Is the product abcd negative?

Question

Is the product abcd negative?
 
(1) a < b < c < d
(2) ad > 0

Vinayak Shenoy · Answer

IMO C

Clearly statement 1 is insufficient.

From statement 2
we know a and d have same signs
but we don't know anything about b and c
Hence insufficient

Combining
a < b < c < d and ad > 0
we can say that abcd= positive

rohit8865 · Answer

(1) a could be negative and b,c,d be +ve ------Yes 
 all a,b,c,d could be +ve-----------------------No
insuff..

(2) a and D are of same sign
no info on b,c--------Not suff

Combining we know all a,b,c,d are on either right side or left side of 0 
any case product is +ve
suff

Ans C

BrentGMATPrepNow · Answer

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 Statement 2 : ad > 0 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 Answer: C Cheers, Brent

Mo2men · Answer

(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

(2) ad > 0

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

Answer: C

ypetrunina · Answer

Hi Brent,
Thank you for a nice solution. Did you mean that the product abcd is positive not negative, right?

BrentGMATPrepNow · Answer

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

Kudos for you!!!

Cheers,
Brent

MathRevolution · Answer

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 a0 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. Therefore, C is the answer. 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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Is the product abcd negative?

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Is the product abcd negative?

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