What is the value of prime number z?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Mon Jun 25, 2018 12:12 am

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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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Source: Beat The GMAT — Data Sufficiency | Mon Jun 25, 2018 12:12 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon Jun 25, 2018 12:40 am

Hello Gmat_mission.

First of all, we know that z is a prime number.

First Statement

(1) z^3 < 25

We have the following:

- 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

(2) z^2 > 1

In this case, we have that any prime number z will satisfy that z^2 > 1. So, this statement is not sufficient.

Therefore, the correct answer is the option A.

I hope it helps you. <i class="em em-smiley"></i>

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 25, 2018 2:33 am

Gmat_mission wrote:What is the value of prime number z?

(1) z^3 < 25
(2) z^2 > 1

Statement 1: zÂ³ < 25
Only one value for z is possible:
z = 2, with the result that zÂ³ = 2Â³ = 8.
If z is any other prime number, the value of zÂ³ will exceed 25.
Thus, z=2.
SUFFICIENT.

Statement 2: zÂ² > 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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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jun 26, 2018 5:26 pm

Gmat_mission wrote:What is the value of prime number z?

(1) z^3 < 25
(2) z^2 > 1

Solution:

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 â‰¥ 3, then z^3 â‰¥ 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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