Prepare a table for 1) and check for all signs for c and d
c 3c d -8d^3
- - - +
+ + + -
+ + - +
- - + -
You can see that 3c = -8d^3 only if the signs of c and d are different. So cd will not be positive for 1).
Consider 2)
d > c +4
Let d = 6 and c = 1
6 > 1 + 4
Let d = 6 and c = -1
6 > -1 + 4
So c and d can have same sign or different signs. Therefore we do not know cd is +ve or -ve.
Choose A
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cd?
Source: Beat The GMAT — Data Sufficiency |
Sorry I always go wrong in aligning. Please prepare the table in your notebook and you will understand
For questions like this, the easiest thing to do (in my opinion) is just plug in simple numbers.grandh01 wrote:Is the product of cd positive?
1) 3c= -8d^3
2) d> c + 4
QUESTION: is cd positive?
For cd to be positive that means they have to have the same sign (++ or --)
STATEMENT ONE: 3c=-8d^3
Solve for either c or d^3. we get: -(8/3)*c = d^3.
Now say c=1, plug and go. If c=1 than d^3= -(8/3) You don't need to solve for D. Just notice when c is +, D is -. That means CD = a - number. Remember any number x raised to an odd number (ie x^3) preserves the sign of x. This statement is sufficient.
STATEMENT TWO: d> c + 4
This doesn't really help if c is -3, then d is +, but if c is -100, then d is -. We don't know for sure, insufficient.
The correct answer is thus A.
Hope this helps
A useful website I found that has every quant OG video explanation:
https://www.beatthegmat.com/useful-websi ... tml#475231
https://www.beatthegmat.com/useful-websi ... tml#475231
Here we go, lets start fith the 2nd option that seems prettier:-)
2. d>c+4, let c=-1 then d>3, hence cd<0
let c=0 then d>4, hence cd=0
let c=2 then d>6, hence cd>0
Thus, Cross B and D out as the 2nd option is Insufficient
1. 3C=-8D^3, here we get -0.375*C = D^3
Obviously the only way for the equation set forth above to be veracious C and D must have different signs.
For example, let C=1000---->>>>>> D^3 = -375, hence cd<0
let C=-100 -->>>>>>> D^3 = 37.5, hence cd<0
From above we might conclude that the answer can be (A)
Please, correct me if I went awry
2. d>c+4, let c=-1 then d>3, hence cd<0
let c=0 then d>4, hence cd=0
let c=2 then d>6, hence cd>0
Thus, Cross B and D out as the 2nd option is Insufficient
1. 3C=-8D^3, here we get -0.375*C = D^3
Obviously the only way for the equation set forth above to be veracious C and D must have different signs.
For example, let C=1000---->>>>>> D^3 = -375, hence cd<0
let C=-100 -->>>>>>> D^3 = 37.5, hence cd<0
From above we might conclude that the answer can be (A)
Please, correct me if I went awry
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Target question: Is the product cd positive?grandh01 wrote:Is the product of cd positive?
1) 3c = -8d^3
2) d > c + 4
OA is A
Statement 1: 3c = -8d³
Divide both sides by d to get: 3c/d = -8d²
Divide both sides by 3 to get: c/d = -8d²/3
Rewrite as: c/d = (-8/3)(d²)
Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can rewrite our equation as: c/d = (NEGATIVE)(some number greater than or equal to zero)
(NEGATIVE)(some number greater than or equal to zero) = some number that is less than or equal to zero
So, c/d = some number less than or equal to zero
This means the quotient c/d CANNOT be positive
It also mean the product cd CANNOT be positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
ASIDE: the important concept here is that, if c/d is positive, then cd is also positive. Likewise, if c/d is negative, then cd is also negative.
Statement 2: d > c + 4
There are several values of c and d that satisfy statement 2. Here are two:
Case a: c = 1 and d = 10. Here, cd = (1)(10) = 10, so the answer to the target question is YES, cd IS positive
Case b: c = -1 and d = 5. Here, cd = (-1)(5) = -5, so the answer to the target question is NO, cd is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
