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# If a>b>c>d and a,b,c and d are integers, what is the probability that

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Math Expert
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If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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01 Jan 2018, 08:03
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Question Stats:

44% (01:06) correct 56% (01:41) wrong based on 78 sessions

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If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

_________________

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: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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01 Jan 2018, 08:19
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?
1) only one number is on left side of 0 on the number line.
2) $$bc$$ is positive

NEW question

to find probability of $$abcd>0$$

Statement 1: From this we know that one number is negative but others can be positive or $$0$$. Hence $$abcd$$ can be positive or $$0$$. Insufficient

Statement 2: Nothing mentioned about $$a$$ & $$d$$. Insufficient

Combining 1 & 2: we know only 1 number is negative and as $$bc>0$$ so both cannot be negative or $$0$$. hence $$a>b>c>0$$ and $$d<0$$.

Therefore $$abcd<0$$. Sufficient

Option C
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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12 Mar 2018, 01:00
2
Hello chetan2u

Does not statement 1 imply that product abcd can be zero (if c equals zero) or negative (if all 3 c, b and a are positive) but never positive? Which would mean that probability of it being positive is zero? And that would make statement 1 alone sufficient?

Thanks for explaining what I might be missing.
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 06:48
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?
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Please let me know if I am going in wrong direction.
Thanks in appreciation.

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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 06:55
yes ,
there seems a typo in OA.

u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 07:00
gmatbusters wrote:

OA is correct.

u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

What if .... if one of the integers is 0 ?

0 is interger , but neither +ve nor -ve..... now, what the next blunder I am up to
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 07:11
I think C is correct:
A. 1 number is negative, --> a: negative
Case 1: a=-2, b=0, c=1, d=2--> abcd<0
Case 2: a=-2, b=1, c=2, d=3--> abcd>0
Insufficient.
B. insufficient.
a + b: eliminate case 1 --> sufficient.
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 09:12
gmatbusters wrote:

OA is correct.

u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

Hi gmatbusters
Is saying what is the probablilty of abcd>0 the same as Is abcd>0?

If yes what is the difference? and how would we calculate the exact probability?

If not?
Then the question is asking Q.abcd>0?

Statement 1:
Only one term is negative.
has to be D=-ve
A,B,C can be positive or 0
Case 1: Ab positive c=0 d=-ive . Ans 0
SO abcd is not positive.

Case 2: Abc are positive
so abcd will be negative.
so abcd is not positive.

IN both cases the answer is NO.
Hence I marked this statement as suuficient.

Can you tell me where I am going wrong?
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Joined: 02 Aug 2009
Posts: 7209
Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 10:23
u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

Sorry, there was a typo ... edited it.
Thanks
_________________

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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Math Expert
Joined: 02 Aug 2009
Posts: 7209
Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 10:29
nitesh50 wrote:

u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

Hi gmatbusters
Is saying what is the probablilty of abcd>0 the same as Is abcd>0?

If yes what is the difference? and how would we calculate the exact probability?

If not?
Then the question is asking Q.abcd>0?

Statement 1:
Only one term is negative.
has to be D=-ve
A,B,C can be positive or 0
Case 1: Ab positive c=0 d=-ive . Ans 0
SO abcd is not positive.

Case 2: Abc are positive
so abcd will be negative.
so abcd is not positive.

IN both cases the answer is NO.
Hence I marked this statement as suuficient.

Can you tell me where I am going wrong?

Hi..

for answering a probability question we should be aware of the properties of the number in question.
here we have variables and we should know about them. here it literally becomes a question Is abcd positive..
Statement II will not give an answer,,..
since bc is positive, a is surely positive so abc is positive but we still do not know about d, so insuff.
if d is positive probability is 1, if not probability is 0
_________________

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: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 10:52
Statement 1
Only one number is negative. Implies the remaining three are greater than zero or two of them are greater than zero and one of them is zero.
In either case the probability of abcd being positive is zero.
Sufficient

Statement 2
bc is positive. Implies either both 'b' and 'c' are positive or both are negative.
If 'b' and 'c' both are positive, then 'a' must also be positive. So 'd' can be zero or negative. Probability of abcd being positive in both cases is zero.
If 'b' and 'c' are both negative, then 'd' must be negative. But, 'a' can be negative or zero or positive. Hence probability here can't be determined.
Therefore, Insufficient

Sent from my ONEPLUS A6000 using GMAT Club Forum mobile app
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 11:10
chetan2u wrote:
u1983 wrote:
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Hello Mods ( chetan2u , gmatbusters , amanvermagmat , Bunuel , VeritasKarishma )....... could we please check the OA again ?

Sorry, there was a typo ... edited it.
Thanks

Np.

But still I would have got the ans wrong................ again I mixed up DS yes/no VS value Q ....... Thanks a bunch chetan2u .....completely fine ......... Thanks again
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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that  [#permalink]

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06 Nov 2018, 11:37
chetan2u wrote:
If $$a>b>c>d$$ and a,b,c and d are integers, what is the probability that product $$abcd$$ is positive?

(1) Only one number is on left side of 0 on the number line.
(2) $$bc$$ is positive

NEW question

Quite interesting!

We know one number is on the left side of zero so it means we have 1 negative.

- * 3 other options (whether they’re all or all 0)

We get an answer of NO. Because 0 is neither positive nor negative. So it is not positive.

If - * + then we have an answer of NO it is negative not positive.

For statement 2)

BC is positive is not necessarily indicative of anything. It only means they are the same sign either both positive or both negative

b = 3 and c = 2

D could -ve or +ve so we have two different answers

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Re: If a>b>c>d and a,b,c and d are integers, what is the probability that &nbs [#permalink] 06 Nov 2018, 11:37
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