|
|
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.
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:26) correct
26%
(02:48)
wrong
based on 603
sessions
History
Date
Time
Result
Not Attempted Yet
If p and q are positive integers such that when they are divided by 5, the remainder is 3 for each; and when they are divided by 9, the remainder is 4 for each. If q>p, then which of the following must be a factor of q - p ?
A) 12
B) 20
C) 27
D) 36
E) 45
A) 12
B) 20
C) 27
D) 36
E) 45
04 Jul 2017, 05:43
Kudos
Bookmarks
franz711
When p is divided by 5, the remainder is 3: p= 5m + 3, so it can be 3, 8, 13, 18, ...
When p is divided by 9, the remainder is 4: p= 9n + 4, so it can be 4, 13, 22, 31, ...
There is a way to derive general formula for p (of a type p = kx + r, where x is divisor and r is a remainder) based on above two statements:
Divisor x would be the least common multiple of above two divisors 5 and 9, hence x=45.
Remainder r would be the first common integer in above two patterns, hence r = 13.
Therefore general formula based on both statements is p = 45x + 13. (check HERE to know to to derive general formula from these two)
Similarly, general formula for q will be 45y + 13.
q - p = (45y + 13) - (45x + 13) = 45(y - x).
Answer: E.
22 Aug 2017, 06:42
Kudos
Bookmarks
I used this rule: remainder can be added or subtracted directly when adding or subtracting two dividends (the excess needs to be corrected after)
So p and q has the same remainder when divided by 5, therefore q-p will have the remainder of 0, which means q-p is divisible by 5. The same goes for 9.
E) 45 is the only answer that is a multiple of 9 and 5, so E is the right answer.
So p and q has the same remainder when divided by 5, therefore q-p will have the remainder of 0, which means q-p is divisible by 5. The same goes for 9.
E) 45 is the only answer that is a multiple of 9 and 5, so E is the right answer.
, but it wasn't too time consuming because these numbers turn out to be very manageable:
