Last visit was: 26 Jul 2024, 16:40 It is currently 26 Jul 2024, 16:40
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is y < z ? (1) y + z = 1 (2) y^2 < z^2

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
S
GeorgeKo111
Manager
Manager
Joined: 21 Jun 2019
Posts: 83
Own Kudos [?]: 73 [16]
Given Kudos: 39
Location: Canada
Concentration: Finance, Accounting
GMAT 1: 670 Q48 V34
GPA: 3.78
Send PM
Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   03 Jul 2019, 09:25
15
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:54) correct 36% (01:42) wrong based on 301 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
Is y < z ?

(1) y + z = 1

(2) y^2 < z^2
ShowHide Answer
Official Answer
C
User avatar
S
GeorgeKo111
Manager
Manager
Joined: 21 Jun 2019
Posts: 83
Own Kudos [?]: 73 [2]
Given Kudos: 39
Location: Canada
Concentration: Finance, Accounting
GMAT 1: 670 Q48 V34
GPA: 3.78
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   03 Jul 2019, 09:26
1
Kudos
1
Bookmarks
SOLUTION


Choice (C) is correct.

The stem doesn't give us much information to work with, so we can go directly to the statements. They will be sufficient only if y must be less than z or cannot be less than z.

Statement (1): insufficient. This tells us the sum of y and z, but it says nothing about their relative values. It is possible that y and z are equal (if each is 0.5), or that either variable is greater (e.g., y = 1 and z = 0, or vice versa). Eliminate (A) and (D).

Statement (2): insufficient. Let's say that y2 = 9 and that z2 = 25. Then y = 3 or -3 and z = 5 or -5. If y = 3 and z = 5, then z is greater. However, if y = -3 and z = -5, then y is greater. The question cannot be answered definitively, so the statement is insufficient. Eliminate (B).

Statements (1) and (2): sufficient. Picking numbers may be difficult, since there are many possibilities for y and z. Instead, try to work with the equations. Since y + z = 1, it follows that y = 1 - z. Replace y with 1 - z in the equation y2 < z2 to get (1 - z)2 < z2. Using FOIL to expand the left side, you get z2 - 2z + 1 < z2. Subtracting z2 from both sides you have -2z + 1 < 0, or 1 < 2z. Dividing both sides by 2 you are left with < z. Since z must be greater than and y + z = 1, y must be less than . Therefore, y must be less than z. The statements combined are sufficient, so choice (C) is correct.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30868 [2]
Given Kudos: 799
Location: Canada
Send PM
Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   Updated on: 17 May 2021, 08:29
2
Kudos
Expert Reply
Top Contributor
GeorgeKo111 wrote:
Is y < z ?

(1) y + z = 1
(2) y² < z²


Target question: Is y < z ?

Statement 1: y + z = 1
Let's TEST some values.
There are several values of y and z that satisfy statement 1. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z
Case b: y = 1 and z = 0. In this case, the answer to the target question is NO, y is not less than z
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y² < z²
There are several values of y and z that satisfy statement 2. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z
Case b: y = 0 and z = -1. In this case, the answer to the target question is NO, y is not less than z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that: y² < z²
Subtract z² from both sides of the inequality to get: y² - z² < 0
Factor the left side to get: (y + z)(y - z) < 0
Since statement 1 tells us that y + z = 1, we can replace (y + z) with 1 to get: (1)(y - z) < 0
Simplify: y - z < 0
Add z to both sides to get: y < z
The answer to the target question is YES, y is less than z
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 19 Mar 2020, 07:08.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:29, edited 1 time in total.
User avatar
B
akshitab2912
Intern
Intern
Joined: 24 Jan 2020
Posts: 28
Own Kudos [?]: 4 [0]
Given Kudos: 183
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   09 Oct 2020, 23:40
BrentGMATPrepNow wrote:
GeorgeKo111 wrote:
Is y < z ?

(1) y + z = 1
(2) y² < z²


Target question: Is y < z ?

Statement 1: y + z = 1
Let's TEST some values.
There are several values of y and z that satisfy statement 1. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z
Case b: y = 1 and z = 0. In this case, the answer to the target question is NO, y is not less than z
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y² < z²
There are several values of y and z that satisfy statement 2. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z
Case b: y = 0 and z = -1. In this case, the answer to the target question is NO, y is not less than z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that: y² < z²
Subtract z² from both sides of the inequality to get: y² - z² < 0
Factor the left side to get: (y + z)(y - z) < 0
Since statement 1 tells us that y + z = 1, we can replace (y + z) with 1 to get: (1)(y - z) < 0
Simplify: y - z < 0
Add z to both sides to get: y < z
The answer to the target question is YES, y is less than z
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

RELATED VIDEO FROM MY COURSE]


Hi Brent,

Can't we answer the question from statement 2 itself?

y^2-z^2<0
(y+z)(y-z)<0
-z<y<z
So y in any case is less than z from second statement itself, isn't that so?
User avatar
D
QuantMadeEasy
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 470
Own Kudos [?]: 592 [1]
Given Kudos: 74
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE:Engineering (Education)
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   10 Oct 2020, 00:52
1
Kudos
Quote:
Is y < z ?

Step 1: Understanding statement 1 alone
(1) y + z = 1
When y = 0.4, z = 0.6; y < z
When y = 0.6, x = 0.4; y > z
Insufficient

Step 2: Understanding statement 2 alone
(2) y^2 < z^2
Taking square root on both the sides
\(\sqrt{y^2}\) < \(\sqrt{z^2}\)
|y| < |z|
When y = -1, z = 2; y < z
When y = 1, z = -2; y > z
Insufficient

Step 3: Combining statement 1 and 2
y^2 < z^2
y^2 - z^2 < 0
(y - z) ( y+z) < 0
As (y + z) = 1; (y - z) < 0
Hence, y < z
Sufficient

C is correct
User avatar
D
GMATGuruNY
Tutor
Joined: 04 Aug 2010
Posts: 1329
Own Kudos [?]: 3240 [0]
Given Kudos: 9
Schools:Dartmouth College
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   11 Oct 2020, 06:11
Expert Reply
Alternate approach:

GeorgeKo111 wrote:
Is y < z ?

(1) y + z = 1

(2) y^2 < z^2


Statement 1:
Clearly INSUFFICIENT.

Statement 2, rephrased: |y| < |z|
Case 1: y=0 and z=1
In this case, the answer to the question stem is YES.
Case 2: y=0 and z=-1
In this case, the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statements combined:
Substituting z=1-y into |y| < |z|, we get:
|y| < |1-y|
Implication:
The distance between y and 0 is less than the distance between y and 1.
In other words, Y IS CLOSER TO 0 THAN TO 1, implying that y < 1/2.

Substituting y=1-z into |y| < |z|, we get:
|1-z| < |z|
Implication:
The distance between z and 1 is less than the distance between z and 0.
In other words, Z IS CLOSER TO 1 THAN TO 0, implying that z > 1/2.

Since y < 1/2 and z > 1/2, we get:
y < 1/2 < z
y < z
Thus, the answer to the question stem is YES.
SUFFICIENT.

Show Spoiler
C
avatar
S
Saransh123
Manager
Manager
Joined: 11 Dec 2019
Posts: 66
Own Kudos [?]: 51 [0]
Given Kudos: 117
Location: India
Concentration: Technology
Schools: CBS '23 Stern '23 Stanford '23
GPA: 4
Send PM
Reviews Badge
Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   12 Oct 2020, 00:11
I have solved this problem like this
Statement 1 says y+z=1, y=1-z or z=1-y Not Sufficient at all.

Statement 2 says y^2 < z^2

Putting value of y(1-z) in y^2<z^2 = 1-2z+z^2, 1/2<z

Similarly putting value of Z(z=1-y) in y^2<z^2, the result will be y<1/2.

So now after joining them it will give y<1/2<z. Therefore the statements combined are sufficient.

Posted from my mobile device
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9470 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   12 Oct 2020, 11:18
Expert Reply
We want to know if z-y is positive. Statement 1 tells us that z+y is positive, and Statement 2 tells us that z^2 - y^2 is positive. But z^2 - y^2 = (z + y)(z-y), and if z+y is positive, then z-y must also be positive for it to be true that the product (z-y)(z+y) is positive. So the two Statements together are sufficient.

Statement 1 is clearly insufficient alone, because it's symmetric in y and z (if you can find numbers that work for y and z where y < z, you can just flip the numbers and you'll automatically have a situation where z < y). Statement 2 is clearly insufficient alone also, since if y = 0, z can be -100 or +100. So the answer is C.
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [0]
Given Kudos: 432
Location: United States
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   01 Nov 2020, 10:20
Is \(y < z\) ?

(1) \(y + z = 1\\
\)
Clearly insufficient.

(2) \(y^2 < z^2\)

\(y^2 - x^2 < 0\)
\((y+z)(y-z) < 0\)

\((y+z) and (y-z)\) have different signs. We can't conclude y <z, however. INSUFFICIENT.

(1&2)
If \(y+z = 1, then y-z < 0\)
\(y < z\).

SUFFICIENT.

Answer is C.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34108
Own Kudos [?]: 854 [0]
Given Kudos: 0
Send PM
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink] Is y < z ? (1) y + z = 1 (2) y^2 < z^2   08 Feb 2024, 01:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2 [#permalink]
08 Feb 2024, 01:22
Moderator:
Bunuel
Math Expert
94619 posts