What is the value of prime number z?
(1) z^3 < 25
(2) z^2 > 1
[spoiler]OA=A[/spoiler].
Shouldn't be C the correct answer? I am confused. Please, someone help me.
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What is the value of prime number z?
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Gmat_mission
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Vincen
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Hello Gmat_mission.
First of all, we know that z is a prime number.
First Statement
- If z=2 then z^3 = 8 < 25.
- If z=3, then z^3 = 27 > 25.
Therefore, the answer is z=2. So, this statement is sufficient.
Second Statement
Therefore, the correct answer is the option A.
I hope it helps you. <i class="em em-smiley"></i>
First of all, we know that z is a prime number.
First Statement
We have the following:(1) z^3 < 25
- If z=2 then z^3 = 8 < 25.
- If z=3, then z^3 = 27 > 25.
Therefore, the answer is z=2. So, this statement is sufficient.
Second Statement
In this case, we have that any prime number z will satisfy that z^2 > 1. So, this statement is not sufficient.(2) z^2 > 1
Therefore, the correct answer is the option A.
I hope it helps you. <i class="em em-smiley"></i>
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GMATGuruNY
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Statement 1: z³ < 25Gmat_mission wrote:What is the value of prime number z?
(1) z^3 < 25
(2) z^2 > 1
Only one value for z is possible:
z = 2, with the result that z³ = 2³ = 8.
If z is any other prime number, the value of z³ will exceed 25.
Thus, z=2.
SUFFICIENT.
Statement 2: z² > 1
Here, z can be ANY PRIME NUMBER, since the square of any prime number will be greater than 1.
Since the value of z cannot be determined, INSUFFICIENT.
The correct answer is A.
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Solution:Gmat_mission wrote:What is the value of prime number z?
(1) z^3 < 25
(2) z^2 > 1
We are given that z is a prime number and we need to determine its value.
Statement One Alone:
z^3 < 25
Since the only prime whose cube is less than 25 is 2, then z must be 2 (notice that if z ≥ 3, then z^3 ≥ 27). Statement one alone is sufficient.
Statement Two Alone:
z^2 > 1
Since any prime number raised to the second power is greater than 1, z could be any prime number. Statement two alone is not sufficient.
Answer: A
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