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# Is the product abcd negative?

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Is the product abcd negative? [#permalink]
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Bunuel wrote:
Is the product abcd negative?

(1) a < b < c < d

Target question: Is the product abcd negative?

Statement 1: a < b < c < d
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b, c, and d that satisfy statement 1. Here are two:
Case a: a = -1, b = 1, c = 2 and d = 3. In this case, abcd = (-1)(1)(2)(3) = -6. So, the answer to the target question is YES, the product abcd is negative
Case b: a = -2, b = -1, c = 2 and d = 3. In this case, abcd = (-2)(-1)(2)(3) = 12. So, the answer to the target question is NO, the product abcd is not negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Since there's no information about b and c, there's no way to determine whether the product abcd is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that ad > 0
This means that EITHER a and d are both negative OR a and d are both positive.
Let's examine each case separately...

Case a: a and d are both negative. We also know that a < b < c < d. We can see that d is the greatest value. So, if d is negative, then a, b and c are also negative.
So, the product abcd = (NEGATIVE)(NEGATIVE)(NEGATIVE)(NEGATIVE) = POSITIVE. So, in this case, the answer to the target question is NO, the product abcd is not negative

Case b: a and d are both positive. We also know that a < b < c < d. We can see that a is the least value. So, if a is positive, then b, c and d are also positive.
So, the product abcd = (POSITIVE)(POSITIVE)(POSITIVE)(POSITIVE) = POSITIVE. So, in this case, the answer to the target question is NO, the product abcd is not negative

There are only two possible cases (above), and in each case the answer to the target question is the same: NO, the product abcd is not negative
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 31 Mar 2018, 14:58.
Last edited by BrentGMATPrepNow on 01 Apr 2020, 04:52, edited 1 time in total.
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Re: Is the product abcd negative? [#permalink]
Bunuel wrote:
Is the product abcd negative?

(1) a < b < c < d

(1) a < b < c < d

Let a = 1 & b = 2 & c =3 & d=4...........Answer is No

Let a =-1 & b = 2 & c =3 & d=4...........Answer is Yes

Insufficient

It tells us the both a & d have the same sign.
No info about b & c

Insufficient

Combine 1 & 2

If a & d are positive......... b & d are positive as well...............Answer is No

If a & d are negative......... b & d are negative as well...............Answer is No

Sufficient

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Re: Is the product abcd negative? [#permalink]
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GMATPrepNow wrote:
Bunuel wrote:
Is the product abcd negative?

(1) a < b < c < d

Target question: Is the product abcd negative?

Statement 1: a < b < c < d
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b, c, and d that satisfy statement 1. Here are two:
Case a: a = -1, b = 1, c = 2 and d = 3. In this case, abcd = (-1)(1)(2)(3) = -6. So, the answer to the target question is YES, the product abcd is negative
Case b: a = -2, b = -1, c = 2 and d = 3. In this case, abcd = (-2)(-1)(2)(3) = 12. So, the answer to the target question is NO, the product abcd is not negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Since there's no information about b and c, there's no way to determine whether the product abcd is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that ad > 0
This means that EITHER a and d are both negative OR a and d are both positive.
Let's examine each case separately...

Case a: a and d are both negative. We also know that a < b < c < d. We can see that d is the greatest value. So, if d is negative, then a, b and c are also negative.
So, the product abcd = (NEGATIVE)(NEGATIVE)(NEGATIVE)(NEGATIVE) = POSITIVE. So, in this case, the answer to the target question is YES, the product abcd is negative

Case b: a and d are both positive. We also know that a < b < c < d. We can see that a is the least value. So, if a is positive, then b, c and d are also positive.
So, the product abcd = (POSITIVE)(POSITIVE)(POSITIVE)(POSITIVE) = POSITIVE. So, in this case, the answer to the target question is YES, the product abcd is negative

There are only two possible cases (above), and in each case the answer to the target question is the same: YES, the product abcd is negative
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

Hi Brent,
Thank you for a nice solution. Did you mean that the product abcd is positive not negative, right?
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Re: Is the product abcd negative? [#permalink]
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ypetrunina wrote:
Hi Brent,
Thank you for a nice solution. Did you mean that the product abcd is positive not negative, right?

Good catch!
I meant to say "NO, the product abcd is not negative"
I've edited my solution accordingly.

Kudos for you!!!

Cheers,
Brent
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Re: Is the product abcd negative? [#permalink]
Bunuel wrote:
Is the product abcd negative?

(1) a < b < c < d

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 4 variables and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
ad > 0 means that a and d have a same sign.
Both a<b<c<d and ad>0 mean that a, b, c and d have a same sign.
Thus, abcd > 0 and we have an unique answer 'no'

Since both conditions together yield a unique solution, they are sufficient.

Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, both conditions are sufficient, when used together.

Condition 1)

Since we can not figure signs of a, b, c and d, condition 1) does not yield a unique solution obviously, it is not sufficient.

Condition 2)

Since we don't have any information about b and c, condition 2) does not yield a unique solution obviously, it is not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: Is the product abcd negative? [#permalink]
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