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If x, y, and z are positive integers, what is the remainder when 100x

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If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 10 Jun 2008, 21:37
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If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?

(1) y = 6
(2) z = 3
[Reveal] Spoiler: OA

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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 10 Jun 2008, 22:11
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I think it should be E

you can represent 100X+10Y+Z as a three digit number XYZ


now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 --remainder is 2 , 263/7 ----remainder 4

One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution ;-)
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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 10 Jun 2008, 23:40
rpmodi wrote:
I think it should be E

you can represent 100X+10Y+Z as a three digit number XYZ


now from condition 1 and 2 , this three digit number is X63 , plug in different values for X : 163/7 --remainder is 2 , 263/7 ----remainder 4

One more comment on this solution : X , Y , Z can be > 10 ,so represtating 100X+10Y+Z as XYZ will not always be right , but by limiting the scope of X, Y, Z values we can simplyfy the solution ;-)


Thanks rpmodi, smart explaination!and E is OA :P
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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 22 Oct 2013, 13:59
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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 15 Nov 2014, 07:10
Hello from the GMAT Club BumpBot!

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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 07 Dec 2014, 13:16
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sondenso wrote:
If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?

(1) y = 6
(2) z = 3



Hi,

I set this problem up in a slightly different way.

I noticed that it has 1 equation and 4 unknowns, if you include remainder A.

Stmt 1 = With that logic, you substitute 6, you still have 3 unknowns and one equation. NS - Eliminate A
Stmt 2 = Set up the same equation by substituting 3, you still have 3 unknowns and one equation. NS - Eliminate B

If you set up the equation to include y and z (100x +10 (6) + 3)/7 = a) you have one equation and two unknowns Eliminate C.

Therefore, the only possible solution is E.

Does my logic make sense?
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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 24 Dec 2014, 19:04
sondenso wrote:
If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?

(1) y = 6
(2) z = 3



10y when divided by 7 can leave different remainders.
19*6 = 60 leaves remainder 4

z = 3 leaves remainder 3

but 100x when divided by 7 can leave different remainders. As we don't have concrete value for x, the answer is E
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Re: If x, y, and z are positive integers, what is the remainder when 100x [#permalink] New post 25 Dec 2014, 10:37
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Hi All,

This post is from years ago, but the prompt still serves as an example of how TESTing VALUES can help you to prove the correct answer in many DS questions.

We're told that X, Y and Z are POSITIVE INTEGERS. We're asked for the REMAINDER when 100X + 10Y + Z is divided by 7.

Fact 1: Y = 6

Since we don't know the values of X or Z, let's TEST VALUES.

Technically, we can use ANY positive integers for X and Z, but I'm going to keep things simple...
X = 1, Z = 1

(100 + 60 + 1)/7
161/7 = 23r0 so the answer is 0

X = 1, Z = 3
(100 + 60 + 3)/7
163/7 = 23r2 so the answer is 2
Fact 1 is INSUFFICIENT

Fact 2: Z = 3

Again, we can use ANY positive integers for X and Y, but let's keep things simple...

We can use the second example from Fact 1 here...
X = 1, Y = 6, Z = 3
163/7 = 23r2 so the answer is 2

X = 1, Y = 1, Z = 3
(100 + 10 + 3)/7
113/7 = 16r1 so the answer is 1
Fact 2 is INSUFFICIENT

Combined, we know
Y = 6
Z = 3
X = ANY POSITIVE INTEGER

If X = 1 (from our prior work)
163/7 = 23r2 so the answer is 2

If X = 2
(200 + 60 + 3)/7
263/7 = 37r4 so the answer is 4
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


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Re: If x, y, and z are positive integers, what is the remainder when 100x   [#permalink] 25 Dec 2014, 10:37
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