z is an integer such that |z| 3 (2)

Question

z is an integer such that |z| < 6. Is z positive?

(1) |z - 2| > 3
(2) |z| = 2

Rabab36 · Answer

given |z|<6 thereore -63 z-2>3 z>5 -z+2>3 -z>1 z<-1 not sufficient statement 2 |z|=2 therefore z=-2,2 not sufficient combining 1 and 2 z<-1 we get -2 option c correct

Bunuel · Answer

You correctly identified that from (1) we get z < -1 or z > 5. What would be the possible value of z if we also take into the account that |z| < 6 ?

Nabneet · Answer

Bunuel Am I correct ? given |z|<6 -63 z-2>3 z>5 -z+2>3 -z>1 z<-1 NS 2. |z|=2 therefore z=-2,2 NS combining 1 and 2 & |Z|<6 NS Answer E

Bunuel · Answer

The OA is neither C, nor E.

Nabneet · Answer

Sorry my bad,
In statement 1 
z>5 wont be possible , because z is an integer 
So answer will be option A

Bunuel · Answer

z is an integer such that |z| < 6. Is z positive? Since z is an integer and -6 < z < 6, then z can be -5, -4, -3, ..., 5. (1) |z - 2| > 3 z - 2 > 3 or z - 2 < -3 z > 5 or z < -1. z > 5 cannot be true since z can be -5, -4, -3, ..., 5, therefore, z < -1 and the answer to the question is NO, z is not positive. Sufficient. (2) |z| = 2. z = 2 or z = -2, which is clearly not sufficient to say whether z is positive. Answer: A.

Dan1111 · Answer

You correctly identified that from (1) we get z < -1 or z > 5. What would be the possible value of z if we also take into the account that |z| < 6 ? I think this one must be E and here its why ( UPDATE: I founded my error, A its the correct answser ): ''z is an integer such that |z| < 6. Is z positive? (1) |z - 2| > 3 (2) |z| = 2 '' First I wanna say that I understood the question as "can we be sure that z its a positive number?" instead "its possible to z be a positive number?" The text says: ''z is an integer such that |z| < 6.'', so we know that z can assume the values: {-6, -5, -4....5, 6} Here's the error, in |z| < 6, its from -5 to 5; with that, statement (1) becomes sufficient . For (1), lets define the boundarys. Since |x| = { x (in case x>0), -x (in case x<0) } |z - 2| = z - 2 if z - 2 > 0 ---> z >=2 |z - 2| = -z + 2 if z - 2 < 0 ---> z <=2 assuming z >= 2 |z - 2| > 3 z - 2 > 3 z > 5, so we have here z >= 2 AND z > 5 = z > 5. so, z must be equal to 6 In true, thats no positive value that z can assume . assuming z <= 2 |z - 2| > 3 -z + 2 > 3 -z > 1 z < -1 , so we have here z <= 2 AND z < -1 = z < -1. so, z can be -2, -3, -4, -5 and -6 . So z can assume a lot for negative numbers here, so (1) is not sufficient . For example, to z = -2: |z - 2| > 3 |-2 - 2| > 3 |-4| > 3 4 > 3. ( the inequetion its true with z beeing a negative number). (1) is not sufficient For (2), we have: |z| = 2. Since its a equation instead a inequation, we are restrict to z = {2, -2}. Therefore, z can be -2, so (2) its not sufficient . (2) is not sufficient Note that even if you assume the 2 afirmations together, z can assume the value z = -2, as I proved on the example before. So, my answer is Statements 1 and 2 together are not sufficient (E) . Thats the first time that I read a explanation and didnt gone like "omg, now I understand why I got wrong". But instead Im not understanding why this should be "A", so I dare myself to writte this. Plz, if I said something wrong, correct me asap.

SaquibHGMATWhiz · Answer

Solution: Pre Analysis: z is an integer Such that |z|<6 or -6 3 From this we can say z-2>3 and z-2<-3 ⇒z>5 and z<-1 Based on our pre-analysis in step 1, we can infer that z cannot be greater than 5 So, the only possible values of z are -2, -3, -4 and -5 and we can be sure that z is not positive Thus, statement 1 alone is sufficient and we can eliminate options B, C and E Statement 2: |z| = 2 From this, the value of z is either 2 (positive) or -2 (not positive) Thus, statement 2 alone is not sufficient Hence the right answer is Option A

z is an integer such that |z| < 6. Is z positive? (1) |z - 2| > 3 (2)

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