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If x is an integer, is (9x^2 + 10)^2/5 an integer?

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Syumbel
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If x is an integer, is (9x^2 + 10)^2/5 an integer? [#permalink] New post   Updated on: 20 Nov 2023, 14:21
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If x is an integer, is (9x^2 + 10)^2/5 an integer?

(1) x is a prime factor of 60
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient
e) Statements 1) and 2) TOGETHER are not sufficient
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C

Originally posted by Syumbel on 20 Nov 2023, 11:31.
Last edited by Bunuel on 20 Nov 2023, 14:21, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x is an integer, is (9x^2 + 10)^2/5 an integer? [#permalink] New post   21 Nov 2023, 00:35
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If x is an integer, is \(\frac{(9x^2 + 10)^2}{5}\) an integer?

What the question asks: Is \(9x^2+10\) divisible by 5.
Only possibility when x is a multiple of 5.

(1) x is a prime factor of 60
So x can be 2, 3 or 5.
Insufficient

(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x could be any of many possible odd numbers.
1 or 5 when k is 0 or 5
7 or 11 when k is 1
13 or 17 when k is 2
and so on. (One less or 1 more than all multiples of 6)
Insufficient


Combined
x cannot be 2 and 3 as x=6k+1=(2*3)k+1 or (2*3)k+5
Only possibility is 5.
Sufficient

C
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Re: If x is an integer, is (9x^2 + 10)^2/5 an integer? [#permalink] New post   22 Nov 2023, 03:35
Asked: If x is an integer, is (9x^2 + 10)^2/5 an integer?

(1) x is a prime factor of 60
x = 2, 3 or 5
Not Sufficient

(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17
Not sufficient

(1) + (2)
(1) x is a prime factor of 60
x = 2, 3 or 5
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer
x = 1, 5, 7, 11, 13, 17

x = 5
Sufficient

IMO C
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Re: If x is an integer, is (9x^2 + 10)^2/5 an integer? [#permalink] New post   22 Nov 2023, 04:09
given
is (9x^2 + 10)^2/5 an integer
if x is an integer
#1
x is a prime factor of 60
x is 2,3,5
we get no at 2,3 and yes at 5
insufficient
#2
x can be written as 6k+1 or 6k+5, where k is a non-negative integer
again k can be 0,1,2 so on
yes and no
from 1 &2
x is 5 sufficient
option C

Syumbel wrote:
If x is an integer, is (9x^2 + 10)^2/5 an integer?

(1) x is a prime factor of 60
(2) x can be written as 6k+1 or 6k+5, where k is a non-negative integer

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d) EACH statement ALONE is sufficient
e) Statements 1) and 2) TOGETHER are not sufficient
GMAT Club Bot
gmatclubot
Re: If x is an integer, is (9x^2 + 10)^2/5 an integer? [#permalink]
22 Nov 2023, 04:09
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Bunuel
Math Expert
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