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x and y are positive integers. What is the remainder when x is divided

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x and y are positive integers. What is the remainder when x is divided  [#permalink]

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Updated on: 17 Dec 2018, 00:27
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56% (00:49) correct 44% (01:01) wrong based on 43 sessions

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$$x$$ and $$y$$ are positive integers. What is the remainder when $$x$$ is divided by $$2^2$$?

(1) $$y = 7$$

(2) $$x = 3^{78y}$$

Originally posted by blitzkriegxX on 17 Dec 2018, 00:09.
Last edited by blitzkriegxX on 17 Dec 2018, 00:27, edited 2 times in total.
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Joined: 13 Mar 2018
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Re: x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 06:52
Hi i would like to know why ans is B here...since third digit is missing how can one determine what wud b the reminder? please explain
Manager
Joined: 28 Jun 2018
Posts: 93
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4
x and y are positive integers. What is the remainder when x is divided  [#permalink]

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Updated on: 17 Dec 2018, 07:36
Hi SWAPNILP
I don't want to provide the official explanation soo soon. Wanted to give a chance for others to think as well.

Also it is not a digit. It is (78 multiplied by y)

But here is a very big clue for you-
In Gmat a lot of problems depend on pattern recognision. So check the patterns when powers of 3 are divided by 4 mentioned in the question stem.

Edit- oops! Looks like chetan2u gave an awesome response (maybe a little too soon :D).

Originally posted by blitzkriegxX on 17 Dec 2018, 07:02.
Last edited by blitzkriegxX on 17 Dec 2018, 07:36, edited 4 times in total.
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Joined: 02 Aug 2009
Posts: 7200
x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 07:10
SWAPNILP wrote:
Hi i would like to know why ans is B here...since third digit is missing how can one determine what wud b the reminder? please explain

Quote:
$$x$$ and $$y$$ are positive integers. What is the remainder when $$x$$ is divided by $$2^2$$?

(1) $$y = 7$$

(2) $$x = 3^{78y}$$

Hi..
78y is not a 3-digit number but 78*y and you can say this because it is given that y is a positive integer.

so let us see the question..

(1) $$y = 7$$
insuff

(2) $$x = 3^{78y}$$
Now, you should check few multiples of 3 and you will find a pattern ..
3^1 divided by 4 leaves 3 as remainder
3^2 =9 leaves 1 as remainder
3^3=27 leaves 3 as remainder and so on.. so pattern is 3,1,3,1...
$$x = 3^{78y}$$, and this has an even power 78y, so answer will be that remainder is 1...
sufff

B

Ofcourse other way is binomial expansion.. $$x = 3^{78y}=(4-1)^{78y}$$...
In expansion. all terms except $$(-1)^{78y}$$ will be multiple of 4, so remainder = $$(-1)^{78y}=1$$
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 13 Mar 2018
Posts: 9
Re: x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 07:14
chetan2u wrote:
SWAPNILP wrote:
Hi i would like to know why ans is B here...since third digit is missing how can one determine what wud b the reminder? please explain

Quote:
$$x$$ and $$y$$ are positive integers. What is the remainder when $$x$$ is divided by $$2^2$$?

(1) $$y = 7$$

(2) $$x = 3^{78y}$$

Hi..
78y is not a 3-digit number but 78*y and you can say this because it is given that y is a positive integer.

so let us see the question..

(1) $$y = 7$$
insuff

(2) $$x = 3^{78y}$$
Now, you should check few multiples of 3 and you will find a pattern ..
3^1 divided by 4 leaves 3 as remainder
3^2 =9 leaves 1 as remainder
3^3=27 leaves 3 as remainder and so on.. so pattern is 3,1,3,1...
$$x = 3^{78y}$$, and this has an even power 78y, so answer will be that remainder is 1...
sufff

B

Ofcourse other way is binomial expansion.. $$x = 3^{78y}=(4-1)^{78y}$$...
In expansion. all terms except $$(-1)^{78y}$$ will be multiple of 4, so remainder = $$(-1)^{78y}=1$$

thanks chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 7200
Re: x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 07:25
1
blitzkriegxX wrote:
Hi SWAPNILP
I don't want to provide the official explanation soo soon. Wanted to give a chance for others to think as well.

But here is a very big clue for you-
In Gmat a lot of problems depend on pattern recognision. So check the patterns when powers of 3 are divided by 4 mentioned in the question stem.

Edit- oops! Looks like chetan2u gave an awesome response (maybe a little too soon :D).

Hi blitzkriegxX,
I wanted to clarify on 78y as a 3-digit number or a product 78*y.
I think in that process, the solution too came out.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 28 Jun 2018
Posts: 93
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4
x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 07:34
chetan2u wrote:

Hi blitzkriegxX,
I wanted to clarify on 78y as a 3-digit number or a product 78*y.
I think in that process, the solution too came out.

Hey chetan2u
No worries.
And you're right. I did mean the product 78*y.
Is this how the product part is expressed in official gmat questions?
Or should I edit my question to 78*y ?
Math Expert
Joined: 02 Aug 2009
Posts: 7200
Re: x and y are positive integers. What is the remainder when x is divided  [#permalink]

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17 Dec 2018, 07:44
1
blitzkriegxX wrote:
chetan2u wrote:

Hi blitzkriegxX,
I wanted to clarify on 78y as a 3-digit number or a product 78*y.
I think in that process, the solution too came out.

Hey chetan2u
No worries.
And you're right. I did mean the product 78*y.
Is this how the product part is expressed in official gmat questions?
Or should I edit my question to 78*y ?

Hi..
you are perfectly fine with the way you have written, 78y would mean product unless specified otherwise, and y as positive integer also makes it much more clearer, because if 78y were a 3-digit number, y would be a digit, and not integer.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: x and y are positive integers. What is the remainder when x is divided &nbs [#permalink] 17 Dec 2018, 07:44
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