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# What is the probability of (x+3)(x+10) being div by 6?

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Math Expert
Joined: 02 Aug 2009
Posts: 6959
What is the probability of (x+3)(x+10) being div by 6?  [#permalink]

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24 Apr 2016, 21:28
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5
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Difficulty:

95% (hard)

Question Stats:

25% (02:37) correct 75% (01:56) wrong based on 100 sessions

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What is the probability of (x+3)(x+10) being div by 6?

(1) x > 0
(2) y = x+3, where y is an integer greater than 3..

OA in two days

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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

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Re: What is the probability of (x+3)(x+10) being div by 6?  [#permalink]

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24 Apr 2016, 22:32
chetan2u wrote:
What is the probability of (x+3)(x+10) being div by 6?
(1) x > 0
(2) y = x+3, where y is an integer greater than 3..

OA in two days

St 1: I tool x=1 not divisible by 6. so prob = 0. and i took x=2 div by 6. Prob changes.
st 2: Similar steps i followed.

Combining y=4, x=1 not divisible
y=6, x=3 divisible

I went with E
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Re: What is the probability of (x+3)(x+10) being div by 6?  [#permalink]

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25 Apr 2016, 22:55
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chetan2u wrote:
What is the probability of (x+3)(x+10) being div by 6?
(1) x > 0
(2) y = x+3, where y is an integer greater than 3..

OA in two days

hi
the Q asks us probability of (x+3)(x+10) being div by 6..
we are not told if x is an integer or not..

If an integer,
1) (x+3)(x+10) will be div by 2 as ONE of them will be ODD and OTHER will be EVEN..

2) So we are looking for div by 3..
x+3 will have same property of div by 3 as x+3+3 or x+3+3+3 = x+9 will have ..
so in a way, for looking for div by 3, we can x+9 and x+10 to be consecutive..
In any three consecutive integers, 2 of them will satisfy the criteria of div by 6..
so Probability will be $$\frac{2}{3}$$

So, what are we looking for-
Whether x is an integer..

lets see the statements-

(1) x > 0
we just know x is positive but nothing if it is an integer or fraction
Insuff

(2) y = x+3, where y is an integer greater than 3..
We are told y>3 and y=x+3..
so x will be an integer >0..
$$prob = \frac{2}{3}$$
Suff

B
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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

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Re: What is the probability of (x+3)(x+10) being div by 6?  [#permalink]

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22 Nov 2017, 14:49
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Re: What is the probability of (x+3)(x+10) being div by 6? &nbs [#permalink] 22 Nov 2017, 14:49
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