|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
25 Apr 2023, 06:52
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:57) correct
31%
(02:56)
wrong
based on 195
sessions
History
Date
Time
Result
Not Attempted Yet
When a 2-digit positive integer x is divided by 5, the remainder is 2. When the same integer is divided by 16, the remainder is 9. What is the remainder when x\(^2\) is divided by 12?
A. 6
B. 7
C. 9
D. 11
E. Cannot be determined
A. 6
B. 7
C. 9
D. 11
E. Cannot be determined
25 Apr 2023, 07:56
Kudos
Bookmarks
ChandlerBong
When a 2-digit positive integer x is divided by 5, the remainder is 2
\(x = 5q + 2\)
q is the quotient when x is divided by 5
When the same integer is divided by 16, the remainder is 9.
\(x = 16p + 9\)
9 is the quotient when x is divided by 9
So, we can represent x as
x = LCM(5,16)z + First Common Term in both sequence
x = 80z + 57
\(x = 5q + 2\) ⇒ 2, 5, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62 ...
\(x = 16p + 9\) ⇒ 9, 25, 41, 57, 73 ...
The first term that's common to both sequences is 57
\(x = 16p + 9\) ⇒ 9, 25, 41, 57, 73 ...
The first term that's common to both sequences is 57
However, it's also given that x is a two-digit number, hence the only possible value of x ⇒ x = 57
Remainder(\(\frac{x^2}{12}\)) = Remainder(\(\frac{57^2 }{ 12}\))
= Remainder(\(\frac{57}{12}\)) * Remainder (\(\frac{57}{12}\))
= -3 * -3 = 9
Option C
19 Sep 2024, 10:01
Kudos
Bookmarks
gmatophobia
gmatphobia Could you explain the formulas that you are using here for remainders
I was trying to use it to calculate the remainder of 6x6/10
remainder of 6x6/10 = remainder of 6/10 x remainder of 6/10 = 6 * 6 = 36 or -4 x -4 = 16 but actual answer answer is 6
