NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 20:39 It is currently 25 Apr 2024, 20:39
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT 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 GMAT 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

When positive integer x is divided by positive integer y, the quotient

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619044 [7]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
When positive integer x is divided by positive integer y, the quotient [#permalink] New post   12 Jun 2017, 02:34
7
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

87% (01:53) correct 13% (02:21) wrong based on 277 sessions
Hide Show timer Statistics
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211
ShowHide Answer
Official Answer
B
User avatar
L
sashiim20
Director
Director
Joined: 04 Dec 2015
Posts: 620
Own Kudos [?]: 1585 [3]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
Re: When positive integer x is divided by positive integer y, the quotient [#permalink] New post   12 Jun 2017, 03:15
1
Kudos
1
Bookmarks
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211


Required number is in form
\(x = 17y + 3\) ----------- (i)
\(x = 24(y-3) + 5\) -------- (ii)

Equating (i) and (ii), we get;
\(17y + 3 = 24 (y - 3) + 5\)
\(17y + 3 = 24y - 72 + 5\)
\(24y - 17y = 72 + 3 - 5\)
\(7y = 70\)
\(y = 10\)

\(x = 17 (10) + 3 = 170+3 =173\). Answer B...
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: When positive integer x is divided by positive integer y, the quotient [#permalink] New post   14 Jun 2017, 16:21
Expert Reply
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211


We are given that when positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. Thus:

x/y = 17 + 3/y

x = 17y + 3

We are also given that when x is divided by (y−3), the quotient is 24 and the remainder is 5. Thus:

x/(y-3) = 24 + 5/(y-3)

x = 24(y-3) + 5

x = 24y - 72 + 5

x = 24y - 67

We can equate our two equations and we have:

17y + 3 = 24y - 67

70 = 7y

y = 10

Thus, x = 17(10) + 3 = 173.

Answer: B
User avatar
S
nkme2007
Manager
Manager
Joined: 11 Mar 2012
Posts: 176
Own Kudos [?]: 57 [1]
Given Kudos: 103
Location: India
Concentration: General Management, Operations
Schools: IIMB EPGP'22 (M)
GMAT 1: 670 Q50 V31
GPA: 4
WE:Project Management (Real Estate)
Send PM
Reviews Badge
Re: When positive integer x is divided by positive integer y, the quotient [#permalink] New post   09 Jul 2020, 23:57
1
Kudos
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211


The question stem forms two equations as below

x = 17y+3
x=24(y-3)+5

Solving the above 2 equations

x=173

OA: B
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29934 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: When positive integer x is divided by positive integer y, the quotient [#permalink] New post   24 Apr 2022, 06:47
1
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211


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

When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3
So, we can write x = 17y + 3

When x is divided by (y-3), the quotient is 24 and the remainder is 5.
So, we can write x = 24(y - 3) + 5

What is the value of x?
Since we now have two equations that equal to x, we can write: 17y + 3 = 24(y - 3) + 5
Expand and simplify the right side: 17y + 3 = 24y - 67
Add 67 to both sides of the equation: 17y + 70 = 24y
Subtract 17y from both sides of the equation: 70 = 7y
Solve: y = 10

Find the corresponding value of x, just plug y = 10 into one of our two equations.
We get: x = 17(10) + 3 = 170 + 3 = 173

Answer: B
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9245 [2]
Given Kudos: 91
 Q51  V47
Send PM
Re: When positive integer x is divided by positive integer y, the quotient [#permalink] New post   24 Apr 2022, 07:24
2
Kudos
Expert Reply
When we divide x by y, the quotient is 17 and the remainder is 3, so when we divide x by 17, the quotient is y and the remainder is 3 (that's what the equation x = 17y + 3 means -- x is 3 greater than a multiple of 17, so the remainder is 3 when we divide x by 17). Only answer B gives us a remainder of 3 when we divide it by 17, so it has to be right, and we don't need to use the rest of the information in the question.
GMAT Club Bot
gmatclubot
Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
24 Apr 2022, 07:24
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions