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.
x and y are positive integers. When 16x is divided by y, the quotient
[#permalink]
06 Jul 2022, 03:13
06 Jul 2022, 03:13
2
Expert Reply
3
Bookmarks
00:00
Question Stats:
65% (02:19) correct
34% (01:47) wrong based on 29 sessions
Hide Show timer Statistics
x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?
A) 7
B) 12
C) 19
D) 26
E) 41
A) 7
B) 12
C) 19
D) 26
E) 41
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x and y are positive integers. When 16x is divided by y, the quotient
[#permalink]
06 Jul 2022, 07:20
06 Jul 2022, 07:20
1
Carcass wrote:
x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?
A) 7
B) 12
C) 19
D) 26
E) 41
A) 7
B) 12
C) 19
D) 26
E) 41
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
There's a nice rule that say, "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
------NOW ONTO THE QUESTION------------------------------
When 16x is divided by y, the quotient is x, and the remainder is 4.
Applying the above rule, we can write: 16x = (y)(x) + 4
Subtract xy from both sides: 16x - xy = 4
Factor: x(16 - y) = 4
Since x and (16 - y) are both positive integers, there are 3 possible solutions:
#1: x = 1 and (16 - y) = 4, in which case y = 12
#2: x = 2 and (16 - y) = 2, in which case y = 14
#3: x = 4 and (16 - y) = 1, in which case y = 15
What is the sum of all possible y-values?
SUM = 12 + 14 + 15
= 41
Answer: E
RELATED VIDEO FROM OUR COURSE
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
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: x and y are positive integers. When 16x is divided by y, the quotient
[#permalink]
03 Oct 2022, 02:59
03 Oct 2022, 02:59
1
When 16x is divided by y, the quotient is x, and the remainder is 4
When a positive integer m is divided by 17, the remainder is 3
Theory: Dividend = Divisor*Quotient + Remainder
16x -> Dividend
y -> Divisor
x -> Quotient
4 -> Remainders
=> 16x = y*x + 4 = xy + 4
=> y = \(\frac{16x - 4}{x}\) = \(\frac{16x}{x} - \frac{4}{x}\) = \(16 - \frac{4}{x}\)
Since y is an integer => \(\frac{4}{x}\) will be an integer
=> 4 should be divisible by x
=> x = 1, 2 or 4
x = 1
16x = xy + 4
=> 16*1 = 1*y + 4
=> y = 16 - 4 = 12
x = 2
16x = xy + 4
=> 16*2 = 2*y + 4
=> y = \(\frac{32 - 4}{2}\)= 14
x = 4
16x = xy + 4
=> 16*4 = 4*y + 4
=> y = \(\frac{64 - 4}{4}\)= 15
=> Sum of all values of y = 12 + 14 + 15 = 41
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Remainders
When a positive integer m is divided by 17, the remainder is 3
Theory: Dividend = Divisor*Quotient + Remainder
16x -> Dividend
y -> Divisor
x -> Quotient
4 -> Remainders
=> 16x = y*x + 4 = xy + 4
=> y = \(\frac{16x - 4}{x}\) = \(\frac{16x}{x} - \frac{4}{x}\) = \(16 - \frac{4}{x}\)
Since y is an integer => \(\frac{4}{x}\) will be an integer
=> 4 should be divisible by x
=> x = 1, 2 or 4
x = 1
16x = xy + 4
=> 16*1 = 1*y + 4
=> y = 16 - 4 = 12
x = 2
16x = xy + 4
=> 16*2 = 2*y + 4
=> y = \(\frac{32 - 4}{2}\)= 14
x = 4
16x = xy + 4
=> 16*4 = 4*y + 4
=> y = \(\frac{64 - 4}{4}\)= 15
=> Sum of all values of y = 12 + 14 + 15 = 41
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Remainders
