If x and y are both positive integers and x>y , what is the remainder when x is divided by y ?
(1) y is a two-digit prime number.
(2) x= qy+9 , for some positive integer q
[spoiler]OA: C[/spoiler]
tricky remainder
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Statement 1 tells us that y is a two digit prime number. We know that x > y. If y = 11 and x = 22, the remainder would be 0. Alternatively, y could be 11 and x could be 21 and the remainder 10.buoyant wrote:If x and y are both positive integers and x>y , what is the remainder when x is divided by y ?
(1) y is a two-digit prime number.
(2) x= qy+9 , for some positive integer q
[spoiler]OA: C[/spoiler]
Insufficient
One might be tempted to say that Statement 2 is sufficient because it tells us that x = (a multiple of y) + 9. So one's initial inclination might be to jump and say the remainder is 9. The problem is that y might be equal to or smaller than 9, in which cases the remainder would be some number less than 9.
Insufficient
Together we know that x = (a multiple of y) + 9 and, since y is a two digit number, that y is greater than 9. So the remainder is 9.
Sufficient
Choose C.
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Statement 1:buoyant wrote:If x and y are both positive integers and x>y , what is the remainder when x is divided by y ?
(1) y is a two-digit prime number.
(2) x= qy+9 , for some positive integer q
No information about x.
INSUFFICIENT.
Statement 2:
Let q=y=1.
Then x = 1*1 + 9 = 10.
In this case, x/y = 10/1 = 10 R0.
Let q=1 and y=2.
Then x = 1*2 + 9 = 11.
In this case, x/y = 11/2 = 5 R1.
Since the remainder can be different values, INSUFFICIENT.
Statement combined:
Case 1: q=1 and y=11
Here, x = 1*11 + 9 = 20.
In this case, x/y = 20/11 = 1 R9.
Case 2: q=2 and y=13
Here, x = 2*13 + 9 = 35.
In this case, x/y = 35/13 = 2 R9.
R=9 in both cases.
One more random case to be safe.
Case 3: q=6 and y=31
Here, x = 6*31 + 9 = 195.
In this case, x/y = 195/31 = 6 R9.
In every case, R=9.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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