If z is an integer, find the value of z. (1) -6z -14 -4z(2) -3z + 15 42a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If z is an integer, find the value of z. (1) ...

If z is an integer, find the value of z.

(1) -6z -14 > -4z

(2) -3z + 15 < 42

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'C'. Can you explain this answer?

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If z is an integer, find the value of z. (1) -6z -14 > -4z(2) -3z ...

Steps 1 & 2: Understand Question and Draw Inferences

We are given that z is an integer, and we have to find the value of z.

Since there is no other information provided in the question, let’s move on to the analysis of statements I and II.

Step 3: Analyze Statement 1

Statement 1 says: -6z -14 > -4z

Let’s try to solve this inequality:

-6z -14 > -4z

By adding 4z + 14 in both sides of the inequality,

-6z -14 + 4z + 14 > -4z + 4z + 14

-2z > 14

Multiplying both sides by -1/2,

z < -7 (Multiplying both sides by negative sign changes the sign of inequality)

So, statement (1) tells us that

z < -7

Thus, possible values of z are {-8, -9, -10, -11 ……. }

Since there are a number of integers less than -7, so we can’t determine the exact value of z.

Hence, statement (1) is not sufficient to answer the question: What is the value of z?

Step 4: Analyze Statement 2

Statement 2 says: -3z + 15 < 42

Let’s try to solve this inequality:

-3z + 15 < 42

By subtracting 15 from both sides of the inequality,

-3z + 15 -15 < 42 -15

-3z < 27

Multiplying both sides by -1/3,

z > -9 (Multiplying both sides by negative sign changes the sign of inequality)

So, statement (2) tells us that

z > -9

Thus, possible values of z: {-8, -7, -6, -5 …….}

Since there are a number of integers greater than -9, so we can’t determine the exact value of z.

Hence, statement (2) is not sufficient to answer the question: What is the value of z?

Step 5: Analyze Both Statements Together (if needed)

Since statement (1) and (2) alone are not sufficient to answer the question, let’s analyse both these statements together:

Per statement (1):

z = -8, -9, -10, -11 …….

Per statement (2):

z = -8, -7, -6, -5 …….

Combining both the statements, we get

z = -8

Hence, statement (1) and (2) together are sufficient to answer the question: What is the value of z?

Answer: Option (C)

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If z is an integer, find the value of z. (1) -6z -14 > -4z(2) -3z + 15 < 42a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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