BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If c and f are integers, is zc > zf?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members

If c and f are integers, is zc > zf?

by VJesus12 » Thu May 03, 2018 10:31 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If c and f are integers, is zc > zf?

(1) z^3*c > z^3*f
(2) z is less than 10

The OA is the option A.

How can I get the correct answer here? Is there someone who can help me? Thanks in advance.
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

by Vincen » Thu May 03, 2018 12:15 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Hello vjesus12.

Here we are asked if zc > zf? Let's see how can we respond this question.

(1) z^3*c > z^3*f

$$z^3\cdot c>z^3\cdot f\ \ \ \ \ \Leftrightarrow\ \ \ \ z^3\cdot c\ -\ z^3\cdot f\ >0$$ $$\Rightarrow\ \ \ z^2\left(zc\ -\ zf\ \right)>0$$ $$\Rightarrow\ \ \ zc\ -\ zf\ >0\ \ \ \text{since}\ \ z^2\ge0\ always$$ $$\Rightarrow\ \ \ zc\ >zf\ .\ \ \ \ SUFFICIENT$$ Hence, this statement is sufficient.

(2) z is less than 10

Here, we don't have information about "c" and "f". Therefore, this statement is NOT sufficient.

In conclusion, the correct answer for this DS question is the option A.

I hope it helps you.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri May 04, 2018 6:13 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

VJesus12 wrote:If c and f are integers, is zc > zf?

(1) z³c > z³f
(2) z is less than 10
Target question: Is zc > zf?

Statement 1: z³c > z³f
This tells us that z ≠ 0
It also means that z² > 0
Since z² is POSITIVE, we can safely divide both sides of the statement 2 inequality by z² to get: xc > zf
PERFECT!!
The answer to the target question is YES, xc IS greater than zf
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z is less than 10
Since we have no information about c or f, we cannot determine whether xc is greater than zf
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1