joined: 07 May 2020
Posts: 20
Own Kudos [?]: 19 [0]
Given Kudos: 0
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12186 [3]
Given Kudos: 136
Send PM
When x is divided by 10, the quotient is y with a remainder [#permalink]
3
sandy wrote:
When x is divided by 10, the quotient is y with a remainder of 4. If x and y are both positive integers, what is the remainder when x is divided by 5?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


APPROACH #1: Test a possible value of x
When it comes to remainders, we have a nice property 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.

So, from the given information, the possible values of x are: 4, 14, 24, 34, 44, 54,....
If you divide any of these possible x-values by 5, you'll always get a remainder of 4.

Answer: E


APPROACH #2: Use algebra

There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

From the given information we can write: x = 10y + 4
We can rewrite this as: x = (5)(2x) + 4
We know that (5)(2x) is a multiple of 5, which means (5)(2x) + 4 is 4 MORE THAN a multiple of 5
So, when we divide (5)(2x) + 4 by 5, the remainder will be 4

Answer: E

RELATED VIDEO
avatar
Manager
Manager
Joined: 15 May 2020
Posts: 91
Own Kudos [?]: 75 [0]
Given Kudos: 0
Send PM
Re: When x is divided by 10, the quotient is y with a remainder [#permalink]
1
Def:

if rem(a/n) = f and rem(b/n) = g, so the remainder of ((a*b)/n) is

f*g, and if f*g is greater than n, the remainder is f*g - n

Now, the problem is:

x = 10*y + 4

If we divide x/5 we have:

remainder(x/f) ) = remainder ((10*y +4)/5)

= rem[(10*y)/5] + remainder (4/5)

= rem [10/5] + 4

= 0 + 4 = 4

Answer is 4.
Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Own Kudos [?]: 960 [1]
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: When x is divided by 10, the quotient is y with a remainder [#permalink]
1
When x is divided by 10, the quotient is y with a remainder of 4

Theory: Dividend = Divisor*Quotient + Remainder

x -> Dividend
10 -> Divisor
y -> Quotient (Assume)
4 -> Remainders
=> x = 10*y + y = 10y + 4

what is the remainder when x is divided by 5

x = 10y + 4
Remainder of x by 5 = Remainder of 10y + 4 by 5 = Remainder of 10y by 5 + Remainder of 4 by 5 = 0 + 4 = 4

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Remainders

Prep Club for GRE Bot
Re: When x is divided by 10, the quotient is y with a remainder [#permalink]
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

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