When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?
A) 0
B) 1
C) 2
D) 3
E) 4
Whats the best way to answer this question ? Please explain your logic.
Thanks in advance.
Divisibility (Remainders): When the pos int x is div by 11,
This topic has expert replies
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Since 11 and 19 have no factors in common, the lowest common multiple will be 11 * 19 and the smallest number that gives a remainder of 3 when divided by both 11 and 19 is 11*19 + 3.II wrote:When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?
A) 0
B) 1
C) 2
D) 3
E) 4
Whats the best way to answer this question ? Please explain your logic.
Thanks in advance.
We know that y is the biggest number of 11s that goes into 11*19 + 3... so y = 19. Finally, 19/19 gives us a remainder of 0: choose (a).
Note, y could have also equalled other mutliples of 19, but the remainder is always going to be 0.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
- Senior | Next Rank: 100 Posts
- Posts: 34
- Joined: Wed Feb 20, 2008 7:15 pm
- Thanked: 6 times
- Followed by:1 members
Can't wrap my brain around that statement. Can anyone help please .We know that y is the biggest number of 11s that goes into 11*19 + 3... so y = 19. Finally, 19/19 gives us a remainder of 0: choose (a).
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Which part?mmukher wrote:Can't wrap my brain around that statement. Can anyone help please .We know that y is the biggest number of 11s that goes into 11*19 + 3... so y = 19. Finally, 19/19 gives us a remainder of 0: choose (a).
The question itself tells us that when x is divided by 11, we get a quotient of y and a remainder of 3.
In other words, x/11 = y + 3/11.
We've determined that one possible value for x is 11*19 + 3.
We know that (11*19 + 3)/11 = (11*19)/11 + 3/11 = 19 + 3/11... so, y=19.
The question asks "What is the remainder when y is divided by 19?"
y=19, so 19/19 = 1. Therefore, the remainder = 0.
[/quote]
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
- Senior | Next Rank: 100 Posts
- Posts: 59
- Joined: Sat Mar 08, 2008 5:15 pm
- Location: Cincinnati
- Thanked: 3 times
Always remember
When X is divided by P & Q, but leaves the same remainder R, then
X = (LCM of P & Q) + R
so in this case
x = (LCM of 11 & 19 ) + 3
x = 199 + 3 = 209 + 3 = 212
you can easily solve many problems.
When X is divided by P & Q, but leaves the same remainder R, then
X = (LCM of P & Q) + R
so in this case
x = (LCM of 11 & 19 ) + 3
x = 199 + 3 = 209 + 3 = 212
you can easily solve many problems.
From the GMATPrep Practice Exam-What is this asking? And the answer anyone?
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a) f(x) =x^2
b) f(x) =x+1
c) f(x) =square root(x)
d) f(x) = 2/x
e) f(x) = -3x
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a) f(x) =x^2
b) f(x) =x+1
c) f(x) =square root(x)
d) f(x) = 2/x
e) f(x) = -3x
From the GMATPrep Practice Exam-What is this asking? And the answer anyone?
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a) f(x) =x^2
b) f(x) =x+1
c) f(x) =square root(x)
d) f(x) = 2/x
e) f(x) = -3x
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a) f(x) =x^2
b) f(x) =x+1
c) f(x) =square root(x)
d) f(x) = 2/x
e) f(x) = -3x
-
- Senior | Next Rank: 100 Posts
- Posts: 93
- Joined: Thu Apr 10, 2008 1:42 pm
- Location: Chicago
- Thanked: 20 times
This is a tough tough question. Not because of the math involved, but because of the translation to normal language. Thats the part that test-takers find to be the toughest to master.m_blooms wrote:From the GMATPrep Practice Exam-What is this asking? And the answer anyone?
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a) f(x) =x^2
b) f(x) =x+1
c) f(x) =square root(x)
d) f(x) = 2/x
e) f(x) = -3x
I will try explaining this as best as I can:
f(a+b) = f(a) + f(b) is a given condition that tells us whether we should retain an answer choice or not.
Let's try with Option A: f(x) =x^2 We have to test whether this function holds true for f(a+b) = f(a) + f(b)
Substitute a+b for X. Therefore, f(a+b) = (a+b) ^2.
Similarly, f(a) = a^2 ...........and................f(b) = b^2
We have to check now if f(a+b) = f(a) + f(b)
But, (a+b)^2 is clearly not equal to a^2 + b^ 2 ........this is a standard algebric rule.
Now that I have shown what the mathematical approach is, lets look at the test-smart way of doing this.
KAPLAN has a beautiful method for any question with "Which of the Following" as part of the question. Since this question has that phrase, we have to start looking from Option E upwards.
Lets do the same thing as I showed for Option A, except this time we'll do Option E: f(x) = -3x. We get the following from substituting a+b, a, AND b into this function.
f(a+b) = -3 (a+b)
f(a) = -3(a) ...................and f(b) = -3(b)
.
We see clearly that f(a+b) = f(a) + f(b) .............since -3(a+b) is indeed equal to -3(a) + -3(b)
Stop right here. Qa is E.............since its a MUST be true situation. We cannot have 2 answers for this. Saves you a bunch of trouble. Excellent Kaplan technique. Works most of the time.
Sorry for the long explanation, but I tried to really break it down for you, instead of just putting up an answer.
For love, not money.
-
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Wed Feb 13, 2008 10:53 am