Source: GMAT Prep
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?
1) If the integer is divided by 45, the remainder is 30.
2) The integer is divisible by 2.
The OA is A
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If a certain positive integer is divided by 9, the remainder
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2207
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Given that the positive integer divided by 9 leaves the remainder 3, we have the number = 9q + 3; where q = quotient.BTGmoderatorLU wrote:Source: GMAT Prep
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?
1) If the integer is divided by 45, the remainder is 30.
2) The integer is divisible by 2.
The OA is A
We have to determine the remainder when the integer 9q + 3 is divided by 5.
Let's take each statement one by one.
1) If the integer is divided by 45, the remainder is 30.
Again, say the number is 45p + 30; where p = quotient.
Thus, we have 9q + 3 = 45p + 30
=> q = 5p + 3
Thus, the number 9q + 3 = 9(5p + 3) + 3 = 45p + 27 + 3 = 45p + 30
The remainder when 45p + 30 divided by 5 is 0 since 45, as well as 30, are divisible by 5. Sufficient.
2) The integer is divisible by 2.
=> The integer 9q + 3 is even.
For 9q + 3 to be even, we must have q = an odd integer
Case 1: Say q = 1; thus 9q + 3 = 9*1 + 3 = 12. The remainder when 12 divided by 5 is 2.
Case 2: Say q = 3; thus 9q + 3 = 9*3 + 3 = 30. The remainder when 30 divided by 5 is 0.
No unique answer. Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review
Locations: Manhattan Review Bangalore | GMAT Prep Chennai | GRE Prep Himayatnagar | Hyderabad GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$N \ge 1\,\,{\mathop{\rm int}} \,\,\,\left( * \right)$$BTGmoderatorLU wrote:Source: GMAT Prep
If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?
1) If the integer is divided by 45, the remainder is 30.
2) The integer is divisible by 2.
$$N = 9M + 3\,\,,\,\,\,M\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} $$
$$N = 5K + R\,\,,\,\,\,K\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} $$
$$0 \le R\,\,\,{\mathop{\rm int}} \le 4$$
$$? = R$$
$$\left( 1 \right)\,\,\,N = 45J + 30\,\,,\,\,\,J\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,\,N\,\,{\rm{is}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,5\,\,\,\, \Rightarrow \,\,\,\,? = 0$$
$$\left( 2 \right)\,\,\,N\,\,{\rm{even}}\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,{\rm{M = 1}}\,\,\,\, \Rightarrow \,\,\,\,N = 12\,\,\,\, \Rightarrow \,\,\,\,? = 2 \hfill \cr
\,{\rm{Take}}\,\,{\rm{M = 3}}\,\,\,\, \Rightarrow \,\,\,\,N = 30\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
