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# Is 96 divisible by integer x?

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Joined: 02 Sep 2009
Posts: 61243
Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 20:39
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Competition Mode Question

Is 96 divisible by integer x?

(1) x is divisible by 8.

(2) x is divisible by 12.

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Joined: 02 Aug 2009
Posts: 8268
Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 21:26
1
Is 96 divisible by integer x?
Is 96=x*y, where y is a positive integer..

(1) x is divisible by 8.
x=8a..
If x is 8*4, 96 is divisible, but if x is 8*13, no

(2) x is divisible by 12.
x=12b..
If x is 12*4, 96 is divisible, but if x is 12*13, no

Combined..
x is divisible by LCM(8,12) or 24..
If x is 24*2, yes, but if x=24*7 or 24*13..no
Insuff

E
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Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 22:58
1
Is 96 divisible by integer x?

X has to be a factor of 96 for 96 to be divisible by x.

(1) x is divisible by 8.
x = 16 Yes
x = 40 No

INSUFFICIENT.

(2) x is divisible by 12.
x = 24 Yes
x = 36 No

INSUFFICIENT.

Together 1 and 2
LCM(8,12) = 24 i.e. x is divisible by 24.Then
x = 48 YES
x = 72 NO

INSUFFICIENT.

Answer E.
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Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 23:05
1
(1) x is divisible by 8.

So x can be 8,(8*5=40),(8*7=56),(12*8=96)(12*8*5=480).....Clearly insuff

(2) x is divisible by 12.
So x can be 12,(12*5=60),(12*8=96)(12*8*5=480)....Clearly insufficient

So by combining both we got below common values..
96,480

96 is divisible by 96
But 96 us not divisible by 480....So.... Insufficient

OA:E
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Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 23:42
1
Is 96 divisible by integer x?

(1) x is divisible by 8.
x is 8, yes 96 is divisible by x
x is 104, no 96 isn't divisible by x
insufficient

(2) x is divisible by 12.
x is 12, yes 96 is divisible by x
x is 144, no 96 isn't divisible by x
insufficient

together,
x is 96, yes 96 is divisible by x
x is 120, no 96 isn't divisible by x

Therefore, E
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Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 23:45
1
examining option A: X is divisible by 8

X= 16 yes 96 is divisible by 16
X=80 No 96 is not divisible by 16

examining option B: X is divisible by 12

X=24 yes
X=60 No

Considering A and B together X is divisible by both 8 and 12= > X is divisible by 24

X=24 yes
X=168 no

therefore the answer is E
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Re: Is 96 divisible by integer x?  [#permalink]

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27 Oct 2019, 23:53
1
Is 96 divisible by integer x?

(Statement1): x is divisible by 8.
--> x could be 24 (96 is divisible by 24--YES)
--> x could be 40 (96 is not divisible by 40--NO)
Insufficient

(Statement2): x is divisible by 12.

--> x could be 24 (96 is divisible by 24--YES)
--> x could be 60 (96 is not divisible by 60--NO)
Insufficient

Taken together 1&2,
LCM(8,12)=24
--> 96 is divisible by 24 (YES)
--> 96 is divisible by 48 (YES)
--> but if x=72, 96 is not divisible by 72
Insufficient

The answer is E.
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Re: Is 96 divisible by integer x?  [#permalink]

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28 Oct 2019, 01:40
1
96 = 2^5*3
#1
x is divisible by 8
so x has to be at least 2^3 ; in that case yes 2^5*3 will be divisible by 2^3 ; sufficient
and x can be 200 5^2*2^3 ; 96 will not be divisible by 5^2*2^3 ; insufficient
#2
x is divisible by 12
12= 2^2*3
x has to be at least 2^2*3 ; so 2^5*3 will be divisible by 2^2*3
x=108
2^2^3^3 so no. 2^5*3 not divisible
insufficient
from 1 &2
LCM of 2^3 and 2^2*3= 2^3*3; 24
yes 96 is divisible by 24,48
and no when x=72
IMO E

Is 96 divisible by integer x?

(1) x is divisible by 8.

(2) x is divisible by 12.
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Re: Is 96 divisible by integer x?  [#permalink]

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28 Oct 2019, 05:52
1
Quote:
Is 96 divisible by integer x?

(1) x is divisible by 8.

(2) x is divisible by 12.

$$primefactors(96)=2^5*3$$

(1) x is divisible by 8. insufic.

$$x/8:x=8=2^3…answer=yes…x=2^3*7…answer=no$$

(2) x is divisible by 12. insufic.

$$x/12:x=12=2^2*3…answer=yes…x=2^2*3*7…answer=no$$

(1 & 2) insufic.

$$x/12…x/8…x=2^3*3…answer=yes…x=2^3*3*7…answer=no$$

Answer (E)
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Re: Is 96 divisible by integer x?  [#permalink]

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28 Oct 2019, 08:47
1
We are to determine if 96 is divisible by x.

96=2^5 * 3
1. x is divisible by 8
Not sufficient because x can be 16 which is divisible by 8 and 96 is divisible by 16. x can also be 40 which is divisible by 8 but 96 is not divisible by 40.

2. x is divisible by 12
Not sufficient because x can be 24 which is divisible by 12 and 96 is divisible by 24. However, when x=60 which is divisible by 12 but 96 is not divisible by 60.

1+2
we have x=24 which is divisible by both 8 and 12, and 96 is divisible by 24. However when x=120, which is divisible by 8 and 12 but 96 is not divisible by 120.
Both statements taken together are still not sufficient.

The answer is therefore E.
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Re: Is 96 divisible by integer x?  [#permalink]

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28 Oct 2019, 21:29
Bunuel wrote:

Competition Mode Question

Is 96 divisible by integer x?

(1) x is divisible by 8.

(2) x is divisible by 12.

Asked: Is 96 divisible by integer x?

(1) x is divisible by 8.
x = 16; 96 is divisible by x(16).
x = 64; 96 is not divisible by x(64)
NOT SUFFICIENT

(2) x is divisible by 12.
x = 12; 96 is divisible by x(12)
x = 36; 96 is not divisible by x(36)
NOT SUFFICIENT

(1) + (2)
(1) x is divisible by 8.
(2) x is divisible by 12.
x is divisible by LCM(8,12) = 24
x = 24; 96 is divisible by x(24)
x = 72; 96 is not divisible by x(72)
NOT SUFFICIENT

IMO E
Re: Is 96 divisible by integer x?   [#permalink] 28 Oct 2019, 21:29
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