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Intern  B
Joined: 04 Jan 2018
Posts: 13
Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 45% (02:34) correct 55% (02:40) wrong based on 53 sessions

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Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

(A). In statement 1, there are two possible
values for k&: 19 and 28. Only 19 has a
11
The Princeton Review Management, LLC 2002
remainder of 3 when divided by 4,
however, so statement 1 is sufficient. All
even values of k will have a remainder of
3 when divided by 4 (can you explain why
this is so?), so statement 2 does not give
you enough information.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

Originally posted by Zed3092 on 24 Jan 2018, 03:44.
Last edited by Bunuel on 24 Jan 2018, 04:42, edited 3 times in total.
Renamed the topic, edited the question and the OA.
Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

hi K&=K^2+3..
so k^2+3 when divided by 4 leaves a remainder of 3..
so K^2 must be divisible by 4... so k could be any even number

1)16<K&<37
$$16<K^2+3<37$$....
$$K^2+3>16.....K^2>13...$$ so K >3 and K is an integer
$$K^2+3<37.....K^2<36..$$ .so K<6
possible values of K are 4 and 5
but 5^2 is not div by 4, so our answer 4..
suff

2) K is a factor of 24
nothing much
insuff

A
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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chetan2u wrote:
Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

hi K&=K^2+3..
so k^2+3 when divided by 4 leaves a remainder of 3..
so K^2 must be divisible by 4... so k could be any even number

1)16<K&<37
$$16<K^2+3<37$$....
$$K^2+3>16.....K^2>13...$$ so K >3 and K is an integer
$$K^2+3<37.....K^2<36..$$ .so K<6
possible values of K are 4 and 5
but 5^2 is not div by 4, so our answer 4..
suff

2) K is a factor of 24
nothing much
insuff

A

This would be correct if we were told that k is a positive integer. From (1) k could also be -4. (2) indirectly tells us that k must be positive, so the answer is C. Not a good question overall.
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Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Bunuel wrote:
chetan2u wrote:
Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

hi K&=K^2+3..
so k^2+3 when divided by 4 leaves a remainder of 3..
so K^2 must be divisible by 4... so k could be any even number

1)16$$16\(K^2+3>16.....K^2>13...$$ so K >3 and K is an integer
$$K^2+3<37.....K^2<36..$$ .so K<6
possible values of K are 4 and 5
but 5^2 is not div by 4, so our answer 4..
suff

2) K is a factor of 24
nothing much
insuff

A

This would be correct if we were told that k is a positive integer. From (1) k could also be -4. (2) indirectly tells us that k must be positive, so the answer is C. Not a good question overall.

yes I agree Bunuel..
and I doubt in GMAT a statement like " k is a factor of 24" would be given to give the info that k is positive..
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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chetan2u wrote:
Bunuel wrote:
chetan2u wrote:

This would be correct if we were told that k is a positive integer. From (1) k could also be -4. (2) indirectly tells us that k must be positive, so the answer is C. Not a good question overall.

yes I agree Bunuel..
and I doubt in GMAT a statement like " k is a factor of 24" would be given to give the info that k is positive..

Yes. That's one reason I think the question is not good.
_________________
Intern  B
Joined: 12 Sep 2017
Posts: 13
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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chetan2u wrote:
Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

hi K&=K^2+3 ..
so k^2+3 when divided by 4 leaves a remainder of 3..
so K^2 must be divisible by 4... so k could be any even number

Can someone explain to me what is going on here? The question states "x& = x^2 + 3" so why do you conclude "K&=K^2+3"??
1)16<K&<37
$$16<K^2+3<37$$....
$$K^2+3>16.....K^2>13...$$ so K >3 and K is an integer
$$K^2+3<37.....K^2<36..$$ .so K<6
possible values of K are 4 and 5
but 5^2 is not div by 4, so our answer 4..
suff

2) K is a factor of 24
nothing much
insuff

A
Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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HarryAxel wrote:
chetan2u wrote:
Given that x& = x^2 + 3, what is the value of integer k if there is a remainder of 3 when k& is divided by 4?

(1) 16 < k& < 37
(2) k is a factor of 24.

Can someone please explain this to me? Why are 19 and 28 the only possibility in statement 1?

hi K&=K^2+3 ..
so k^2+3 when divided by 4 leaves a remainder of 3..
so K^2 must be divisible by 4... so k could be any even number

Can someone explain to me what is going on here? The question states "x& = x^2 + 3" so why do you conclude "K&=K^2+3"??
1)16<K&<37
$$16<K^2+3<37$$....
$$K^2+3>16.....K^2>13...$$ so K >3 and K is an integer
$$K^2+3<37.....K^2<36..$$ .so K<6
possible values of K are 4 and 5
but 5^2 is not div by 4, so our answer 4..
suff

2) K is a factor of 24
nothing much
insuff

A

Hi..

x isa variable and it is basically given to tell you about function '&' ..
x can take any value as it is a variable...
Ofcourse it could have been given as X& too..
_________________
Intern  B
Joined: 12 Sep 2017
Posts: 13
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Ok but it is not stated that "&" is a function right? It could be a number so how can we tell?
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1430
Location: India
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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HarryAxel wrote:
Ok but it is not stated that "&" is a function right? It could be a number so how can we tell?

I believe in GMAT it would be explicitly mentioned. Here its not explicitly mentioned, then we go by the conventions - what we generally follow. We use 'x', 'y', 'z' etc to represent variables (which are supposed to take various numerical values), but we dont use symbols like '&', '\$', '#' etc to represent numbers - these are used for some specific purposes, one of which is to 'define a function'. Eg, here '&' has been defined as a function before which whenever you place any number, you have a result which is square of that placed number and then 3 added.

So, 5& becomes = 5^2 + 3 = 28.
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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HarryAxel wrote:
Ok but it is not stated that "&" is a function right? It could be a number so how can we tell?

As mentioned above, this is not a good question, so you can ignore it and move on.

For more on functions check the links below:

13. Functions

_________________
Intern  Joined: 06 Jan 2018
Posts: 7
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Just a quick question:
If we are told K is a factor, couldn’t K be a negative number?

Sent from my iPhone using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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balhhs0e wrote:
Just a quick question:
If we are told K is a factor, couldn’t K be a negative number?

Sent from my iPhone using GMAT Club Forum mobile app

A factor is a positive divisor.
_________________
Intern  Joined: 06 Jan 2018
Posts: 7
Re: Given that x& = x^2 + 3, what is the value of integer k if there is a  [#permalink]

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Thank you. A multiple could be negative, but NOT a factor. Clear!!!

Sent from my iPhone using GMAT Club Forum Re: Given that x& = x^2 + 3, what is the value of integer k if there is a   [#permalink] 25 Jan 2018, 21:44
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