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Manhattan Question Set # 3

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Manhattan Question Set # 3

by richachampion » Sun Oct 09, 2016 5:56 pm
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

OA:A
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by [email protected] » Sun Oct 09, 2016 7:42 pm
Hi richachamption,

We're told that...
X/11 = Y remainder 3
X/19 = something remainder 3

With the first piece of information, we know that X is 3 greater than a multiple of 11; with the second piece of information, we know that X is 3 greater than a multiple of 19. To have a remainder of 3 when you divide X by BOTH 11 and 19, X must be a number that is 3 greater than a MULTIPLE of BOTH 11 and 19.

We're asked what the remainder would be when Y is divided by 19. At this point, you might recognize that you could choose Y=19 and solve from there. If you don't recognize why that that relationship exists, then here's a more step-heavy way to get to the correct answer:

X = (11)(19) + 3 = 209 + 3 = 212

212/11 = Y remainder 3
212 = 11Y + 3
209 = 11Y
209/11 = Y
19 = Y

We're ultimately asked what the remainder would be when 19 is divided by 19. The remainder is 0.

Final Answer: A

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by GMATGuruNY » Mon Oct 10, 2016 2:27 am
richachampion 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
When x is divided by 19, the remainder is 3.
Implication:
x = 19a + 3, where a is a nonzero integer.
Options for x:
3, 22, 41...

When positive integer x is divided by 11, the quotient is y and the remainder is 3.
Implication:
x = 11y + 3, where y is a nonzero integer.
Options for x:
3, 14...

The smallest value common to both lists is 3.
If x=3, then y=0.
What is the remainder when y is divided by 19?
0/19 = 0 R0.

The correct answer is A.
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by Matt@VeritasPrep » Fri Oct 14, 2016 2:27 am
x = 11*y + 3
x = 19*(some integer) + 3

So x is 3 greater than a multiple of 11 AND 3 greater than a multiple of 19. That means x is 3 greater than a multiple of 11*19.

For simplicity's sake, let's say x = 11*19 + 3. Then y = 19, and the remainder of y / 19 is 0.
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