How many of integers P, Q, and R are zeroes? (1) PQR=0 (2) P+Q+R=0

Question

How many of integers P, Q, and R are zeroes?

(1) PQR = 0 
(2) P + Q + R = 0

EgmatQuantExpert · Answer

Solution 
  To find:  
 • The number of integers, among P, Q and R, that are zero

Analysing Statement 1  
 • PQR = 0, that implies, atleast one among P, Q and R = 0

Therefore, statement 1 is not sufficient

Analysing Statement 2  
P + Q + R = 0
 • From this statement we can infer that, none of them or all of them or any one of them can be equal to 0

Therefore, statement 2 is not sufficient

Combining Both Statements  
Combining both, we get two cases,
 • All the three integers are 0, or
• One of them is zero, and the other two are not zeroes, but their sum is 0

Therefore, both statements together are not sufficient

Hence, the correct answer is Option E.

Answer: E

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-NP-e1533292073470.jpg

Archit3110 · Answer

from1 :
any of PQR can be 0 so not sufficient

fro 2 : again P,Q can be same integer with opposite sign or all three can be 0 so not sufficient

from 1& 2 :

value of all three integers could be 0 or two integers could be of opposite sign and third 0 
IMO E

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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since we have 3 variables ( P, Q and R ) 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) If P = 0, Q = 1 and R = -1 , then the number of zeros of P, Q and R is 1 . If P = 0, Q = 0 and R = 0 , then the number of zeros of P, Q and R is 3 . Since both conditions together do not yield a unique solution, they are not sufficient. Therefore, E 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.

How many of integers P, Q, and R are zeroes? (1) PQR=0 (2) P+Q+R=0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

How many of integers P, Q, and R are zeroes? (1) PQR=0 (2) P+Q+R=0

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards