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

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

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Answers

A

B

C

D

E

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Difficulty—

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.
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Source: — Data Sufficiency |
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by Vincen » Thu May 03, 2018 12:15 pm
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.
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by Brent@GMATPrepNow » Fri May 04, 2018 6:13 am
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
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