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# Is the integer x a multiple of 5 ? (1) x divided by 3 leaves a remaind

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Is the integer x a multiple of 5 ? (1) x divided by 3 leaves a remaind  [#permalink]

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20 Dec 2018, 02:21
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Difficulty:

35% (medium)

Question Stats:

68% (01:23) correct 32% (01:34) wrong based on 84 sessions

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Is the integer x a multiple of 5 ?

(1) x divided by 3 leaves a remainder of 2.
(2) x divided by 4 leaves no remainder.

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Re: Is the integer x a multiple of 5 ? (1) x divided by 3 leaves a remaind  [#permalink]

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20 Dec 2018, 04:49
Bunuel wrote:
Is the integer x a multiple of 5 ?

(1) x divided by 3 leaves a remainder of 2.
(2) x divided by 4 leaves no remainder.

1) x leaves a remained of 2 when divided by 3, x=3m+2, could be 2,5, 8, 11, 14, 17, 20, 23 etc. x can or cannot be multiple of 5. Insufficient.

2) x is divisible by 4. could be, 4,8,16,20,24... etc. Similarly, x can or cannot be multiple of 5, Insufficient.

(1)+(2), x=8,20,32, 44 etc. Again, x can or cannot be a multiple of 5. Insufficient.

Hence, IMO, Option E.
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Re: Is the integer x a multiple of 5 ? (1) x divided by 3 leaves a remaind  [#permalink]

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20 Dec 2018, 05:42
1
x multiple of 5? This means x=5k?

Remember that Dividend = Divisor * Quotient + Remainder

(1) x divided by 3 leaves a remainder of 2.
We can write: X=3*Q+2
So X can take these values X= 2,5,8,11,14,17,20....
As you can see X=5 is a multiple of 5 but X=2,8,11,14.... are not multiple of 5.
INSUFFICIENT

(2) x divided by 4 leaves no remainder.
We can write X=4*Q+0 ; which means that X is a multiple of 4
X can take these values : 0,4,8,12,16,20,24....
As you can see X=20 is a multiple of 5 but X=4,8,12,16,20,24.... are not multiple of 5
INSUFFICIENT

(1) and (2)
From 1; X =2,5,8,11,14,17,20....
From 2; X=4,8,12,16,20,24....

This means that X = 8,20, ....
As you can see X =20 is a multiple of 5 but X=8 is not a multiple of 5.
INSUFFICIENT

Ans E
Re: Is the integer x a multiple of 5 ? (1) x divided by 3 leaves a remaind   [#permalink] 20 Dec 2018, 05:42
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