Is x < y?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Mar 27, 2018 2:51 am

Is x < y?

(1) z < y
(2) z < x

The OA is the option E.

If we subtract both statements we will get that x<y. Why is the correct answer E?

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 27, 2018 2:51 am

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 » Tue Mar 27, 2018 4:39 am

VJesus12 wrote:Is x < y?

(1) z < y
(2) z < x

Statement 1:
No information about x.
INSUFFICIENT.

Statement 2:
No information about y.
INSUFFICIENT.

Statements combined:
Case 1: z=0, y=2 and x=1
In this case, x < y so the answer to the question stem is YES.
Case 2: z=0, y=1 and x=2
In this case, x > y, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

The correct answer is E.

If we subtract both statements we will get that x<y. Why is the correct answer E?

We cannot subtract inequalities; we can only ADD them.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 27, 2018 7:07 am

VJesus12 wrote:Is x < y?

(1) z < y
(2) z < x

The OA is the option E.

If we subtract both statements we will get that x<y. Why is the correct answer E?

Don't subtract inequalities
Doing so can yield erroneous statements.

Consider this example:
5 < 6
0 < 9

When we subtract these inequalities , we get 5 - 0 < 6 - 9
Evaluate to get 5 < -3 (not true)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Mar 29, 2018 4:48 pm

VJesus12 wrote:Is x < y?

(1) z < y
(2) z < x

We need to determine if x < y

Statement One Alone:

z < y

Since we know nothing about x, statement one alone is not sufficient to answer the question.

Statement Two Alone:

z < x

Since we know nothing about y, statement one alone is not sufficient to answer the question.

Statements One and Two Together:

Although we know that both x and y are greater than z, we still cannot determine whether y is greater than x.

Answer: E

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